expectedKL {catSurv}

Expected Kullback-Leibler Information

Description

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

Usage

expectedKL(catObj, item)

Arguments

catObj

An object of class Cat

item

An integer indicating the index of the question item

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)