d1LL {catSurv} R Documentation

## 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

 catObj An object of class Cat theta A numeric or an integer indicating the value for \theta_j use_prior A logical indicating whether to calculate based on the log-likelihood or log-posterior

### 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.

Cat-class, prior

### Examples

## Loading ltm Cat object
data(ltm_cat)