We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

Bayesian item response theory (IRT) modeling stages include (a) specifying the IRT likelihood model, (b) specifying the parameter prior distributions, (c) obtaining the posterior distribution, and (d) making appropriate inferences. The latter stage, and the focus of this research, includes model criticism. Choice of priors with the posterior…

Person-fit assessment may help the researcher to obtain additional information regarding the answering behavior of persons. Although several researchers examined person fit, there is a lack of research on person-fit assessment for mixed-format tests. In this article, the lz statistic and the ?2 statistic, both of which have been used for tests…

The derivation of the variance of similarity judgments is made from the 3-D process in nonlinear psychophysics. The idea of separability of dimensions in metric space theories of similarity is replaced by one parameter that represents the degree of a form of interdimensional cross-sampling. (SLD)

Analysis of a two-way sample of means is considered when corresponding population means are believed a priori to satisfy a partial order restriction. Simulation and the Gibbs sampler are used to summarize posterior distributions, and the posterior distribution is used to predict GPAs of first-year students at University of Iowa. (SLD)