estimateSE: Standard Error of Ability Parameter Estimate

In erossiter/catSurv: Computerized Adaptive Testing for Survey Research

Standard Error of Ability Parameter Estimate

Description

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

Usage

estimateSE(catObj)

Arguments

catObj

An object of class Cat

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 θ 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 θ.

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)

erossiter/catSurv documentation built on Dec. 11, 2022, 6:36 p.m.