estimateTheta {catSurv}

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

catObj

An object of class Cat

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)