Computerized Adaptive Testing Survey (catSurv) Object

Description

Creates an object of class Cat. Cat objects are used in administering Computerized Adaptive Testing (CAT) Surveys. These objects contain several pieces of information relevant for CAT surveys, and are used as input in the main functions of the catSurv package.

Details

Assume we have a survey battery with I questions. An object of the class Cat has the following slots:

• ids A vector of length I of unique question identifiers. Default is the column names of response data frame used to calibrate Cat object.

• guessing A vector of length I of guessing parameters. Guessing parameters are only applicable for Cat objects fit with the "tpm" model, using the tpmCat function.

• discrimination A vector of length I of discrimination parameters.

• difficulty A vector or list of length I of difficulty parameters. For Cat objects of the "ltm" or "tpm" model, difficulty is a vector that contains a parameter for each item. For Cat objects of the "grm" or "gpcm" model, difficulty is a list that contains a vector for each item, and each vector contains parameters for each response option.

• answers A vector of length I of answers to questions as given by the survey respondent. Unanswered questions have the value NA. Questions respondent has skipped or refused to answer have a value of -1.

• priorName A character vector of length one giving the prior distribution to use for the ability parameter estimates. The options are "NORMAL" for the normal distribution, "STUDENT_T" for the student's t distribution, and "UNIFORM" for the uniform distribution. The default value is "NORMAL".

• priorParams A numeric vector of length two of parameters for the distribution specified in the priorName slot. When priorName is set to "NORMAL", the first element of priorParams is the mean, and the second element is the standard deviation. When priorName is set to "STUDENT_T", the first element of priorParams is the location parameter and the second is degrees of freedom. When priorName is set to "UNIFORM", the elements of priorParams are lower and upper bound, respectively. Note that the uniform distribution is only applicable for the "EAP" estimation method. The default values are 0,1.

• lowerBound A numeric indicating the lower bound of the interval of the latent scale used in estimation. The default value is -5.

• upperBound A numeric indicating the upper bound of the interval of the latent scale used in estimation. The default value is 5.

• model A string indicating the model fit to the data. The options are "ltm" for the latent trait model, "tpm" for Birnbaum's three parameter model, "grm" for the graded response model, and "gpcm" for the generalized partial credit model.

• estimation A string indicating the approach to estimating ability parameters. The options are "EAP" for the expected a posteriori approach, "MAP" for the modal a posteriori approach, "MLE" for the maximum likelihood approach, and "WLE" for the weighted maximum likelihood approach. The default value is "EAP".

• estimationDefault A string indicating the approach to estimating ability parameters when the primary estimation choice indicated in the estimation slot is "MLE" or "WLE" and this estimation fails to converge. The options are "EAP" and "MAP". The default value is "MAP".

• selection A string indicating the approach for selecting the next item. The options are "EPV" for minimum expected posterior variance, "MEI" for maximum expected information, "MFI" for maximum Fisher information, "MPWI" for maximum posterior weighted information, "MLWI" for maximum likelihood weighted information, "KL" for the maximum expected Kullback-Leibler (KL) information, "LKL" maximum likelihood weighted KL information, "PKL" maximum posterior weighted KL information, "MFII" for maximum Fisher interval information, and "RANDOM" where the next item is chosen randomly. The default value is "EPV".

• z A numeric used in calculating \delta. \delta is used in determining the bounds of integration for some selectItem methods. See selectItem for more information. Default value is 0.9.

• lengthThreshold A numeric. The number of questions answered must be greater than or equal to this threshold to stop administering items. The default value is NA.

• seThreshold A numeric. The standard error estimate of the latent trait must be less than this threshold to stop administering items. The default value is NA.

• infoThreshold A numeric. The Fisher's information for all remaining items must be less than this threshold to stop administering items. The default value is NA.

• gainThreshold A numeric. The absolute value of the difference between the standard error of the latent trait estimate and the square root of the expected posterior variance for each item must be less than this threshold to stop administering items. The default value is NA.

• lengthOverride A numeric. The number of questions answered must be less than this override to continue administering items. The default value is NA.

• gainOverride A numeric. The absolute value of the difference between the standard error of the latent trait estimate and the square root of the expected posterior variance for each item must be less than this override to continue administering items. The default value is NA.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

checkStopRules, estimateTheta, gpcmCat, grmCat, ltmCat, selectItem, tpmCat

Agreeableness Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 20-item Agreeableness dimension of the 100-item IPIP representation of Costa and McCrae's Five Factor Model

Usage

data(agree_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 774,410 response profiles by myPersonality Poject and 1500 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (.113) and a standard deviation (1.5) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are 1=Very inaccurate; 2=Moderately inaccurate; 3=Neither inaccurate nor accurate; 4=Moderately accurate; 5=Very accurate.

The wording of the question items:

I...

q86

Have a good word for everyone.

q6

Believe that others have good intentions.

q66

Respect others.

q46

Accept people as they are.

q36

Make people feel at ease.

q26

Am concerned about others.

q56

Trust what people say.

q76

Sympathize with others' feelings.

q13

Am easy to satisfy.

q96

Treat all people equally.

q82

Have a sharp tongue.

q9

Cut others to pieces.

q22

Suspect hidden motives in others.

q32

Get back at others.

q92

Insult people.

q42

Believe that I am better than others.

q52

Contradict others.

q62

Make demands on others.

q2

Hold a grudge.

q72

Am out for my own personal gain.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Costa, P. T., Jr., & McCrae, R. R. (1992). Revised NEO Personality Inventory (NEO PI-R) and NEO Five-Factor Inventory (NEO-FFI): Professional manual. Odessa, FL: Psychological Assessment Resources.

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

See Also

Cat-class, grmCat

Check if Stop and/or Override Rules are Met

Description

Evaluates the specified stopping and/or override rules to check if respondent should be asked further questions.

Usage

checkStopRules(catObj)

Arguments

Details

The stopping rule thresholds are stored in the following Cat object slots: lengthThreshold, seThreshold, infoThreshold, and gainThreshold. The override thresholds are stored in the following Cat object slots: lengthOverride, gainOverride. A value of NA indicates the rule will not be used in evaluating if further questions should be administered. A user can specify any combination of stopping rules and/or overrides.

Stopping Rules:

lengthThreshold: Number of question's answered \geq a

seThreshold: SE(\hat{\theta}) < a

infoThreshold: FI < a \forall remaining items

gainThreshold: SE(\hat{\theta}) - \sqrt{EPV} | < a \forall remaining items

Overrides:

lengthOverride: Number of question's answered < a

gainOverride: |SE(\hat{\theta}) - \sqrt{EPV} | \geq a \forall remaining items

Value

The function checkStopRules returns a boolean. TRUE indicates all specified stopping rules are met and no specified overrides are met. No further items should be administered. FALSE indicates at least one specified stopping rule is not met, or if any specified override threshold is met. Additional items should be administered.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Babcock, Ben, and David J. Weiss. 2009. “Termination Criteria in Computerized Adaptive Tests: Variable-Length CATs are not Biased." Proceedings of the 2009 GMAC Conference on Computerized Adaptive Testing. Vol. 14.

See Also

Cat-class, estimateSE, expectedPV, fisherInf

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1,0,0,0,1,1, rep(NA, 30))

## Stop administering items if standard error of ability
## estimate is low enough
setSeThreshold(ltm_cat) <- .5
checkStopRules(ltm_cat)

## Now stop if standard error is low enough, but only if respondent has
## answered 11 questions 
setLengthOverride(ltm_cat) <- 11
checkStopRules(ltm_cat)

## When respondent has answered 11 questions and standard error
## of ability estimate is below .5, stop administering items
setAnswers(ltm_cat) <- c(1,0,1,0,1,0,0,0,1,1,0, rep(NA, 29))
checkStopRules(ltm_cat)

Conscientiousness Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 20-item Conscientiousness dimension of the 100-item IPIP representation of Costa and McCrae's Five Factor Model

Usage

data(consc_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 774,410 response profiles by myPersonality Project and 1500 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (.455) and a standard deviation (1.5) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are 1=Very inaccurate; 2=Moderately inaccurate; 3=Neither inaccurate nor accurate; 4=Moderately accurate; 5=Very accurate.

The wording of the question items:

I...

q15

Am always prepared.

q85

Pay attention to details.

q75

Get chores done right away.

q95

Carry out my plans.

q55

Make plans and stick to them.

q5

Complete tasks successfully.

q25

Do things according to a plan.

q45

Am exacting in my work.

q65

Finish what I start.

q35

Follow through with my plans.

q28

Waste my time.

q88

Find it difficult to get down to work.

q98

Do just enough work to get by.

q78

Don't see things through.

q20

Shirk my duties.

q38

Mess things up.

q58

Leave things unfinished.

q48

Don't put my mind on the task at hand.

q68

Make a mess of things.

q8

Need a push to get started.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Costa, P. T., Jr., & McCrae, R. R. (1992). Revised NEO Personality Inventory (NEO PI-R) and NEO Five-Factor Inventory (NEO-FFI): Professional manual. Odessa, FL: Psychological Assessment Resources.

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

See Also

Cat-class, grmCat

The First Derivative of the Log-Likelihood

Description

Calculates either the first derivative of the log-likelihood or the first derivative of the log-posterior evaluated at point \theta.

Usage

d1LL(catObj, theta, use_prior)

Arguments

Details

When the usePrior argument is FALSE, the function d1LL evaluates the first derivative of the log-likelihood at point \theta.

When the usePrior argument is TRUE, the function d1LL evaluates the first derivative of the log-posterior at point \theta.

If the argument use_prior is TRUE, the function d1LL must use the the normal prior distribution.

Value

The function d1LL returns a numeric of the derivative of the log-likelihood (or log-posterior) given a respondent's answer profile.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Choi, Seung W. and Richard J. Swartz. 2009. “Comparison of CAT Item Selection Criteria for Polytomous Items." Applied Psychological Measurement 33(6):419-440.

Muraki, Eiji. 1992. “A generalized partial credit model: Application of an EM algorithm." ETS Research Report Series 1992(1):1-30.

van der Linden, Wim J. 1998. “Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216.

See Also

Cat-class, prior

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## d1LL for Cat object of the ltm model
d1LL(ltm_cat, theta = 1, use_prior = FALSE)

The Second Derivative of the Log-Likelihood

Description

Calculates either the second derivative of the log-likelihood or the second derivative of the log-posterior evaluated at point \theta.

Usage

d2LL(catObj, theta, use_prior)

Arguments

Details

When the usePrior argument is FALSE, the function d2LL evaluates the second derivative of the log-likelihood at point \theta.

When the usePrior argument is TRUE, the function d2LL evaluates the second derivative of the log-posterior at point \theta.

If the argument use_prior is TRUE, the function d2LL must use the the normal prior distribution.

Value

The function d2LL returns a numeric of the second derivative of the log-likelihood (or log-posterior) given a respondent's answer profile.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Choi, Seung W. and Richard J. Swartz. 2009. “Comparison of CAT Item Selection Criteria for Polytomous Items." Applied Psychological Measurement 33(6):419-440.

Muraki, Eiji. 1992. “A generalized partial credit model: Application of an EM algorithm." ETS Research Report Series 1992(1):1-30.

van der Linden, Wim J. 1998. “Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216.

See Also

Cat-class, d1LL, prior

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## d2LL for Cat object of the ltm model
d2LL(ltm_cat, theta = 1, use_prior = FALSE)

Empathizing Quotient Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 40-item Empathy Quotient personality inventory

Usage

data(empathy_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 13976 response profiles collected by myPersonality Project, 3050 response profiles collected by Qualtrics in June 2018, and 1500 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (-0.363) and a standard deviation (1.5) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are 1=Strongly disagree; 2=Slightly disagree; 3=Slightly agree; 4=Strongly agree

The wording of the question items:

q1

I can easily tell if someone else wants to enter a conversation.

q4

I find it difficult to explain to others things that I understand easily, when they don't understand it first time.

q6

I really enjoy caring for other people.

q8

I find it hard to know what to do in a social situation.

q10

People often tell me that I went too far in driving my point home in a discussion.

q11

It doesn't bother me too much if I am late meeting a friend.

q12

Friendships and relationships are just too difficult, so I tend not to bother with them.

q14

I often find it difficult to judge if something is rude or polite.

q15

In a conversation, I tend to focus on my own thoughts rather than on what my listener might be thinking.

q18

When I was a child, I enjoyed cutting up worms to see what would happen.

q19

I can pick up quickly if someone says one thing but means another.

q21

It is hard for me to see why some things upset people so much.

q22

I find it easy to put myself in somebody else's shoes.

q25

I am good at predicting how someone will feel.

q26

I am quick to spot when someone in a group is feeling awkward or uncomfortable.

q27

If I say something that someone else is offended by, I think that that's their problem, not mine.

q28

If anyone asked me if I liked their haircut, I would reply truthfully, even if I didn't like it.

q29

I can't always see why someone should have felt offended by a remark.

q32

Seeing people cry doesn't really upset me.

q34

I am very blunt, which some people take to be rudeness, even though this is unintentional.

q35

I don't tend to find social situations confusing.

q36

Other people tell me I am good at understanding how they are feeling and what they are thinking.

q37

When I talk to people, I tend to talk about their experiences rather than my own.

q38

It upsets me to see an animal in pain.

q39

I am able to make decisions without being influenced by people's feelings.

q41

I can easily tell if someone else is interested or bored with what I am saying.

q42

I get upset if I see people suffering on news programs.

q43

Friends usually talk to me about their problems as they say that I am very understanding.

q44

I can sense if I am intruding, even if the other person doesn't tell me.

q46

People sometimes tell me that I have gone too far with teasing.

q48

Other people often say that I am insensitive, though I don't always see why.

q49

If I see a stranger in a group, I think that it is up to them to make an effort to join in.

q50

I usually stay emotionally detached when watching a film.

q52

I can tune into how someone else feels rapidly and intuitively.

q54

I can easily work out what another person might want to talk about.

q55

I can tell if someone is masking their true emotion.

q57

I don't consciously work out the rules of social situations.

q58

I am good at predicting what someone will do.

q59

I tend to get emotionally involved with a friend's problems.

q60

I can usually appreciate the other person's viewpoint, even if I don't agree with it.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Baron-Cohen, Simon, and Sally Wheelwright. "The empathy quotient: an investigation of adults with Asperger syndrome or high functioning autism, and normal sex differences." Journal of autism and developmental disorders 34, no. 2 (2004): 163-175.

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

See Also

Cat-class, grmCat

Standard Error of Ability Parameter Estimate

Description

Estimates the standard error for a respondent's ability parameter estimate, \theta.

