Previous work on the mathematical and implementation details of the marginalized maximum likelihood estimation procedure is extended to encompass the marginalized Bayesian procedure for estimating item parameters of R. J. Mislevy (1986) and to communicate this procedure to users of the BILOG computer program. (SLD)

Comparing variability of test scores across alternate forms, test conditions, or subpopulations is a fundamental problem in psychometrics. A confidence interval for a ratio of standard deviations is proposed that performs as well as the classic method with normal distributions and performs dramatically better with nonnormal distributions. A simple…

A mathematical model is proposed to describe how group differences in distributions of abilities, which are distinct from the target ability, influence the probability of a correct item response. In the multidimensional approach, differential item functioning is considered a function of the educational histories of the examinees. (SLD)