catSurv (version 1.5.0)

d2LL: 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)

Value

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

Arguments

catObj

An object of class Cat

theta

A numeric or an integer indicating the value for \(\theta\)

use_prior

A logical indicating whether to calculate based on the log-likelihood or log-posterior

Author

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

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.

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)