Usage

estimateSE(catObj)

Arguments

Details

The function estimateSE estimates the standard error of the ability estimate given the estimation approach of the Cat object, specified in estimation slot of Cat object.

The expected a posteriori approach is used when estimation slot is "EAP". This method involves integration. See Note for more information.

The modal a posteriori approach is used when estimation slot is "MAP". This method is only available using the normal prior distribution.

The maximum likelihood approach is used when estimation slot is "MLE". When the likelihood of the ability estimate is undefined, the MAP or EAP method will be used, determined by what is specified in the estimationDefault slot in Cat object.

The weighted maximum likelihood approach is used when estimation slot is "WLE". Estimating \theta requires root finding with the “Brent” method in the GNU Scientific Library (GSL) with initial search interval of [-5,5].

Value

The function estimateSE returns a numeric for the standard error for \theta.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the lowerBound and upperBound slots of the Cat object.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

estimateTheta

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Set different estimation procedures and calculate ability estimate and its standard error
setEstimation(ltm_cat) <- "EAP"
estimateTheta(ltm_cat)
estimateSE(ltm_cat)

setEstimation(ltm_cat) <- "MAP"
estimateTheta(ltm_cat)
estimateSE(ltm_cat)

setEstimation(ltm_cat) <- "MLE"
estimateTheta(ltm_cat)
estimateSE(ltm_cat)

setEstimation(ltm_cat) <- "WLE"
estimateTheta(ltm_cat)
estimateSE(ltm_cat)

Estimate of the Respondent's Ability Parameter

Description

Estimates the expected value of the ability parameter \theta, conditioned on the observed answers, prior, and the item parameters.

Usage

estimateTheta(catObj)

Arguments

Details

Estimation approach is specified in estimation slot of Cat object.

The expected a posteriori approach is used when estimation slot is "EAP". This method involves integration. See Note for more information.

The modal a posteriori approach is used when estimation slot is "MAP". This method is only available using the normal prior distribution.

The maximum likelihood approach is used when estimation slot is "MLE". When the likelihood is undefined, the MAP or EAP method will be used, determined by what is specified in the estimationDefault slot in Cat object.

The weighted maximum likelihood approach is used when estimation slot is "WLE". Estimating \theta requires root finding with the “Brent” method in the GNU Scientific Library (GSL) with initial search interval of [-5,5].

Value

The function estimateTheta returns a numeric consisting of the expected value of the respondent's ability parameter.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the lowerBound and upperBound slots of the Cat object.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

van der Linden, Wim J. 1998. "Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216.

Van der Linden, Wim J., and Peter J. Pashley. 2009. "Item Selection and Ability Estimation in Adaptive Testing." Elements of Adaptive Testing. Springer New York, 3-30.

See Also

Cat-class, estimateSE

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Set different estimation procedures and estimate ability parameter
setEstimation(ltm_cat) <- "EAP"
estimateTheta(ltm_cat)

setEstimation(ltm_cat) <- "MAP"
estimateTheta(ltm_cat)

setEstimation(ltm_cat) <- "MLE"
estimateTheta(ltm_cat)

setEstimation(ltm_cat) <- "WLE"
estimateTheta(ltm_cat)

Estimates of Ability Parameters for a Dataset of Response Profiles

Description

Estimates the expected value of the ability parameter \theta, conditioned on the observed answers, prior, and the item parameters for complete response profiles for a dataset of respondents.

Usage

## S4 method for signature 'Cat'
estimateThetas(catObj, responses)

Arguments

Details

Estimation approach is specified in estimation slot of Cat object.

The expected a posteriori approach is used when estimation slot is "EAP". This method involves integration. See Note for more information.

The modal a posteriori approach is used when estimation slot is "MAP". This method is only available using the normal prior distribution.

The maximum likelihood approach is used when estimation slot is "MLE". When the likelihood is undefined, the MAP or EAP method will be used, determined by what is specified in the estimationDefault slot in Cat object.

The weighted maximum likelihood approach is used when estimation slot is "WLE". Estimating \theta requires root finding with the “Brent” method in the GNU Scientific Library (GSL) with initial search interval of [-5,5].

Value

The function estimateThetas returns a vector containing respondents' estimated ability parameters.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the lowerBound and upperBound slots of the Cat object.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

Cat-class, estimateTheta

Examples

## Loading ltm Cat object
data(ltm_cat)

## Set different estimation procedures and estimate ability parameter
data(npi)
setEstimation(ltm_cat) <- "EAP"
estimateThetas(ltm_cat, responses = npi[1:25, ])

Example Qualtrics Data for Adaptive Inventory

Description

Example data when including an adaptive inventory on a Qualtrics survey

Usage

data(ex_qualtrics_results)

Format

An object of class data.frame with 6 rows and 9 columns.

Details

This data set includes four example responses to a length four adaptive inventory for the agreeableness battery.

See agree_cat for details regarding the Cat object structure and battery items.

See readQualtrics for how to clean adaptive inventory response profiles.

See Also

agree_cat, readQualtrics

Example Qualtrics Data for Multiple Adaptive Inventories

Description

Example data when including multiple adaptive inventory on a Qualtrics survey

Usage

data(ex_qualtrics_results_multiple)

Format

An object of class data.frame with 6 rows and 17 columns.

Details

This data set includes four example responses to length four adaptive inventories for both the agreeableness and neuroticism batteries.

See agree_cat and neuro_cat for details regarding the Cat object structure and battery items.

See readQualtrics for how to clean adaptive inventory response profiles.

See Also

agree_cat, neuro_cat,readQualtrics

Expected Kullback-Leibler Information

Description

Calculates the expected Kullback-Leibler information for an individual question item.

Usage

expectedKL(catObj, item)

Arguments

Details

The function expectedKL calculates the expected value of the Kullback-Leibler information for a specified item where the bounds of integration are \hat{\theta} \pm \delta, where \delta is qnorm(z) times the square root of the Fisher test information and z is specified in the z slot of the Cat object. See Note for more information on integration.

Value

The function expectedKL returns a numeric indicating the expected Kullback-Leibler information for the specified item, given the current answer profile and ability parameter estimate.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

likelihoodKL, posteriorKL, selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Estimate KL for different unasked items
expectedKL(ltm_cat, item = 10)
expectedKL(ltm_cat, item = 20)
expectedKL(ltm_cat, item = 30)

Expected Observed Information

Description

Calculates the expected information, which is the observed information attained from a specific response set times the probability of that profile occurring.

Usage

expectedObsInf(catObj, item)

Arguments

Value

The function expectedObsInf returns a numeric value of the expected information. **Not implemented for three parameter model for binary data.**

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

estimateSE,obsInf, probability, selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Expected observed information for different items
expectedObsInf(ltm_cat, item = 10)
expectedObsInf(ltm_cat, item = 20)

Expected Posterior Variance

Description

Estimates the expected posterior variance for a respondent's estimated ability parameter for an item yet to be answered based on a respondent's ability parameter estimate from the already-answered items.

Usage

expectedPV(catObj, item)

Arguments

Value

The function expectedPV returns a numeric value indicating a respondent's expected posterior variance for an unasked item.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

estimateSE, probability, selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Estimate EPV for different unasked items
expectedPV(ltm_cat, item = 10)
expectedPV(ltm_cat, item = 20)
expectedPV(ltm_cat, item = 30)

Extraversion Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 20-item Extraversion dimension of the 100-item IPIP representation of Costa and McCrae's Five Factor Model

Usage

data(extra_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 774,410 response profiles by myPersonality Project and 1500 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (-.367) and a standard deviation (1.3) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are 1=Very inaccurate; 2=Moderately inaccurate; 3=Neither inaccurate nor accurate; 4=Moderately accurate; 5=Very accurate.

The wording of the question items:

I...

q83

Feel comfortable around people.

q10

Make friends easily.

q73

Am skilled in handling social situations.

q63

Am the life of the party.

q53

Know how to captivate people.

q93

Start conversations.

q33

Warm up quickly to others.

q43

Talk to a lot of different people at parties.

q3

Don't mind being the center of attention.

q23

Cheer people up.

q39

Have little to say.

q14

Keep in the background.

q89

Would describe my experiences as somewhat dull.

q59

Don't like to draw attention to myself.

q29

Don't talk a lot.

q18

Avoid contacts with others.

q99

Am hard to get to know.

q79

Retreat from others.

q69

Find it difficult to approach others.

q49

Keep others at a distance.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Costa, P. T., Jr., & McCrae, R. R. (1992). Revised NEO Personality Inventory (NEO PI-R) and NEO Five-Factor Inventory (NEO-FFI): Professional manual. Odessa, FL: Psychological Assessment Resources.

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

See Also

Cat-class, grmCat

Fisher's Information

Description

Calculates the expected value of the observed information of the likelihood evaluated at the input value \theta.

Usage

fisherInf(catObj, theta, item)

Arguments

Details

For the dichotomous case, this Fisher's information is equivalent to the observed information.

Value

The function fisherInf returns a numeric of the expected value of the observed information of the likelihood evaluated at the input value \theta.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

fisherTestInfo, obsInf, selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Fisher's information for different items, at ability parameter of 1
fisherInf(ltm_cat, theta = 1, item = 10)
fisherInf(ltm_cat, theta = 1, item = 20)

Fisher's Test Information

Description

Calculates the total information gained for a respondent for all answered items, conditioned on \theta.

Usage

fisherTestInfo(catObj, theta)

Arguments

Value

The function fisherTestInfo returns a numeric indicating the total information gained for a respondent, given a specific answer set and the current estimate of \theta.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

fisherInf

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Fisher's test information for answer profile
fisherTestInfo(ltm_cat, theta = 2)

Convert JSON object to Cat object

Description

This function object of class Cat.

Usage

## S4 method for signature 'json'
fromJSONCat(jsonObj)

## S4 method for signature 'character'
fromJSONCat(jsonObj)

Arguments

Details

The jsonObj argument of the function fromJSONCat is an object of class json from the rjson package. This function simply populates a Cat object with the information provided in the jsonObj, thus element and slot names must match.

Value

The function fromJSONCat returns an object of class Cat with slots populated with the corresponding information stored in the jsonObj.

See Cat-class for required Cat object slots.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

Cat-class

Methods for Accessing Cat Object Slots

Description

Getter methods to access slots of a Cat object.

Usage

## S4 method for signature 'Cat'
getModel(catObj)

## S4 method for signature 'Cat'
getGuessing(catObj)

## S4 method for signature 'Cat'
getDiscrimination(catObj)

## S4 method for signature 'Cat'
getDifficulty(catObj)

## S4 method for signature 'Cat'
getAnswers(catObj)

## S4 method for signature 'Cat'
getIds(catObj)

## S4 method for signature 'Cat'
getPriorName(catObj)

## S4 method for signature 'Cat'
getPriorParams(catObj)

## S4 method for signature 'Cat'
getLowerBound(catObj)

## S4 method for signature 'Cat'
getUpperBound(catObj)

## S4 method for signature 'Cat'
getEstimation(catObj)

## S4 method for signature 'Cat'
getEstimationDefault(catObj)

## S4 method for signature 'Cat'
getSelection(catObj)

## S4 method for signature 'Cat'
getZ(catObj)

## S4 method for signature 'Cat'
getLengthThreshold(catObj)

## S4 method for signature 'Cat'
getSeThreshold(catObj)

## S4 method for signature 'Cat'
getInfoThreshold(catObj)

## S4 method for signature 'Cat'
getGainThreshold(catObj)

## S4 method for signature 'Cat'
getLengthOverride(catObj)

## S4 method for signature 'Cat'
getGainOverride(catObj)

Arguments

Value

These functions return the respective slot from Cat object.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Montgomery, Jacob M., and Erin L. Rossiter. "So many questions, so little time: Integrating adaptive inventories into public opinion research." Journal of Survey Statistics and Methodology (2019).

See Also

Cat-class, setters

Examples

## Loading ltm Cat object
data(ltm_cat)

## Getting estimation slot before and after change
getEstimation(ltm_cat)
setEstimation(ltm_cat) <- "MAP"
getEstimation(ltm_cat)

## Getting discrimination slot before and after change
getDiscrimination(ltm_cat)
setDiscrimination(ltm_cat) <- rep(1, 40)
getDiscrimination(ltm_cat)

Computerized Adaptive Testing Generalized Partial Credit Model

Description

This function fits the generalized partial credit model for ordinal polytomous data and populates the fitted values for discrimination and difficulty parameters to an object of class Cat.

Usage

## S4 method for signature 'data.frame'
gpcmCat(data, quadraturePoints = 21, ...)

## S4 method for signature 'gpcm'
gpcmCat(data, quadraturePoints = NULL, ...)

Arguments

Details

The data argument of the function gpcmCat is either a data frame or an object of class gpcm from the ltm package. If it is a data frame each row represents a respondent and each column represents a question item. If it is an object of the class gpcm, it is output from the gpcm function in the ltm package.

The quadraturePoints argument of the function gpcmCat is used only when the data argument is a data frame. quadraturePoints is then passed to the gpcm function from the ltm package when fitting the generalized partial credit model to the data and is used when approximating the value of integrals.

Value

The function gpcmCat returns an object of class Cat with changes to the following slots:

• difficulty A list of difficulty parameters, where each element in the list corresponds to the difficulty parameters for an item.

• discrimination A vector consisting of of discrimination parameters for each item.

• model The string "gpcm", indicating this Cat object corresponds to a generalized partial credit model.

See Cat-class for default values of Cat object slots. See Examples and setters for example code to change slot values.

Note

This Cat object should be used for testing package functionality only.

In case the Hessian matrix at convergence is not positive definite try to use start.val = "random".

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Muraki, Eiji. 1992. “A generalized partial credit model: Application of an EM algorithm." ETS Research Report Series 1992(1):1-30.

Rizopoulos, Dimitris. 2006. “ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses." Journal of Statistical Software 17(5):1-25.

See Also

Cat-class, grmCat, polknowTAPS, probability

Examples

## Not run: 
## Creating Cat object with fitted object of class gpcm
data(polknowTAPS)
gpcm_fit <- gpcm(polknowTAPS, constraint = "gpcm", control = list(iter.qN = 200, GHk = 100))
class(gpcm_fit)
gpcm_cat <- gpcmCat(gpcm_fit)

## End(Not run)

## Creating Cat objects from large datasets is computationally expensive
## Load the Cat object created from the above code
data(gpcm_cat)

## Slots that have changed from default values
getModel(gpcm_cat)
getDifficulty(gpcm_cat)
getDiscrimination(gpcm_cat)

## Changing slots from default values
setEstimation(gpcm_cat) <- "MLE"
setSelection(gpcm_cat) <- "MFI"

gpcm Cat Object

Description

An object of class Cat created using the gpcmCat function with the polknowTAPS dataset. To have a better fitting model, we first fit an object of class gpcm from the ltm package which provides for additional control values to be used in fitting. See gpcmCat.

