A class of models is presented for gamma distributed random variables. These additive, multiplicative, and combined additive-multiplicative models are more flexible than classical linear models with respect to the structure that can be imposed on expected values. As a special case, a class of psychometric models for reaction times is presented.…

Some examinees' test-taking behavior may be so idiosyncratic that their test scores are not comparable to those of more typical examinees. A new theoretical approach to appropriateness measurement is proposed that specifies a likelihood ratio test and an efficient computer algorithm for computing the test statistic. (TJH)

Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

A probabilistic item response theory (IRT) model is developed for pair-comparison design in which the unfolding principle governing the choice process uses a discriminant process analogous to Thurstone's Law of Comparative Judgment. A simulation study demonstrates the feasibility of estimation, and two examples illustrate the implications for…

The effects of a multidimensional latent trait space on estimation of item and person parameters by the computer program LOGIST are examined. Several item pools were simulated that ranged from truly unidimensional to an inconsequential general latent trait. Item pools with intermediate levels of prepotency of the general latent trait were also…

This paper reviews the basic elements of the EM approach to estimating item parameters and illustrates its use with one simulated and one real data set. In order to illustrate the use of the BILOG computer program, runs for 1-, 2-, and 3-parameter models are presented for the two sets of data. First is a set of responses from 1,000 persons to five…