likelihood function

Likelihood of the Specified Response Set

Calculates the likelihood of a respondent, with ability parameter $\theta$, having offered the specific set of responses stored in the Cat objects answers slot. All calculations are conditional on the item-level parameters stored in the Cat object.

likelihood(catObj, theta)

Arguments

• catObj: An object of class Cat
• theta: A numeric or an integer indicating the value for $\theta$

Returns

The function likelihood returns a numeric value of the likelihood of the respondent having offered the provided response profile. Note that when no questions have been answered, likelihood evaluates to 1.

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.

Examples

## Loading ltm Cat object
## Likelihood for Cat object of the ltm model
data(ltm_cat)
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))
likelihood(ltm_cat, theta = 1)

## Loading grm Cat object
## Likelihood for Cat object of the grm model
data(grm_cat)
setAnswers(grm_cat) <- c(1,1,5,2,5, rep(NA, 13))
likelihood(grm_cat, theta = 1)

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, probability

Author(s)

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