Usage

data(gpcm_cat)

Format

An object of class Cat. See Cat-class for more details.

See Also

Cat-class, gpcmCat, polknowTAPS

Examples

## Not run: 
## How this Cat object was created
data(polknowTAPS)
gpcm_fit <- gpcm(polknowTAPS, constraint = "gpcm", control = list(iter.qN = 200, GHk = 100))
gpcm_cat <- gpcmCat(gpcm_fit)

## End(Not run)

## How to load this Cat object for usage
data(gpcm_cat)

Computerized Adaptive Testing Graded Response Model

Description

This function fits the graded response model for ordinal polytomous data and populates the fitted values for discrimination and difficulty parameters to an object of class Cat.

Usage

## S4 method for signature 'data.frame'
grmCat(data, quadraturePoints = 21, ...)

## S4 method for signature 'grm'
grmCat(data, quadraturePoints = NULL, ...)

Arguments

Details

The data argument of the function grmCat is either a data frame or an object of class grm from the ltm package. If it is a data frame each row represents a respondent and each column represents a question item. If it is an object of the class grm, it is output from the grm function in the ltm package.

The quadraturePoints argument of the function grmCat is used only when the data argument is a data frame. quadraturePoints is then passed to the grm function from the ltm package when fitting the graded response model to the data and is used when approximating the value of integrals.

Value

The function grmCat returns an object of class Cat with changes to the following slots:

• difficulty A list of difficulty parameters, where each element in the list corresponds to the difficulty parameters for an item.

• discrimination A vector consisting of discrimination parameters for each item.

• model The string "grm", indicating this Cat object corresponds to a graded response model.

See Cat-class for default values of Cat object slots. See Examples and setters for example code to change slot values.

Note

In case the Hessian matrix at convergence is not positive definite try to use start.val = "random".

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Samejima, Fumiko. 1969. “Estimation of Latent Ability Using a Response Pattern of Graded Scores." Psychometrika monograph supplement 34(4):100-114.

Rizopoulos, Dimitris. 2006. “ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses.“ Journal of Statistical Software 17(5):1-25.

See Also

Cat-class, gpcmCat, nfc, probability

Examples

## Not run: 
## Creating Cat object with raw data
data(nfc)
grm_cat1 <- grmCat(nfc, quadraturePoints = 100)

## Creating Cat object with fitted object of class grm
grm_fit <- grm(nfc, control = list(GHk = 100)) ## from ltm package
class(grm_fit)
grm_cat2 <- grmCat(grm_fit)

## Note the two Cat objects are identical
identical(grm_cat1, grm_cat2)

## End(Not run)

## Creating Cat objects from large datasets is computationally expensive
## Load the Cat object created from the above code
data(grm_cat)

## Slots that have changed from default values
getModel(grm_cat)
getDifficulty(grm_cat)
getDiscrimination(grm_cat)

## Changing slots from default values
setEstimation(grm_cat) <- "MLE"
setSelection(grm_cat) <- "MFI"

grm Cat Object

Description

An object of class Cat created using the grmCat function with the nfc dataset.

Usage

data(grm_cat)

Format

An object of class Cat. See Cat-class for more details.

See Also

Cat-class, grmCat, nfc

Examples

## Not run: 
## How this Cat object was created
data(nfc)
grm_cat <- grmCat(nfc, quadraturePoints = 100)

## End(Not run)

## How to load this Cat object for usage
data(grm_cat)

Likelihood of the Specified Response Set

Description

Calculates the likelihood of a respondent, with ability parameter \theta, having offered the specific set of responses stored in the Cat objects answers slot. All calculations are conditional on the item-level parameters stored in the Cat object.

Usage

likelihood(catObj, theta)

Arguments

Value

The function likelihood returns a numeric value of the likelihood of the respondent having offered the provided response profile. Note that when no questions have been answered, likelihood evaluates to 1.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Choi, Seung W. and Richard J. Swartz. 2009. “Comparison of CAT Item Selection Criteria for Polytomous Items." Applied Psychological Measurement 33(6):419-440.

Muraki, Eiji. 1992. “A generalized partial credit model: Application of an EM algorithm." ETS Research Report Series 1992(1):1-30.

van der Linden, Wim J. 1998. “Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216.

See Also

Cat-class, probability

Examples

## Loading ltm Cat object
## Likelihood for Cat object of the ltm model
data(ltm_cat)
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))
likelihood(ltm_cat, theta = 1)

## Loading grm Cat object
## Likelihood for Cat object of the grm model
data(grm_cat)
setAnswers(grm_cat) <- c(1,1,5,2,5, rep(NA, 13))
likelihood(grm_cat, theta = 1)

Expected Kullback-Leibler Information, Weighted by Likelihood

Description

Calculates the expected Kullback-Leibler information, weighted by likelihood, for a specified item.

Usage

likelihoodKL(catObj, item)

Arguments

Details

The function likelihoodKL calculates the expected Kullback-Leibler information for question item, where the proposed values of the true ability parameter are weighted by the current likelihood.

This function involves integration. See Note for more information.

Value

The function likelihoodKL returns a numeric indicating the expected Kullback-Leibler information weighted by the likelihood for the specified item, given the current answer profile and ability parameter estimate.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the lowerBound and upperBound slots of the Cat object.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

expectedKL, posteriorKL, selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Estimate EPV for different unasked items
likelihoodKL(ltm_cat, item = 10)
likelihoodKL(ltm_cat, item = 20)
likelihoodKL(ltm_cat, item = 30)

Look Ahead to Select Next Item

Description

Selects the next item that would be asked for all possible response options to the question the respondent is currently answering.

Usage

lookAhead(catObj, item)

Arguments

Value

A function lookAhead returns a data.frame. The the first column of the data frame is the possible response option to the question the respondent is currently answering and the second column is the next item that should be asked given each response.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## What should be asked next if respondent is currently answering item 6
lookAhead(ltm_cat, 6)

## Loading grm Cat object
data(grm_cat)

## Store example answers
setAnswers(grm_cat) <- c(4,3,5,1,1, rep(NA, 13))

## What should be asked next if respondent is currently answering item 6
lookAhead(grm_cat, 6)

Computerized Adaptive Testing Latent Trait Model

Description

This function fits the latent trait model for binary data and populates the fitted values for discrimination and difficulty parameters to an object of class Cat.

Usage

## S4 method for signature 'data.frame'
ltmCat(data, quadraturePoints = 21, ...)

## S4 method for signature 'ltm'
ltmCat(data, quadraturePoints = NULL, ...)

Arguments

Details

The data argument of the function ltmCat is either a data frame or an object of class ltm from the ltm package. If it is a data frame each row represents a respondent and each column represents a question item. If it is an object of the class ltm, it is output from the ltm function in the ltm package.

The quadraturePoints argument of the function ltmCat is used only when the data argument is a data frame. quadraturePoints is then passed to the ltm function from the ltm package when fitting the latent trait model to the data and is used when approximating the value of integrals.

Value

The function ltmCat returns an object of class Cat with changes to the following slots:

• difficulty A vector consisting of difficulty parameters for each item.

• discrimination A vector consisting of discrimination parameters for each item.

• model The string "ltm", indicating this Cat object corresponds to a latent trait model.

See Cat-class for default values of Cat object slots. See Examples and setters for example code to change slot values.

Note

In case the Hessian matrix at convergence is not positive definite try to use start.val = "random".

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Rizopoulos, Dimitris. 2006. “ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses." Journal of Statistical Software 17(5):1-25.

See Also

Cat-class, npi, probability, tpmCat

Examples

## Not run: 
## Creating Cat object with raw data
data(npi)
ltm_cat1 <- ltmCat(npi, quadraturePoints = 100)

## Creating Cat object with fitted object of class ltm
ltm_fit <- ltm(npi ~ z1, control = list(GHk = 100)) ## from ltm package
class(ltm_fit)
ltm_cat2 <- ltmCat(ltm_fit)

## Note the two Cat objects are identical
identical(ltm_cat1, ltm_cat2)

## End(Not run)

## Creating Cat objects from large datasets is computationally expensive
## Load the Cat object created from the above code
data(ltm_cat)

## Slots that have changed from default values
getModel(ltm_cat)
getDifficulty(ltm_cat)
getDiscrimination(ltm_cat)

## Changing slots from default values
setEstimation(ltm_cat) <- "MLE"
setSelection(ltm_cat) <- "MFI"

ltm Cat Object

Description

An object of class Cat created using the ltmCat function with the npi dataset.

Usage

data(ltm_cat)

Format

An object of class Cat. See Cat-class for more details.

See Also

Cat-class, ltmCat, npi

Examples

## Not run: 
## How this Cat object was created
data(npi)
ltm_cat <- ltmCat(npi, quadraturePoints = 100)

## End(Not run)

## How to load this Cat object for usage
data(ltm_cat)

Machiavellianism Personality Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 20 item machiavellianism inventory

Usage

data(mach_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 3020 response profiles collected by Qualtrics in June 2018 and 12299 response profiles collected by the Open Source Psychometrics Project in 2012.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the Qualtrics sample (-0.713) and a standard deviation (1) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are: 5 = Strongly agree, 4 = Somewhat agree, 3 = Neither agree nor disagree, 2 = Somewhat disagree, 1 = Strongly disagree

The wording of the item responses is:

Q1

Never tell anyone the real reason you did something unless it is useful to do so.

Q2

The best way to handle people is to tell them what they want to hear.

Q3

One should take action only when sure it is morally right.

Q4

Most people are basically good and kind.

Q5

It is safest to assume that all people have a vicious streak and it will come out when they are given a chance.

Q6

Honesty is the best policy in all cases.

Q7

There is no excuse for lying to someone else.

Q8

Generally speaking, people won't work hard unless they're forced to do so.

Q9

All in all, it is better to be humble and honest than to be important and dishonest.

Q10

When you ask someone to do something for you, it is best to give the real reasons for wanting it rather than giving reasons which carry more weight.

Q11

Most people who get ahead in the world lead clean, moral lives.

Q12

Anyone who completely trusts anyone else is asking for trouble.

Q13

The biggest difference between most criminals and other people is that the criminals are stupid enough to get caught.

Q14

Most people are brave.

Q15

It is wise to flatter important people.

Q16

It is possible to be good in all respects.

Q17

P.T. Barnum was wrong when he said that there's a sucker born every minute.

Q18

It is hard to get ahead without cutting corners here and there.

Q19

People suffering from incurable diseases should have the choice of being put painlessly to death.

Q20

Most people forget more easily the death of their parents than the loss of their property.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

See https://openpsychometrics.org/_rawdata/, maintained by Eric Jorgenson, for the raw Open Source Psychometrics Project data.

References

Christie, R., F. L. Geis, and D. Berger (1970), Studies in Machiavellianism, New York: Academic Press.

Open Source Psychometrics Project. https://openpsychometrics.org/_rawdata/

See Also

Cat-class, grmCat

Make Tree of Possible Question Combinations

Description

Pre-calculates a complete branching scheme of all possible questions-answer combinations and stores it as a list of lists or a flattened table of values.

Usage

makeTree(catObj, flat = FALSE)

Arguments

Details

The function takes a Cat object and generates a tree of all possible question-answer combinations, conditional on previous answers in the branching scheme and the current \theta estimates for the branch. The tree is stored as a list of lists, iteratively generated by filling in a possible answer, calculating the next question via selectItem, filling in a possible answer for that question, and so forth.

The length of each complete branching scheme within the tree is dictated by the lengthThreshold slot within the Cat object.

Value

The function makeTree returns either a list or a table. If the argument flat is FALSE, the default value, the function returns a list of lists.

If the argument flat is TRUE, the function takes the list of lists and configures it into a flattened table where the columns represent the battery items and the rows represent the possible answer profiles.

Note

This function is computationally expensive. If there are k response options and the researcher wants a complete branching scheme to include n items, k^{n-1} complete branching schemes will be calculated. Setting n is done via the lengthThreshold slot in the Cat object. See Examples.

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

Cat-class, checkStopRules, selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Setting complete branches to include 3 items
setLengthThreshold(ltm_cat) <- 3

## Object returned is list of lists
ltm_list <- makeTree(ltm_cat)

## Object returned is table
ltm_table <- makeTree(ltm_cat, flat = TRUE)

Neuroticism Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 20-item Neuroticism dimension of the 100-item IPIP representation of Costa and McCrae's Five Factor Model

Usage

data(neuro_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 774,410 response profiles by myPersonality Project and 1500 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (-.025) and a standard deviation (1.2) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are 1=Very inaccurate; 2=Moderately inaccurate; 3=Neither inaccurate nor accurate; 4=Moderately accurate; 5=Very accurate.

The wording of the question items:

I...

q12

Often feel blue.

q30

Dislike myself.

q80

Am often down in the dumps.

q70

Have frequent mood swings.

q50

Panic easily.

q90

Am filled with doubts about things.

q100

Feel threatened easily.

q17

Get stressed out easily.

q40

Fear for the worst.

q60

Worry about things.

q37

Seldom feel blue.

q11

Feel comfortable with myself.

q67

Rarely get irritated.

q19

Am not easily bothered by things.

q97

Am very pleased with myself.

q27

Am relaxed most of the time.

q77

Seldom get mad.

q47

Am not easily frustrated.

q87

Remain calm under pressure.

q57

Rarely lose my composure.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Costa, P. T., Jr., & McCrae, R. R. (1992). Revised NEO Personality Inventory (NEO PI-R) and NEO Five-Factor Inventory (NEO-FFI): Professional manual. Odessa, FL: Psychological Assessment Resources.

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

See Also

Cat-class, grmCat

Need for Affect Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 26 item Need for Affect inventory

Usage

data(nfa_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 2507 response profiles from MTurk, 4990 response profiles collected by Qualtrics in June 2018, and 1512 response profiles from The American Panel Survey (TAPS) in December 2014. TAPS is a monthly online panel survey of about 2,000 adults in the United States. The panel was recruited in the fall of 2011 using an address-based sampling frame. TAPS surveys are administered online. Selected panelists who do not have a computer or online service are provided a computer and internet access by TAPS.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the TAPS sample (.236) and a standard deviation (1.3) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are:

5 = Strongly agree, 4 = Somewhat agree, 3 = Neither agree nor disagree, 2 = Somewhat disagree, 1 = Strongly disagree

The wording of the question items is:

q1

It is important for me to be in touch with my feelings.

q2

I think that it is very important to explore my feelings.

q3

I am a very emotional person.

q4

It is important for me to know how others are feeling.

q5

Emotions help people get along in life.

q6

Strong emotions are generally beneficial.

q7

I feel that I need to experience strong emotions regularly.

q8

I approach situations in which I expect to experience strong emotions.

q9

I feel like I need a good cry every now and then.

q10

I like to dwell on my emotions.

q11

We should indulge our emotions.

q12

I like decorating my bedroom with a lot of pictures and posters of things emotionally significant to me.

q13

The experience of emotions promotes human survival.

q14

I do not know how to handle my emotion, so I avoid them.

q15

I find strong emotions overwhelming and therefore try to avoid them.

q16

Emotions are dangerous—they tend to get me into situations that I would rather avoid.

q17

I would prefer not to experience either the lows or highs of emotion.

q18

If I reflect on my past, I see that I tend to be afraid of emotions.

q19

I would love to be like Mr. Spock, who is totally logical and experiences little emotion.

q20

I have trouble telling the people close to me that I love them.

q21

Displays of emotions are embarrassing.

q22

Acting on ones emotions is always a mistake.

q23

I am sometimes afraid of how I might act if I become too emotional.

q24

Avoiding emotional events helps me sleep better at night.

q25

I wish I could feel less emotion.

q26

People can function most effectively when they are not experiencing strong emotions.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

See https://wc.wustl.edu for raw TAPS data.

References

Maio, Gregory R., and Victoria M. Esses. "The need for affect: Individual differences in the motivation to approach or avoid emotions." Journal of personality 69.4 (2001): 583-614.

See Also

Cat-class, grmCat

Need For Cognition

Description

Data of survey respondents' responses to 18 NFC questions, which is a reduced version of NFC (Cacioppo and Petty 1984). For each question, respondents could choose one of five response options: 1 = agree strongly, 2 = agree somewhat, 3 = neither agree nor disagree, 4 = disagree somewhat, 5 = disagree strongly. Missingness is optional. Observations come from one of three administrations of the survey: The American Panel Survey, Amazon's Mechanical Turk in fall of 2014, or Amazon's Mechanical Turk in spring of 2015.

Usage

data(nfc)

Format

A data frame with 4043 observations on the following 18 variables.

NFC1

I really enjoy a task that involves coming up with new solutions to problems

NFC4

I would prefer a task that is intellectual, difficult, and important to one that is somewhat important but does not require much thought

NFC10

Learning new ways to think doesn't excite me very much

NFC12

I usually end up deliberating about issues even when they do not affect me personally

NFC15

The idea of relying on thought to make my way to the top appeals to me

NFC16

The notion of thinking abstractly is appealing to me

NFC19

I only think as hard as I have to

NFC21

I think tasks that require little thought once I've learned them

NFC22

I prefer to think about small, daily projects to long-term ones

NFC23

I would rather do something that requires little thought than something that is sure to challenge my thinking abilities

NFC24

I find satisfaction in deliberating hard and for long hours

NFC29

I like to have the responsibility of handing a situation that requires a lot of thinkings

NFC31

I feel relief rather than satisfaction after completing a task that required a lot of mental effort

NFC32

Thinking is not my idea of fun

NFC33

I try to anticipate and avoid situations where there is likely a chance I will have to think in depth about something

NFC39

I prefer my life to be filed with puzzles that I must solve

NFC40

I would prefer complex to simple problems

NFC43

Its enough for me that something gets the job done; I don't care how or why it works

References

Cacioppo, John T. and Richard E. Petty. 1984. "The Efficient Assessment of Need for Cognition." Journal of Personality Assessment 48(3):306-307.

Need for Cognition Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 34 item Need for Cognition inventory

Usage

data(nfc_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 4985 response profiles collected by Qualtrics in June 2018 and 1512 response profiles from The American Panel Survey (TAPS) in December 2014. TAPS is a monthly online panel survey of about 2,000 adults in the United States. The panel was recruited in the fall of 2011 using an address-based sampling frame. TAPS surveys are administered online. Selected panelists who do not have a computer or online service are provided a computer and internet access by TAPS.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the TAPS sample (.003) and a standard deviation (1.6) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are:

5 = Strongly agree, 4 = Somewhat agree, 3 = Neither agree nor disagree, 2 = Somewhat disagree, 1 = Strongly disagree

The wording of the question items is:

q1

I would prefer complex to simple problems.

q2

I don't like to have the responsibility for handling a situation that requires a lot of thinking.

q3

Thinking is not my idea of fun.

q4

I would rather do something that requires little thought than something that is sure to challenge my thinking abilities.

q5

I try to anticipate and avoid situations where there is a likely chance I will have to think in depth about something.

q6

I find little satisfaction in deliberating hard and for long hours.

q7

I only think as hard as I have to.

q8

I prefer to think about small, daily projects more than long-term ones.

q9

I like tasks that require little thought once I've learned them.

q10

The idea of relying on thought to make my way to the top does not appeal to me.

q11

I really enjoy a task that involves coming up with new solutions to problems.

q12

Learning new ways to think doesn't excite me very much.

q13

I prefer my life to be filled with puzzles that I must solve.

q14

The notion of thinking abstractly is not appealing to me.

q15

I would prefer a task that is intellectual, difficult, and important to one that is somewhat important but does not require much thought.

q16

I feel relief rather the satisfaction after completing a task that required a lot of mental effort.

q17

Its enough for me that something gets the job done, I don't care how or why it works.

q18

I usually end up deliberating about issues even when they do not affect me personally.

q19

I tend to set goals that can be accomplished only by expending considerable mental effort.

q20

I am usually tempted to put more thought into a task than the job minimally requires.

q21

I am hesitant about making important decisions after thinking about them.

q22

I prefer just to let things happen rather than try to understand why they turned out that way.

q23

I have difficulty thinking in new and unfamiliar situations.

q24

I am an intellectual.

q25

I don't reason well under pressure.

q26

I more often talk with other people about the reasons/possible solutions to international problems than about gossip or tidbits about what famous people are doing.

q27

These days, I see little chance for performing well, even in intellectual jobs, unless one knows the right people.

q28

More often than not, more thinking just leads to more errors.

q29

I appreciate opportunities to discover the strengths and weaknesses of my own reasoning.

q30

I prefer watching educational programs more than entertainment programs.

q31

I think best when those around me are very intelligent.

q32

Simply knowing the answer rather than understanding the reasons for the answer to a problem is fine with me.

q33

Ignorance is bliss.

q34

I enjoy thinking about an issue even when the results of my thought will have no effect on the outcome of the issue.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

See https://wc.wustl.edu for raw TAPS data.

References

Cacioppo, John T., and Richard E. Petty. "The need for cognition." Journal of personality and social psychology 42.1 (1982): 116.

See Also

Cat-class, grmCat

Narcissistic Personality Inventory

Description

Data from the 40 item Narcissistic Personality Inventory (Raskin and Terry 1988) collected by by the Open Source Psychometrics Project in 2012.

Usage

data(npi)

Format

A data frame with 11,243 observations on the following 40 variables.

Q1

0 = I have a natural talent for influencing people. 1 = I am not good at influencing people.

Q2

0 = Modesty doesn't become me. 1 = I am essentially a modest person.

Q3

0 = I would do almost anything on a dare. 1 = I tend to be a fairly cautious person.

Q4

0 = When people compliment me I sometimes get embarrassed. 1 = I know that I am good because everybody keeps telling me so.

Q5

0 = The thought of ruling the world frightens the hell out of me. 1 = If I ruled the world it would be a better place.

Q6

0 = I can usually talk my way out of anything. 1 = I try to accept the consequences of my behavior.

Q7

0 = I prefer to blend in with the crowd. 1 = I like to be the center of attention.

Q8

0 = I will be a success. 1 = I am not too concerned about success.

Q9

0 = I am no better or worse than most people. 1 = I think I am a special person.

Q10

0 = I am not sure if I would make a good leader. 1 = I see myself as a good leader.

Q11

0 = I am assertive. 1 = I wish I were more assertive.

Q12

0 = I like to have authority over other people. 1 = I don't mind following orders.

Q13

0 = I find it easy to manipulate people. 1 = I don't like it when I find myself manipulating people.

Q14

0 = I insist upon getting the respect that is due me. 1 = I usually get the respect that I deserve.

Q15

0 = I don't particularly like to show off my body. 1 = I like to show off my body.

Q16

0 = I can read people like a book. 1 = People are sometimes hard to understand.

Q17

0 = If I feel competent I am willing to take responsibility for making decisions. 1 = I like to take responsibility for making decisions.

Q18

0 = I just want to be reasonably happy. 1 = I want to amount to something in the eyes of the world.

Q19

0 = My body is nothing special. 1 = I like to look at my body.

Q20

0 = I try not to be a show off. 1 = I will usually show off if I get the chance.

Q21

0 = I always know what I am doing. 1 = Sometimes I am not sure of what I am doing.

Q22

0 = I sometimes depend on people to get things done. 1 = I rarely depend on anyone else to get things done.

Q23

0 = Sometimes I tell good stories. 1 = Everybody likes to hear my stories.

Q24

0 = I expect a great deal from other people. 1 = I like to do things for other people.

Q25

0 = I will never be satisfied until I get all that I deserve. 1 = I take my satisfactions as they come.

Q26

0 = Compliments embarrass me. 1 = I like to be complimented.

Q27

0 = I have a strong will to power. 1 = Power for its own sake doesn't interest me.

Q28

0 = I don't care about new fads and fashions. 1 = I like to start new fads and fashions.

Q29

0 = I like to look at myself in the mirror. 1 = I am not particularly interested in looking at myself in the mirror.

Q30

0 = I really like to be the center of attention. 1 = It makes me uncomfortable to be the center of attention.

Q31

0 = I can live my life in any way I want to. 1 = People can't always live their lives in terms of what they want.

Q32

0 = Being an authority doesn't mean that much to me. 1 = People always seem to recognize my authority.

Q33

0 = I would prefer to be a leader. 1 = It makes little difference to me whether I am a leader or not.

Q34

0 = I am going to be a great person. 1 = I hope I am going to be successful.

Q35

0 = People sometimes believe what I tell them. 1 = I can make anybody believe anything I want them to.

Q36

0 = I am a born leader. 1 = Leadership is a quality that takes a long time to develop.

Q37

0 = I wish somebody would someday write my biography. 1 = I don't like people to pry into my life for any reason.

Q38

0 = I get upset when people don't notice how I look when I go out in public. 1 = I don't mind blending into the crowd when I go out in public.

Q39

0 = I am more capable than other people. 1 = There is a lot that I can learn from other people.

Q40

0 = I am much like everybody else. 1 = I am an extraordinary person.

Details

Item responses are paired. Respondents had to choose the one that fit them the best.

References

Raskin, Robert and Howard Terry. 1988. "A Principal-Components Analysis of the Narcissistic Personality Inventory and Further Evidence of Its Construct Validity." Journal of Personality and Social Psychology 54(5):890-902.

Open Source Psychometrics Project. https://openpsychometrics.org/_rawdata/

Narcissistic personality inventory question items

Description

A list where each element is a length three vector containin the text of the the question item and the two response options.

Usage

data(npi_battery)

Format

An object of class list of length 40.

References

Raskin, R., and H. Terry (1988), "A Principal-Components Analysis of the Narcissistic Personality Inventory and Further Evidence of Its Construct Validity," Journal of Personality and Social Psychology, 54, 890-902.

See Also

npi_cat

Examples

data(npi_battery)

# Item 1
npi_battery$Q1[1]

# Response options for item 1
npi_battery$Q1[2:3]

Narcissistic Personality Cat Object

Description

Cat object containing item parameters for latent trait model fit with responses to the 40 item Narcissistic Personality inventory

Usage

data(npi_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for latent trait model fit with 2945 response profiles collected by Qualtrics in June 2018 and 10440 response profiles collected by the Open Source Psychometrics Project in 2012.

See Cat-class for details regarding the Cat object structure. See ltmCat for details regarding the latent trait model.

A normal prior was chosen with mean from the theta estimates from the Qualtrics sample (-.069) and a standard deviation (1) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Item responses are paired. Respondents had to choose the one that fit them the best.

The wording of the item responses is:

Q1*

0 = I am not good at influencing people. 1 = I have a natural talent for influencing people.

Q2

0 = Modesty doesn't become me. 1 = I am essentially a modest person.

Q3

0 = I would do almost anything on a dare. 1 = I tend to be a fairly cautious person.

Q4

0 = When people compliment me I sometimes get embarrassed. 1 = I know that I am good because everybody keeps telling me so.

Q5

0 = The thought of ruling the world frightens the hell out of me. 1 = If I ruled the world it would be a better place.

Q6

0 = I can usually talk my way out of anything. 1 = I try to accept the consequences of my behavior.

Q7

0 = I prefer to blend in with the crowd. 1 = I like to be the center of attention.

Q8

0 = I will be a success. 1 = I am not too concerned about success.

Q9

0 = I am no better or worse than most people. 1 = I think I am a special person.

Q10

0 = I am not sure if I would make a good leader. 1 = I see myself as a good leader.

Q11

0 = I am assertive. 1 = I wish I were more assertive.

Q12

0 = I like to have authority over other people. 1 = I don't mind following orders.

Q13

0 = I find it easy to manipulate people. 1 = I don't like it when I find myself manipulating people.

Q14

0 = I insist upon getting the respect that is due me. 1 = I usually get the respect that I deserve.

Q15

0 = I don't particularly like to show off my body. 1 = I like to show off my body.

Q16

0 = I can read people like a book. 1 = People are sometimes hard to understand.

Q17

0 = If I feel competent I am willing to take responsibility for making decisions. 1 = I like to take responsibility for making decisions.

Q18

0 = I just want to be reasonably happy. 1 = I want to amount to something in the eyes of the world.

Q19

0 = My body is nothing special. 1 = I like to look at my body.

Q20

0 = I try not to be a show off. 1 = I will usually show off if I get the chance.

Q21

0 = I always know what I am doing. 1 = Sometimes I am not sure of what I am doing.

Q22

0 = I sometimes depend on people to get things done. 1 = I rarely depend on anyone else to get things done.

Q23

0 = Sometimes I tell good stories. 1 = Everybody likes to hear my stories.

Q24

0 = I expect a great deal from other people. 1 = I like to do things for other people.

Q25

0 = I will never be satisfied until I get all that I deserve. 1 = I take my satisfactions as they come.

Q26

0 = Compliments embarrass me. 1 = I like to be complimented.

Q27

0 = I have a strong will to power. 1 = Power for its own sake doesn't interest me.

Q28

0 = I don't care about new fads and fashions. 1 = I like to start new fads and fashions.

Q29

0 = I like to look at myself in the mirror. 1 = I am not particularly interested in looking at myself in the mirror.

Q30

0 = I really like to be the center of attention. 1 = It makes me uncomfortable to be the center of attention.

Q31

0 = I can live my life in any way I want to. 1 = People can't always live their lives in terms of what they want.

Q32

0 = Being an authority doesn't mean that much to me. 1 = People always seem to recognize my authority.

Q33

0 = I would prefer to be a leader. 1 = It makes little difference to me whether I am a leader or not.

Q34

0 = I am going to be a great person. 1 = I hope I am going to be successful.

Q35

0 = People sometimes believe what I tell them. 1 = I can make anybody believe anything I want them to.

Q36

0 = I am a born leader. 1 = Leadership is a quality that takes a long time to develop.

Q37

0 = I wish somebody would someday write my biography. 1 = I don't like people to pry into my life for any reason.

Q38

0 = I get upset when people don't notice how I look when I go out in public. 1 = I don't mind blending into the crowd when I go out in public.

Q39

0 = I am more capable than other people. 1 = There is a lot that I can learn from other people.

Q40

0 = I am much like everybody else. 1 = I am an extraordinary person.

*Note that Item 1 is "reverse coded" from the coding that is typically used. This is because item parameter estimation constrains the first item's discrimination parameter to be positive. So the reverse coding was done for the more intuitive interpretation of item parameters and theta estimates as larger, positive values indicate "more" of the latent trait.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

See https://openpsychometrics.org/_rawdata/, maintained by Eric Jorgenson, for the raw Open Source Psychometrics Project data.

References

Raskin, R., and H. Terry (1988), "A Principal-Components Analysis of the Narcissistic Personality Inventory and Further Evidence of Its Construct Validity," Journal of Personality and Social Psychology, 54, 890-902.

Open Source Psychometrics Project. https://openpsychometrics.org/_rawdata/

See Also

Cat-class, ltmCat

Need to Evaluate

Description

4005 full response profiles to 16 Need to Evaluate inventory. Observations come from one of three administrations of the survey: The American Panel Survey, Amazon's Mechanical Turk in fall of 2014, or Amazon's Mechanical Turk in spring of 2015.

Usage

data(nte)

Format

An object of class data.frame with 4005 rows and 16 columns.

Details

See nte_cat for detailed information on question wordings and response options.

References

Jarvis, W. Blair G., and Richard E. Petty. "The need to evaluate." Journal of personality and social psychology 70.1 (1996): 172.

See Also

nte_cat

Need to Evaluate Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 16 item Need to Evaluate inventory

Usage

data(nte_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 2534 response profiles from MTurk, 4993 response profiles collected by Qualtrics in June 2018, and 1512 response profiles from The American Panel Survey (TAPS) in December 2014. TAPS is a monthly online panel survey of about 2,000 adults in the United States. The panel was recruited in the fall of 2011 using an address-based sampling frame. TAPS surveys are administered online. Selected panelists who do not have a computer or online service are provided a computer and internet access by TAPS.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the TAPS sample (.002) and a standard deviation (1.3) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are:

5 = Extremely characteristic of me, 4 = Somewhat characteristic of me, 3 = Uncertain, 2 = Somewhat uncharacteristic of me, 1 = Extremely uncharacteristic of me

The wording of the question items is:

q1

I form opinions about everything.

q2

I prefer to avoid taking extreme positions.

q3

It is very important to me to hold strong opinions.

q4

I want to know exactly what is good and bad about everything.

q5

I often prefer to remain neutral about complex issues.

q6

If something does not affect me, I do not usually determine if it is good or bad.

q7

I enjoy strongly liking and disliking things.

q8

There are many things for which I do not have a preference.

q9

It bothers me to remain neutral.

q10

I like to have strong opinions even when I am not personally involved.

q11

I have many more opinions than the average person.

q12

I would rather have a strong opinion than no opinion at all.

q13

I pay a lot of attention to whether things are good or bad.

q14

I only form strong opinions when I have to.

q15

I like to decide that new things are really good or really bad.

q16

I am pretty much indifferent to many important issues.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

See https://wc.wustl.edu for raw TAPS data.

References

Jarvis, W. Blair G., and Richard E. Petty. "The need to evaluate." Journal of personality and social psychology 70.1 (1996): 172.

See Also

Cat-class, grmCat

Observed Information

Description

Calculates the observed information of the likelihood of a respondent's ability \theta for a given item.

Usage

obsInf(catObj, theta, item)

Arguments

Details

The observed information is equivalent to the negative second derivative of the log-likelihood evaluated at \theta. This function should never be called when the respondent has answered no questions as the likelihood is not defined.

Value

The function obsInf returns a numeric value of the observed information of the likelihood, given \theta, for a given question item.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

estimateTheta, expectedObsInf

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Calculate observed information for different ability parameters and items
obsInf(ltm_cat, theta = 1, item = 10)
obsInf(ltm_cat, theta = 1, item = 11)
obsInf(ltm_cat, theta = 0, item = 10)
obsInf(ltm_cat, theta = 0, item = 11)

Openness to Experience Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 20-item Openness dimension of the 100-item IPIP representation of Costa and McCrae's Five Factor Model

Usage

data(open_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 774,410 response profiles by myPersonality Project and 1500 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (-.674) and a standard deviation (1.2) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are 1=Very inaccurate; 2=Moderately inaccurate; 3=Neither inaccurate nor accurate; 4=Moderately accurate; 5=Very accurate.

The wording of the question items:

I...

q91

Believe in the importance of art.

q1

Have a vivid imagination.

q51

Tend to vote for liberal political candidates.

q41

Carry the conversation to a higher level.

q61

Enjoy hearing new ideas.

q31

Enjoy thinking about things.

q21

Can say things beautifully.

q16

Enjoy wild flights of fantasy.

q81

Get excited by new ideas.

q71

Have a rich vocabulary.

q24

Am not interested in abstract ideas.

q74

Do not like art.

q7

Avoid philosophical discussions.

q34

Do not enjoy going to art museums.

q44

Tend to vote for conservative political candidates.

q4

Do not like poetry.

q94

Rarely look for a deeper meaning in things.

q84

Believe that too much tax money goes to support artists.

q54

Am not interested in theoretical discussions.

q64

Have difficulty understanding abstract ideas.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Costa, P. T., Jr., & McCrae, R. R. (1992). Revised NEO Personality Inventory (NEO PI-R) and NEO Five-Factor Inventory (NEO-FFI): Professional manual. Odessa, FL: Psychological Assessment Resources.

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

See Also

Cat-class, grmCat

Find Answer Profile that Minimizes Bias

Description

Generating all possible combinations of length n from a response profile to determine the possible response profile best able to estimate the true value of theta.

Usage

## S4 method for signature 'Cat'
oracle(catObj, theta, responses, approx = FALSE, parallel = FALSE)

Arguments

Details

lengthThreshold slot should specify how many questions to ask. Note this function uses the estimateTheta method specified in the supplied cat object

Value

A data.frame where the first column is the user-supplied true value of theta, the second column is the best possible theta estimate given n questions are asked, and the remaining columns are the answer profile leading to the best possible theta estimation.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

Plotting function for Cat object

Description

Function to plot item response functions, item characteristic functions, and item information functions for Cat objects.

Usage

## S4 method for signature 'Cat'
plot(x, item, plotType, xlim = c(-5, 5), ...)

Arguments

MTurk Political Knowledge

Description

Data from Amazon Mechanical Turkers in 2012 responding to 64 political knowledge questions. Political knowledge questions had a varying number of response options, noted below. This dataset codes answers as either correct (a value of 0) or incorrect (a value of 1).

Usage

data(polknowMT)

Format

A data frame with 810 observations on the following 64 questions.

Q1

How long is one term for the President of the United States?

Eight years; Six years; Four years; Two years

Q2

The FDA is part of the national government primarily responsible for regulating

Food quality; The national parks; Electricity production and energy; Pollution and the environment

Q3

Who is the Vice President of the United States?

Leon Panetta; William Daley; Hillary Clinton; Joe Biden

Q4

The federal debt is

Much smaller than it was 20 years ago; The difference between imports and exports with foreign countries; The annual difference between spending and tax revenues; The accumulated borrowing of the federal government that has not been repaid

Q5

How many times can an individual be elected President of the United States under current laws?

Any number of terms; Three times; Twice; Once

Q6

What do we call the first ten amendments to the Constitution?

The Articles of Confederation; The inalienable right; The Bill of Rights; The Declaration of Independence

Q7

Is the U.S. federal budget deficit, the amount by which the governments spending exceeds the amount of money it collects, now bigger, about the same, or smaller than it was during most of the 1990s?

Smaller; About the same; Bigger

Q8

Who signs bills to become laws?

The President; The Vice President; The Chief Justice of the Supreme Court; The Secretary of State

Q9

Which party is generally more supportive of creating a way for immigrants who are in the U.S. illegally to eventually become citizens?

The Republican Party; The Democratic Party

Q10

In what month do we vote for the President?

November; October; February; January

Q11

What are the two parts of the U.S. Congress?

The Senate and the Supreme Court; The House of Lords and the House of Commons; The House of Representative and the Supreme Court; The Senate and House of Representatives

Q12

Which party is generally more supportive of restricting access to abortion?

The Republican Party; The Democratic Party

Q13

Which of these political parties is considered most conservative?

Green Party; Republican Party; Democratic Party

Q14

The NRA is an organization that advocates for

Clean elections; A cleaner environment; The rights of gun owners; Women's rights

Q15

Compared to 30 years ago, is the difference in incomes between the top 20% of households and the bottom 20% of households now bigger, smaller, or the same?

The difference is now the same as 30 years ago; The difference is now smaller than 30 years ago; The difference is now bigger than 30 years ago

Q16

The EPA is part of the national government primarily responsible for regulating

Food quality; The national parks; Electricity production and energy; Pollution and the environment

Q17

Which party is generally more supportive of reducing the size of the defense budget?

The Republican Party; The Democratic Party

Q18

Which party is generally more supportive of increasing taxes on higher income people to reduce the federal budget deficit?

The Republican Party; The Democratic Party

Q19

Which party is generally more supportive of allowing drilling for oil in the Arctic National Wildlife Refuge?

The Republican Party; The Democratic Party

Q20

Who is the Commander in Chief of the military?

The Attorney General; The President; The Secretary of Defense; The Vice President

Q21

The First Amendment to the United States Constitution guarantees all of these rights EXCEPT

Right to remain silent; Right to the free exercise of religion; Right to free speech; Right to peaceably assemble

Q22

Roe v Wade is a case decided by the Supreme Court that relates to

Executive power; Campaign finance; Birth control; Abortion

Q23

Social Security is

Funded by the personal income tax; Operated by state government; The responsibility of the Department of Defense; The benefit program for senior citizens

Q24

What is Medicare?

A private, non-profit organization that runs free health clinic; A private health insurance plan sold to individuals in all 50 states; A program run by state governments to provide health care to poor people; A program run by the U.S. federal government to pay for old people's health care

Q25

How many senators are elected from each state?

It depends on the population of the state; Four; Two; One

Q26

How many votes are required in Congress to override a presidential veto

A simple majority of both houses of Congress; A simple majority of one house of Congress; A two-thirds majority of both houses of Congress; A two-thirds majority of one house of Congress

Q27

The Secretary of State

Serves a two-year term; Serves the state governments; Is nominated by the president; Heads the armed services

Q28

Near the end of an election campaign, a polls shows that an issue that no candidate has mentioned is of great concern to voters. What is most likely to happen?

Some candidates will drop out of the race; Candidates will start talking about the issue; Newspapers will not report the results of the poll; The election will be postponed

Q29

Liberals are generally said to

Support pro-life policies; Oppose all tax increases; Support military spending; Support government programs to give government assistance the needy

Q30

Which party is generally more supportive of reducing the size and scope of the federal government?

The Republican Party; The Democratic Party

Q31

The ability of a minority of senators to prevent a vote on a bill is known as Suspension of the rules; Enrollment; A veto; A filibuster

Q32

conservatives are generally said to

Support pro-choice policies; Support tax cuts; Oppose military spending; Support government programs to give government assistance to the needy

Q33

Which of these regions of the country is generally considered to be most supportive of Republican candidates

Midwest; South; West Coast; New England

Q34

The presiding officer in the House of Representatives is

The Majority Leader; The Sergeant at Arms; The Vice President of the United States; The Speaker

Q35

Which of these countries is NOT a permanent member of the U.N. Security Council

United Kingdom; France; India; China

Q36

Which part has a majority of seats in the U.S. House of Representatives?

Neither; Democrats; Republicans

Q37

What state holds the first primary election in Presidential primaries?

Florida; Nevada; South Carolina; New Hampshire

Q38

Who is the Speaker of the House of Representatives?

Mitt Romney; Eric Holder; Harry Reid; John Boehner

Q39

Most cases are considered by the Supreme Court

In even-numbered years; At the request of the Congress; Upon order of the president; With the approval of at least four justices

Q40

How many Justices typically serve on the U.S. Supreme Court

Eleven; Nine; Eight; Seven

Q41

What job or political office is no held by Ben Bernanke?

None of these; Minority Whip of the U.S. House; Chief Justice of the United States Supreme Court; Majority leader of the U.S. Senate, Chairman of the Federal Reserve

Q42

Whose responsibility is it to nominate judges to the Federal Courts

The state governors; The Supreme Court; Congress; President

Q43

Who is the Chief Justice of the U.S. Supreme Court?

Larry Thompson; Anthony Kennedy; David Cole; John Roberts

Q44

The U.S. Senate

Votes to confirm nominees to the U.S. Supreme court chosen by the House of Representatives; Plays no role in choosing the members of the U.S. Supreme Court; Chooses members of the U.S. Supreme Court; Votes to confirm nominees to the U.S. Supreme Court chosen by the President

Q45

Which party has a majority of seats in the U.S. Senate

Neither; Democrats; Republicans

Q46

Which of the states listed below has the greatest number of electoral college votes in the U.S. Presidential Elections?

Puerto Rico; Nevada; North Dakota; Washington, D.C.

Q47

Citizens United v the FEC is a case decided by the Supreme Court that relates to

Executive power; Campaign finance; Birth control; Abortion

Q48

For how many years is a United States Senator elected that is, how many years are there in one full term of office for a U.S. Senator?

None of these; Eight years; Six years; Four years; Two years

Q49

Who is the Prime Minister of the United Kingdom?

Richard Branson; Tony Hayward; Nick Clegg; David Cameron

Q50

The president of Afghanistan is named

Bashar al-Assad; Hosni Mubarak; Hamid Karzai; Nouri al-Maliki

Q51

The House of Representatives has how many voting members?

Four hundred and forty-one; Four hundred and thirty-five; Two hundred; One hundred

Q52

The President of the Senate is

The Majority Leader; The Sergeant at Arms; The Vice President of the United States; The senior senator of the majority party

Q53

On which of the following federal programs is the most money spent each year?

Medicare; Education; Subsidies to farmers; Aid to foreign countries

Q54

What do all constitutional governments have?

Separation of church and state; A bill of rights; A President as the head of government; Limits on political power

Q55

One which of the following does the U.S. federal government spend the least money?

Social Security; National defense; Medicare; Foreign aid

Q56

The head of the Department of Justice is

Kathleen Sebelius; Eric Holder; Timothy Geithner; Hillary Clinton

Q57

The president may NOT

Declare war; Pardon criminals without justification; Appoint federal officials when Congress is in recess; Refuse to sign legislation passed by Congress

Q58

Which of these is NOT primarily the responsibility of the Federal government in Washington?

Interstate commerce; Negotiating treaties with foreign countries; Education; National defense

Q59

Who is the current president of Mexico?

Vincente Fox; Hugo Chavez; Dilma Rousseff; Felipe Calderon

Q60

Which of the following actions does the United States federal government commonly take to finance a budget deficit?

Expanding public-works projects; Borrowing from the public; Imposing import quotas; Printing more money

Q61

Common Cause is an organization that advocates for

Women's rights; Clean elections; A cleaner environment; The right of gun owners

Q62

The Byrd Rule is relevant

During the confirmation of cabinet members; For national party conventions; During Congressional debates over non-budgetary policies; For the Reconciliation process

Q63

The Majority Leader of the House of Representative is

Nancy Pelosi; Kevin McCarthy; Eric Cantor; John Boehner

Q64

On which of the following does the U.S. federal government spend the most money each year?

Education; Medicare; Interest on the national debt; National defense

Source

https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/19381

References

Jacob M. Montgomery and Joshua Cutler. 2013. "Computerized Adaptive Testing for Public Opinion Surveys." Political Analysis (Spring 2013) 21 (2): 172-192.

TAPS Political Knowledge (Ordered Response Options)

Description

Data of responses to a political knowledge battery from the May 2013 wave of The American Panel Survey (TAPS) out of Washington University in St. Louis.

Usage

data(polknowOrdered)

Format

A data frame with 1340 observations (only complete cases) of the following 10 questions.

Q1

Members of the U.S. Supreme Court serve

3 = two-year terms. 4 = ten-year terms. 5 = life terms. 2 = terms determined by the president. 1 = Don't know.

Q2

Who is the Chief Justice of the U.S. Supreme Court?

5 = John Roberts. 4 = Antonin Scalia. 3 = Mitt Romney. 2 = Hillary Clinton. 1 = Don't know.

Q3

Social Security is

5 = the benefit program for senior citizens. 2 = the responsibility of the Department of Defense. 3 = operated by state governments. 4 = funded by the personal income tax. 1 = Don't know.

Q4

On which of the following programs is the most money spent each year?

4 = aid to foreign countries. 5 = Medicare. 2 = subsidies to farmers. 3 = education. 1 = Don't know.

Q5

Which party holds a majority of seats in the U.S. House of Representatives in Washington?

4 = Democrats. 3 = Republicans. 2 = Independents. 1 = Don't know.

Q6

How many votes are required in Congress to override a presidential veto?

2 = a simple majority of one house of Congress. 3 = a simple majority of both houses of Congress. 4 = a two-thirds majority of one house of Congress. 5 = a two-thirds majority of both houses of Congress. 1 = Don't know.

Q7

How long is one term for a member of the U.S. Senate?

3 = two years. 4 = four years. 5 = six years. 2 = eight years. 1 = Don't know.

Q8

The ability of a minority of senators to prevent a vote on a bill is known as

4 = a veto. 5 = a filibuster. 3 = enrollment. 2 = suspension of the rules. 1 = Don't know.

Q9

Who is the Vice President of the United States?

4 = Nancy Pelosi. 3 = John Boehner. 5 = Joseph Biden. 2 = Harry Reid. 1 = Don't know.

Q10

A president may serve

3 = one term. 5 = two terms. 4 = three terms. 2 = any number of terms. 1 = Don't know.

Details

TAPS is a monthly online panel survey of about 2,000 adults in the United States. The panel was recruited in the fall of 2011 using an address-based sampling frame. TAPS surveys are administered online. Selected panelists who do not have a computer or online service are provided a computer and internet access by TAPS.

Source

https://wc.wustl.edu/

TAPS Political Knowledge

Description

Data of responses to a political knowledge battery from the May 2013 wave of The American Panel Survey (TAPS) out of Washington University in St. Louis.

Usage

data(polknowTAPS)

Format

A data frame with 1496 observations on the following 10 questions.

Q1

Members of the U.S. Supreme Court serve

1 = two-year terms. 2 = ten-year terms. 3 = life terms. 4 = terms determined by the president. 5 = Don't know.

Q2

Who is the Chief Justice of the U.S. Supreme Court?

1 = John Roberts. 2 = Antonin Scalia. 3 = Mitt Romney. 4 = Hillary Clinton. 5 = Don't know.

Q3

Social Security is

1 = the benefit program for senior citizens. 2 = the responsibility of the Department of Defense. 3 = operated by state governments. 4 = funded by the personal income tax. 5 = Don't know.

Q4

On which of the following programs is the most money spent each year?

1 = aid to foreign countries. 2 = Medicare. 3 = subsidies to farmers. 4 = education. 5 = Don't know.

Q5

Which party holds a majority of seats in the U.S. House of Representatives in Washington?

1 = Democrats. 2 = Republicans. 3 = Independents. 4 = Don't know.

Q6

How many votes are required in Congress to override a presidential veto?

1 = a simple majority of one house of Congress. 2 = a simple majority of both houses of Congress. 3 = a two-thirds majority of one house of Congress. 4 = a two-thirds majority of both houses of Congress. 5 = Don't know.

Q7

How long is one term for a member of the U.S. Senate?

1 = two years. 2 = four years. 3 = six years. 4 = eight years. 5 = Don't know.

Q8

The ability of a minority of senators to prevent a vote on a bill is known as

1 = a veto. 2 = a filibuster. 3 = enrollment. 4 = suspension of the rules. 5 = Don't know.

Q9

Who is the Vice President of the United States?

1 = Nancy Pelosi. 2 = John Boehner. 3 = Joseph Biden. 4 = Harry Reid. 5 = Don't know.

Q10

A president may serve

1 = one term. 2 = two terms. 3 = three terms. 4 = any number of terms. 5 = Don't know.

Details

TAPS is a monthly online panel survey of about 2,000 adults in the United States. The panel was recruited in the fall of 2011 using an address-based sampling frame. TAPS surveys are administered online. Selected panelists who do not have a computer or online service are provided a computer and internet access by TAPS.

Source

https://wc.wustl.edu/

Expected Kullback-Leibler Information, Weighted by the Prior

Description

Calculates the expected Kullback-Leibler information, weighted by likelihood and prior beliefs, for a specified item.

Usage

posteriorKL(catObj, item)

Arguments

Details

The function posteriorKL calculates the expected Kullback-Leibler information for question item, where the proposed values of the true ability parameter are weighted by the prior.

This function involves integration. See Note for more information.

Value

The function posteriorKL returns a numeric indicating the expected Kullback-Leibler information weighted by the likelihood for the specified item, given the current answer profile and ability parameter estimate.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the lowerBound and upperBound slots of the Cat object.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

expectedKL, likelihoodKL, selectItem

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Estimate EPV for different unasked items
posteriorKL(ltm_cat, item = 10)
posteriorKL(ltm_cat, item = 20)
posteriorKL(ltm_cat, item = 30)

Evaluate the Prior Density Distribution at Position theta

Description

Calculates the density at theta of either the normal, Student's t, or uniform distribution.

Usage

prior(catObj, theta)

Arguments

Details

The priorName slot of Cat object needs to be either "UNIFORM", "NORMAL", or "STUDENT_T".

When priorName slot is "NORMAL", the first element of priorParams slot is the mean, the second element is the standard deviation.

When priorName slot is "STUDENT_T", the first element of priorParams slot is the non-centrality parameters and the second is degrees of freedom.

When priorName slot is "UNIFORM", the elements of the priorParams slot are the lower and upper bounds, of the interval, respectively. Note that the "UNIFORM" is only applicable for the expected a posteriori (EAP) estimation method.

Value

The function prior returns a numeric consisting of prior value, \pi(\theta), given the value \theta.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses Boost C++ source libraries for the uniform and Student's t distributions and calls dnorm4 written in C which is identical to that of dnorm in R.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

Cat-class

Examples

## Loading ltm Cat object
data(ltm_cat)

## Prior calculation for different distributions
ltm_cat@priorName <- "NORMAL"
ltm_cat@priorParams <- c(0, 1) ## Parameters are mean and standard deviation
prior(ltm_cat, theta = 1)

ltm_cat@priorName <- "STUDENT_T"
ltm_cat@priorParams <- c(1, 3) ## Parameters are non-centrality param and degrees of freedom
prior(ltm_cat, theta = 1)

ltm_cat@priorName <- "UNIFORM"
ltm_cat@priorParams <- c(-1, 1) ## Parameters are lower bound and upper bound of interval
prior(ltm_cat, theta = 1)

Probability of Responses to a Question Item or the Left-Cumulative Probability of Responses

Description

Calculates the probability of specific responses or the left-cumulative probability of responses to item conditioned on a respondent's ability (\theta).

Usage

probability(catObj, theta, item)

Arguments

Details

For the ltm model, the probability of non-zero response for respondent j on item i is

Pr(y_{ij}=1|\theta_j)=\frac{\exp(a_i + b_i \theta_j)}{1+\exp(a_i + b_i \theta_j)}

where \theta_j is respondent j 's position on the latent scale of interest, a_i is item i 's discrimination parameter, and b_i is item i 's difficulty parameter.

For the tpm model, the probability of non-zero response for respondent j on item i is

Pr(y_{ij}=1|\theta_j)=c_i+(1-c_i)\frac{\exp(a_i + b_i \theta_j)}{1+\exp(a_i + b_i \theta_j)}

where \theta_j is respondent j 's position on the latent scale of interest, a_i is item i 's discrimination parameter, b_i is item i 's difficulty parameter, and c_i is item i 's guessing parameter.

For the grm model, the probability of a response in category k or lower for respondent j on item i is

Pr(y_{ij} < k|\theta_j)=\frac{\exp(\alpha_{ik} - \beta_i \theta_{ij})}{1+\exp(\alpha_{ik} - \beta_i \theta_{ij})}

where \theta_j is respondent j 's position on the latent scale of interest, \alpha_ik the k-th element of item i 's difficulty parameter, \beta_i is discrimination parameter vector for item i. Notice the inequality on the left side and the absence of guessing parameters.

For the gpcm model, the probability of a response in category k for respondent j on item i is

Pr(y_{ij} = k|\theta_j)=\frac{\exp(\sum_{t=1}^k \alpha_{i} [\theta_j - (\beta_i - \tau_{it})])} {\sum_{r=1}^{K_i}\exp(\sum_{t=1}^{r} \alpha_{i} [\theta_j - (\beta_i - \tau_{it}) )}

where \theta_j is respondent j 's position on the latent scale of interest, \alpha_i is the discrimination parameter for item i, \beta_i is the difficulty parameter for item i, and \tau_{it} is the category t threshold parameter for item i, with k = 1,...,K_i response options for item i. For identification purposes \tau_{i0} = 0 and \sum_{t=1}^1 \alpha_{i} [\theta_j - (\beta_i - \tau_{it})] = 0. Note that when fitting the model, the \beta_i and \tau_{it} are not distinct, but rather, the difficulty parameters are \beta_{it} = \beta_{i} - \tau_{it}.

Value

When the model slot of the catObj is "ltm", the function probability returns a numeric vector of length one representing the probability of observing a non-zero response.

When the model slot of the catObj is "tpm", the function probability returns a numeric vector of length one representing the probability of observing a non-zero response.

When the model slot of the catObj is "grm", the function probability returns a numeric vector of length k+1, where k is the number of possible responses. The first element will always be zero and the (k+1)th element will always be one. The middle elements are the cumulative probability of observing response k or lower.

When the model slot of the catObj is "gpcm", the function probability returns a numeric vector of length k, where k is the number of possible responses. Each number represents the probability of observing response k.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Choi, Seung W. and Richard J. Swartz. 2009. “Comparison of CAT Item Selection Criteria for Polytomous Items." Applied Psychological Measurement 33(6):419-440.

Muraki, Eiji. 1992. “A generalized partial credit model: Application of an EM algorithm." ETS Research Report Series 1992(1):1-30.

van der Linden, Wim J. 1998. “Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216.

See Also

Cat-class

Examples

## Loading ltm Cat object
## Probability for Cat object of the ltm model
data(ltm_cat)
probability(ltm_cat, theta = 1, item = 1)

## Loading tpm Cat object
## Probability for Cat object of the tpm model
probability(tpm_cat, theta = 1, item = 1)

## Loading grm Cat object
## Probability for Cat object of the grm model
probability(grm_cat, theta = 1, item = 1)

## Loading gpcm Cat object
## Probability for Cat object of the gpcm model
probability(gpcm_cat, theta = -3, item = 2)
 

Qualtrics AJAX Handler

Description

Qualtrics AJAX Handler used to implement catSurv functionality in a Qualtrics survey

Usage

## S4 method for signature 'character'
processAJAX(catObj, item)

Arguments

Details

This function is not intended for researcher use, rather it is a public facing function of the package because it is used by catSurv to integrate computerized adaptive testing into a Qualtrics survey.

Author(s)

Joshua Landman

Clean adaptive inventory responses from Qualtrics

Description

This function cleans the adaptive inventory responses stored as embedded data in Qualtrics

Usage

## S4 method for signature 'character'
readQualtrics(catObj, responseID)

Arguments

Details

This function cleans the adaptive inventory responses contained in the Qualtrics survey results. Because different respondents recieve different adaptive inventories, their answers to the battery are not stored as usual as separate columns in the Data & Analysis tab in the Qualtrics toolbar. Rather, the respondents' answers to the adaptive battery are saved in the catObj embedded data object. To access the answers, click "Export & Import", and then "Export Data." In the window that appears, we recommend downloading the data as a .csv file. Then, feed this function the catObj column and the responseID column.

Value

This function returns a data frame containing cleaned adaptive inventory responses.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

Cat-class, ex_qualtrics_results, ex_qualtrics_results_multiple

Examples

data(ex_qualtrics_results) # loads example results
cat_vect <- ex_qualtrics_results$catObj[-c(1,2)] # vector of Cat embedded data objects
ids <- ex_qualtrics_results$ResponseId[-c(1,2)] # vector of respondent identifiers

# clean answer profiles
clean_df <- readQualtrics(catObj = cat_vect, responseID = ids)

# estimate respondents' positions
setEstimation(agree_cat) <- "MAP"
estimateThetas(catObj = agree_cat, responses = clean_df)

Right Wing Authoritarianism Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 20 item Right Wing Authoritarianism inventory

Usage

data(rwa_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 2056 response profiles from Lucid, 2519 response profiles from MTurk, and 1423 response profiles collected by YouGov in June 2018. The sample from MTurk was a convenience sample The respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (.241) and a standard deviation (1) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are:

5 = Strongly agree, 4 = Somewhat agree, 3 = Neither agree nor disagree, 2 = Somewhat disagree, 1 = Strongly disagree

The wording of the question items is:

q1

Our country desperately needs a mighty leader who will do what has to be done to destroy the radical new ways and sinfulness that are ruining us.

q2

Gays and lesbians are just as healthy and moral as anybody else.

q3

It is always better to trust the judgment of the proper authorities in government and religion than to listen to the noisy rabble-rousers in our society who are trying to create doubt in people's minds.

q4

Atheists and others who have rebelled against the established religions are no doubt every bit as good and virtuous as those who attend church regularly.

q5

The only way our country can get through the crisis ahead is to get back to our traditional values, put some tough leaders in power, and silence the troublemakers spreading bad ideas.

q6

There is absolutely nothing wrong with nudist camps.

q7

Our country needs free thinkers who have the courage to defy traditional ways, even if this upsets many people.

q8

Our country will be destroyed someday if we do not smash the perversions eating away at our moral fiber and traditional beliefs.

q9

Everyone should have their own lifestyle, religious beliefs, and sexual preferences, even if it makes them different from everyone else.

q10

The "old-fashioned ways" and the "old-fashioned values" still show the best way to live.

q11

You have to admire those who challenged the law and the majority's view by protesting for women's abortion rights, for animal rights, or to abolish school prayer.

q12

What our country really needs is a strong, determined leader who will crush evil, and take us back to our true path.

q13

Some of the best people in our country are those who are challenging our government, criticizing religion, and ignoring the "normal way things are supposed to be done."

q14

God's laws about abortion, pornography and marriage must be strictly followed before it is too late, and those who break them must be strongly punished.

q15

There are many radical, immoral people in our country today, who are trying to ruin it for their own godless purposes, whom the authorities should put out of action.

q16

A "woman's place" should be wherever she wants to be. The days when women are submissive to their husbands and social conventions belong strictly in the past.

q17

Our country will be great if we honor the ways of our forefathers, do what the authorities tell us to do, and get rid of the "rotten apples" who are ruining everything.

q18

There is no "ONE right way" to live life; everybody has to create their own way.

q19

Homosexuals and feminists should be praised for being brave enough to defy "traditional family values."

q20

This country would work a lot better if certain groups of troublemakers would just shut up and accept their group's traditional place in society.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Altemeyer, Bob. Enemies of freedom: Understanding right-wing authoritarianism. Jossey-Bass, 1988.

See Also

Cat-class, grmCat

Social Dominance Orientation Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 15 item Social Dominance Orientation inventory

Usage

data(sdo_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 2042 response profiles from Lucid, 1192 response profiles from MTurk, and 1482 response profiles collected by YouGov in June 2018. The sample from MTurk was a convenience sample The respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (.19) and a standard deviation (1) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are:

5 = Strongly agree, 4 = Somewhat agree, 3 = Neither agree nor disagree, 2 = Somewhat disagree, 1 = Strongly disagree

The wording of the question items is:

q1

Some groups of people are simply inferior to other groups.

q2

In getting what you want, it is sometimes necessary to use force against other groups.

q3

It's OK if some groups have more of a chance in life than others.

q4

To get ahead in life, it is sometimes necessary to step on other groups.

q5

If certain groups stayed in their place, we would have fewer problems.

q6

It's probably a good thing that certain groups are at the top and other groups are at the bottom.

q7

Inferior groups should stay in their place.

q8

Sometimes other groups must be kept in their place.

q9

It would be good if groups could be equal.

q10

Group equality should be our ideal.

q11

All groups should be given an equal chance in life.

q12

We should do what we can to equalize conditions for different groups.

q13

Increased social equality is beneficial to society.

q14

We would have fewer problems if we treated people more equally.

q15

We should strive to make incomes as equal as possible.

q16

No group should dominate in society.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Pratto, F., J. Sidanius, L. M. Stallworth, and B. F. Malle (1994), "Social Dominance Orientation: A Personality Variable Predicting Social and Political Attitudes," Journal of Personality and Social Psychology, 67, 741.

See Also

Cat-class, grmCat

Select Next Item

Description

Selects the next item in the question set to be administered to respondent based on the specified selection method.

Usage

selectItem(catObj)

Arguments

Details

Selection approach is specified in the selection slot of the Cat object.

The minimum expected posterior variance criterion is used when the selection slot is "EPV". This method calls expectedPV for each unasked item.

The maximum Fisher's information criterion is used when the selection slot is "MFI". This method calls fisherInf for each unasked item.

The maximum likelihood weighted information criterion is used when the selection slot is "MLWI". Note that when no questions have been answered, likelihood evaluates to 1. This method involves integration. See Note for more information.

The maximum posterior weighted information criterion is used when the selection slot is "MPWI". Note that when no questions have been answered, likelihood evaluates to 1. This method involves integration. See Note for more information.

The maximum expected information criterion is used when the selection slot is "MEI". This method calls expectedObsInf for each unasked item. **Not implemented for three parameter model for binary data.**

The maximum Kullback-Leibler information criterion is used when the selection slot is "KL". This method calls expectedKL for each unasked item. See expectedKL for more information.

The maximum likelihood weighted Kullback-Leibler information criterion is used when the selection slot is "LKL". This method calls likelihoodKL for each unasked item.

The maximum posterior weighted Kullback-Leibler information criterion is used when the selection slot is "PKL". This method calls posteriorKL for each unasked item.

The maximum Fisher interval information criterion is used when the selection slot is "MFII". This method involves integration. See Note for more information. The bounds of integration are \hat{\theta} \pm \delta, where \delta is qnorm(z) times the square root of the Fisher test information and z is specified in the z slot of the Cat object.

A random number generator is used when the selection slot is "RANDOM".

Value

The function selectItem returns a list with three elements:

estimates: a data frame with a row for each unasked question and three columns representing the item index number, the item name, and the item value (calculated by the specified selection method), and

next_item: a numeric representing the index of the item that should be asked next.

next_item_name: a string representing the unique identifier of the item that should be asked next.

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the lowerBound and upperBound slots of the Cat object unless otherwise noted.

The "RANDOM" item selection criterion uses the package RcppArmadillo to randomly choose the next item among unasked questions. RcppArmadillo provides an exact reproduction of R's sample function that can be called from C++.

In the rare instance that item parameters are identical, it may be that that selectItem must choose between two items with the same value calculated by the selection criterion. In such an instance, selectItem will choose the item with the lower question index.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

van der Linden, Wim J. 1998. "Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216.

Van der Linden, Wim J., and Peter J. Pashley. 2009. "Item Selection and Ability Estimation in Adaptive Testing." Elements of Adaptive Testing. Springer New York, 3-30.

Veldkamp, B.P., 2003. Item Selection in Polytomous CAT. In New Developments in Psychometrics (pp. 207-214). Springer Japan.

See Also

estimateTheta, expectedPV, fisherInf

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Set different selection criterion and choose next item
setSelection(ltm_cat) <- "EPV"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "MFI"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "MLWI"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "MPWI"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "MEI"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "KL"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "LKL"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "PKL"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "MFII"
selectItem(ltm_cat)

setSelection(ltm_cat) <- "RANDOM"
selectItem(ltm_cat)

Methods for Setting Value(s) to Cat Object Slots

Description

Setter methods to control changes to the slots of a Cat object.

Usage

## S4 replacement method for signature 'Cat'
setGuessing(catObj) <- value

## S4 replacement method for signature 'Cat'
setDiscrimination(catObj) <- value

## S4 replacement method for signature 'Cat'
setDifficulty(catObj) <- value

## S4 replacement method for signature 'Cat'
setAnswers(catObj) <- value

## S4 replacement method for signature 'Cat'
setIds(catObj) <- value

## S4 replacement method for signature 'Cat'
setModel(catObj) <- value

## S4 replacement method for signature 'Cat'
setPriorName(catObj) <- value

## S4 replacement method for signature 'Cat'
setPriorParams(catObj) <- value

## S4 replacement method for signature 'Cat'
setLowerBound(catObj) <- value

## S4 replacement method for signature 'Cat'
setUpperBound(catObj) <- value

## S4 replacement method for signature 'Cat'
setEstimation(catObj) <- value

## S4 replacement method for signature 'Cat'
setEstimationDefault(catObj) <- value

## S4 replacement method for signature 'Cat'
setSelection(catObj) <- value

## S4 replacement method for signature 'Cat'
setZ(catObj) <- value

## S4 replacement method for signature 'Cat'
setLengthThreshold(catObj) <- value

## S4 replacement method for signature 'Cat'
setSeThreshold(catObj) <- value

## S4 replacement method for signature 'Cat'
setGainThreshold(catObj) <- value

## S4 replacement method for signature 'Cat'
setInfoThreshold(catObj) <- value

## S4 replacement method for signature 'Cat'
setLengthOverride(catObj) <- value

## S4 replacement method for signature 'Cat'
setGainOverride(catObj) <- value

Arguments

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

Cat-class, getters

Examples

## Loading ltm Cat object
data(ltm_cat)

## Setting estimation slot
getEstimation(ltm_cat)
setEstimation(ltm_cat) <- "MAP"
getEstimation(ltm_cat)

## Setting distrimination slot
getDiscrimination(ltm_cat)
setDiscrimination(ltm_cat) <- rep(1, 40)
getDiscrimination(ltm_cat)

Calculates Fisher Information under different adaptive battery specifications

Description

Takes in a a Cat object, a set of respondents, and their corresponding theta values, and calculates the amount of information given an adaptive battery.

Usage

simulateFisherInfo(catObjs = list(), theta, responses)

Arguments

Details

The function takes a Cat object, theta, and response profiles. The user defines the selection type, estimation type, etc. so that the questions can be applied adaptively These adaptive profiles are then used to calculate the total inforamtion gained for a respondent for all answered items, conditioned on theta.

Value

The function simulateFisherInfo returns a dataframe where each Cat object corresponds to a column and each respondent corresponds to a row.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil, Jaerin Kim, Dominique Lockett

See Also

Cat-class, fisherTestInfo, selectItem

Examples

## Not run: 
# Example takes > 2.5 min to run
# Load Cat object
data(grm_cat)
   
# Simulate respondents
respondents <- plyr::adply(.data = matrix(c(-1, 0, 1)),
                           .margins = 1,
                           .id = NULL,
                           .fun = simulateRespondents, cat = grm_cat, n = 10)

# A stopping rule (here, a common one) is required
grm_cat@lengthThreshold <- 3

# Specify different adaptive inventory procedures
grm_MAP <- grm_EAP <- grm_cat
grm_MAP@estimation <- "MAP"
grm_EAP@estimation <- "EAP"

# List of Cat objects 
grmList <- list(grm_MAP, grm_EAP)

# Results
fisher_inf_results <- simulateFisherInfo(catObjs = grmList,
                              theta = rep(c(-1, 0, 1),
                              each = 10),
                              responses = respondents)

## End(Not run)

Simulate answer profiles given some true value of theta

Description

The function simulates n answer profiles given a true value of theta and a battery's item parameters stored in a Cat object.

Usage

## S4 method for signature 'Cat'
simulateRespondents(catObj, theta, n)

Arguments

Value

Function returns a dataframe where each row is a possible answer profile simulated given the provided value of theta

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

Examples

# Load Cat object
data(grm_cat)

# Simulate 5 response profiles given a theta of 2
sim_resp <- simulateRespondents(catObj = grm_cat, theta = 2, n = 5)

Estimates theta under different adaptive battery specifications

Description

Takes in response profiles from multiple respondents and multiple Cat object (i.e., adaptive battery) specifications and returns a set of theta estimates

Usage

simulateThetas(catObjs = list(), responses, return_adaptive = FALSE)

Arguments

Details

The function takes multiple Cat objects, stored in a list, and generates an estimation for theta.

Value

The function simulateThetas returns a dataframe where each Cat object corresponds to a column and each respondent corresponds to a row if return_adaptive is FALSE, the default. Optionally, simulateThetas returns a list containing that dataframe plus dataframes for the answer profiles simulated via each adaptive design if return_adaptive is TRUE.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil, Jaerin Kim, Dominique Lockett

See Also

Cat-class, apply, selectItem

Examples

## Not run: 
# Example takes > 2.5 min to run
# Load Cat object
data(grm_cat)
   
# Simulate respondents
respondents <- plyr::adply(.data = matrix(c(-1, 0, 1)),
                           .margins = 1,
                           .id = NULL,
                           .fun = simulateRespondents, cat = grm_cat, n = 10)
 
# A stopping rule (here, a common one) is required
grm_cat@lengthThreshold <- 3

# Specify different adaptive inventory procedures
grm_MAP <- grm_EAP <- grm_cat
grm_MAP@estimation <- "MAP"
grm_EAP@estimation <- "EAP"

# List of Cat objects 
grmList <- list(cat1 = grm_MAP, cat2 = grm_EAP)

# Results
theta_est_results <- simulateThetas(catObjs = grmList, responses = respondents)

## End(Not run)

Update Answer to Single Item

Description

Stores answer to item k to the Cat object's answers slot.

Usage

## S4 method for signature 'Cat'
storeAnswer(catObj, item, answer, returnJSON = FALSE)

## S4 method for signature 'character'
storeAnswer(catObj, item, answer, returnJSON = FALSE)

Arguments

Details

The function storeAnswer updates the Cat object, but the updated object must be assigned to an object for the changes to be stored. See Examples.

Value

The function storeAnswer returns an updated object of class Cat with the answers slot reflecting the newly stored answer to the indicated item. All previously stored answers remain the same, and all unanswered questions remain NA.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

Examples

## Loading ltm Cat object
data(ltm_cat)

## Printing current answers slot
getAnswers(ltm_cat)

## Storing answer of 0 to item 1
ltm_cat <- storeAnswer(ltm_cat, item = 1, answer = 0)

## Now object reflects answer to item 1
getAnswers(ltm_cat)

Conservation (Schwartz Values) Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the Conservation (Schwartz Values) inventory

Usage

data(sv_conservation_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 8,173 response profiles by the myPersonality Project and 718 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (.480) and a standard deviation (1.4) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options for the Schwartz Values survey are:

0 - means the value is not at all important, it is not relevant as a guiding principle for you. 3 - means the value is important. 6 - means the value is very important.

-1 is for rating any values opposed to the principles that guide you. 7 is for rating a value of supreme importance as a guiding principle in your life; ordinarily there are no more than two such values.

However, for computerized adaptive testing methods, the 0-7 response option range as been shifted to a 1-9 range.

The wording of the question items:

q11

POLITENESS (courtesy, good manners)

q20

SELF-DISCIPLINE (self-restraint, resistance to temptation)

q40

HONORING OF PARENTS AND ELDERS (showing respect)

q47

OBEDIENT (dutiful, meeting obligations)

q18

RESPECT FOR TRADITION (preservation of time-honored customs)

q32

MODERATE (avoiding extremes of feeling & action)

q36

HUMBLE (modest, self-effacing)

q44

ACCEPTING MY PORTION IN LIFE (submitting to life's circumstances)

q51

DEVOUT (holding to religious faith & belief)

q8

SOCIAL ORDER (stability of society)

q13

NATIONAL SECURITY (protection of my nation from enemies)

q15

RECIPROCATION OF FAVORS (avoidance of indebtedness)

q22

FAMILY SECURITY (safety for loved ones)

q56

CLEAN (neat, tidy)

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

Schwartz, Shalom H. "Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries." Advances in experimental social psychology. Vol. 25. Academic Press, 1992. 1-65.

See Also

Cat-class, grmCat

Openness to Change (Schwartz Values) Cat Object

Description

Cat model created for the Openness to Change (Schwartz Values) inventory

Usage

data(sv_open_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 8,448 response profiles by myPersonality Project and 718 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (-3.54) and a standard deviation (1.2) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options for the Schwartz Values survey are:

0 - means the value is not at all important, it is not relevant as a guiding principle for you. 3 - means the value is important. 6 - means the value is very important.

-1 is for rating any values opposed to the principles that guide you. 7 is for rating a value of supreme importance as a guiding principle in your life; ordinarily there are no more than two such values.

However, for computerized adaptive testing methods, the 0-7 response option range as been shifted to a 1-9 range.

The wording of the question items:

q5

FREEDOM (freedom of action and thought)

q15

RECIPROCATION OF FAVORS (avoidance of indebtedness)

q31

INDEPENDENT (self-reliant, self-sufficient)

q41

CHOOSING OWN GOALS (selecting own purposes)

q53

CURIOUS (interested in everything, exploring)

q9

AN EXCITING LIFE (stimulating experiences)

q25

A VARIED LIFE (filled with challenge, novelty and change)

q37

DARING (seeking adventure, risk)

q4

PLEASURE (gratification of desires)

q50

ENJOYING LIFE (enjoying food, sex, leisure, etc.)

q57

SELF-INDULGENT (doing pleasant things)

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

Schwartz, Shalom H. "Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries." Advances in experimental social psychology. Vol. 25. Academic Press, 1992. 1-65.

See Also

Cat-class, grmCat

Self-Enhancement (Schwartz Values) Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the Self-Enhancement(Schwartz Values) inventory

Usage

data(sv_selfenhance_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 8,497 response profiles by myPersonality Project and 718 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (-.09) and a standard deviation (1.2) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options for the Schwartz Values survey are:

0 - means the value is not at all important, it is not relevant as a guiding principle for you. 3 - means the value is important. 6 - means the value is very important.

-1 is for rating any values opposed to the principles that guide you. 7 is for rating a value of supreme importance as a guiding principle in your life; ordinarily there are no more than two such values.

However, for computerized adaptive testing methods, the 0-7 response option range as been shifted to a 1-9 range.

The wording of the question items:

q4

PLEASURE (gratification of desires)

q50

ENJOYING LIFE (enjoying food, sex, leisure, etc.)

q57

SELF-INDULGENT (doing pleasant things)

q34

AMBITIOUS (hard-working, aspiring)

q39

INFLUENTIAL (having an impact on people and events)

q43

CAPABLE (competent, effective, efficient)

q55

SUCCESSFUL (achieving goals)

q3

SOCIAL POWER (control over others, dominance)

q12

WEALTH (material possessions, money)

q27

AUTHORITY (the right to lead or command)

q46

PRESERVING MY PUBLIC IMAGE (protecting my "face")

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

Schwartz, Shalom H. "Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries." Advances in experimental social psychology. Vol. 25. Academic Press, 1992. 1-65.

See Also

Cat-class, grmCat

Self-Transcendence (Schwartz Values) Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the Self-Transcendence (Schwartz Values) inventory

Usage

data(sv_selftransc_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 8,415 response profiles by myPersonalit Project and 718 response profiles collected by YouGov in June 2018. The sample from myPersonality Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (.004) and a standard deviation (1.2) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options for the Schwartz Values survey are:

0 - means the value is not at all important, it is not relevant as a guiding principle for you. 3 - means the value is important. 6 - means the value is very important.

-1 is for rating any values opposed to the principles that guide you. 7 is for rating a value of supreme importance as a guiding principle in your life; ordinarily there are no more than two such values.

However, for computerized adaptive testing methods, the 0-7 response option range as been shifted to a 1-9 range.

The wording of the question items:

q1

EQUALITY (equal opportunity for all)

q17

A WORLD AT PEACE (free of war and conflict)

q24

UNITY WITH NATURE (fitting into nature)

q26

WISDOM (a mature understanding of life)

q29

A WORLD OF BEAUTY (beauty of nature and the arts)

q30

SOCIAL JUSTICE (correcting injustice, care for the weak)

q35

BROADMINDED (tolerant of different ideas and beliefs)

q38

PROTECTING THE ENVIRONMENT (preserving nature)

q33

LOYAL (faithful to my friends, group)

q45

HONEST (genuine, sincere)

q49

HELPFUL (working for the welfare of others)

q52

RESPONSIBLE (dependable, reliable)

q54

FORGIVING (willing to pardon others)

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

References

Stillwell, David, and Michal Kosinski. 2007. "myPersonality Project." https://sites.google.com/michalkosinski.com/mypersonality

Schwartz, Shalom H. "Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries." Advances in experimental social psychology. Vol. 25. Academic Press, 1992. 1-65.

See Also

Cat-class, grmCat

Systemizing Quotient Cat Object

Description

Cat object containing item parameters for graded response model fit with responses to the 40-item Systemizing Quotient personality inventory

Usage

data(systemizing_cat)

Format

An object of class Cat of length 1.

Details

Cat object containing item parameters for graded response model fit with 13,256 response profiles collected by the Open Source Psychometrics Project in 2012, 3050 response profiles collected by Qualtrics in June 2018, and 1500 response profiles collected by YouGov in June 2018. The sample from the Open Source Psychometrics Project was a convenience sample, and the respondents from YouGov were matched to a sampling frame on gender, age, race, and education.

See Cat-class for details regarding the Cat object structure. See grmCat for details regarding the graded response model.

A normal prior was chosen with mean from the theta estimates from the YouGov sample (.033) and a standard deviation (1.4) wide enough to envelope the range of estimated theta values across both samples.

Note that due to how the item parameters were estimated, large, positive values indicate "more" of the latent trait.

Response options are 1=Strongly disagree; 2=Slightly disagree; 3=Slightly agree; 4=Strongly agree

The wording of the question items:

q1

When I listen to a piece of music, I always notice the way it's structured.

q4

I prefer to read non-fiction than fiction.

q5

If I were buying a car, I would want to obtain specific information about its engine capacity.

q6

When I look at a painting, I do not usually think about the technique involved in making it.

q7

If there was a problem with the electrical wiring in my home, I'd be able to fix it myself.

q11

I rarely read articles or webpages about new technology.

q12

I do not enjoy games that involve a high degree of strategy.

q13

I am fascinated by how machines work.

q15

In math, I am intrigued by the rules and patterns governing numbers.

q18

I find it difficult to understand instruction manuals for putting appliances together.

q19

When I look at an animal, I like to know the precise species it belongs to.

q20

If I were buying a computer, I would want to know exact details about its hard drive capacity and processor speed.

q23

When I cook, I do not think about exactly how different methods and ingredients contribute to the final product.

q24

I find it difficult to read and understand maps.

q25

If I had a collection (e.g. CDs, coins, stamps), it would be highly organized.

q26

When I look at a piece of furniture, I do not notice the details of how it was constructed.

q28

When I learn about historical events, I do not focus on exact dates.

q29

When I read the newspaper, I am drawn to tables of information, such as football league scores or stock market indices.

q30

When I learn a language, I become intrigued by its grammatical rules.

q31

I find it difficult to learn my way around a new city.

q32

I do not tend to watch science documentaries on television or read articles about science and nature.

q33

If I were buying a stereo, I would want to know about its precise technical features.

q34

I find it easy to grasp exactly how odds work in betting.

q35

I am not very meticulous when I carry out D.I.Y.

q37

When I look at a building, I am curious about the precise way it was constructed.

q38

When an election is being held, I am not interested in the results for each constituency.

q40

I find it difficult to understand information the bank sends me on different investment and saving systems.

q41

When traveling by train, I often wonder exactly how the rail networks are coordinated.

q42

When I buy a new appliance, I do not read the instruction manual very thoroughly.

q43

If I were buying a camera, I would not look carefully into the quality of the lens.

q44

When I read something, I always notice whether it is grammatically correct.

q45

When I hear the weather forecast, I am not very interested in the meteorological patterns.

q48

When I look at a mountain, I think about how precisely it was formed.

q49

I can easily visualize how the highways in my region link up.

q51

When I'm in a plane, I do not think about the aerodynamics.

q53

When I am walking in the country, I am curious about how the various kinds of trees differ.

q55

I am interested in knowing the path a river takes from its source to the sea.

q56

I do not read legal documents very carefully.

q57

I am not interested in understanding how wireless communication works.

q60

I do not care to know the names of the plants I see.

Source

See https://dataverse.harvard.edu/dataverse/pdsl for the raw YouGov and/or Qualtrics data.

See https://openpsychometrics.org/_rawdata/, maintained by Eric Jorgenson, for the raw Open Source Psychometrics Project site data.

References

Baron-Cohen, Simon, Jennifer Richler, Dheraj Bisarya, Nhishanth Gurunathan, and Sally Wheelwright. "The systemizing quotient: an investigation of adults with Asperger syndrome or high-functioning autism, and normal sex differences." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1430 (2003): 361-374.

Open Source Psychometrics Project. https://openpsychometrics.org/_rawdata/

See Also

Cat-class, grmCat

Convert Cat object to JSON

Description

This function object of class Cat.

Usage

## S4 method for signature 'Cat'
toJSONCat(catObj)

Arguments

Value

The function toJSONCat returns a JSON object with list elements corresponding to information stored in the catObj.

See Cat-class for required Cat object slots.

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

See Also

Cat-class

Computerized Adaptive Testing Birnbaum's Three Parameter Model

Description

This function fits Birnbaum's three parameter model for binary data and populates the fitted values for discrimination, difficulty, and guessing parameters to an object of class Cat.

Usage

## S4 method for signature 'data.frame'
tpmCat(data, quadraturePoints = 21, ...)

## S4 method for signature 'tpm'
tpmCat(data, quadraturePoints = NULL, ...)

Arguments

Details

The data argument of the function tpmCat is either a data frame or an object of class tpm from the ltm package. If it is a data frame each row represents a respondent and each column represents a question item. If it is an object of the class tpm, it is output from the tpm function in the ltm package.

The quadraturePoints argument of the function tpmCat is used only when the data argument is a data frame. quadraturePoints is then passed to the tpm function from the ltm package when fitting Birnbaum's three parameter model to the data and is used when approximating the value of integrals.

Value

The function tpmCat returns an object of class Cat with changes to the following slots:

• difficulty A vector consisting of difficulty parameters for each item.

• discrimination A vector consisting of discrimination parameters for each item.

• model The string "tpm", indicating this Cat object corresponds to Birnbaum's three parameter model.

See Cat-class for default values of Cat object slots. See Examples and setters for example code to change slot values.

Note

In case the Hessian matrix at convergence is not positive definite try to use start.val = "random".

Author(s)

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Birnbaum, Allan. 1968. Some Latent Trait Models and their Use in Inferring an Examinee's Ability. In F. M. Lord and M. R. Novick (Eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Rizopoulos, Dimitris. 2006. “ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses." Journal of Statistical Software 17(5):1-25.

See Also

Cat-class, ltmCat, polknowMT, probability

Examples

## Creating Cat objects from large datasets is computationally expensive
## Load the Cat object created from the above code
data(tpm_cat)

## Slots that have changed from default values
getModel(tpm_cat)
getDifficulty(tpm_cat)
getDiscrimination(tpm_cat)

## Changing slots from default values
setEstimation(tpm_cat) <- "MLE"
setSelection(tpm_cat) <- "MFI"

tpm Cat Object

Description

An object of class Cat created using the tpmCat function with the first twenty questions of the polknowMT dataset.

Usage

data(tpm_cat)

Format

An object of class Cat. See Cat-class for more details.

See Also

Cat-class, tpmCat, polknowMT

Examples

## Not run: 
## How this Cat object was created
data(polknowMT)
tpm_cat <- tpmCat(polknowMT[,1:20], quadraturePoints = 100, start.val = "random")

## End(Not run)

## How to load this Cat object for usage
data(tpm_cat)