The posterior distribution of the bivariate correlation is analytically derived given a data set where "X" is completely observed, but "Y" is missing at random for a portion of the sample. Interval estimates of the correlation are constructed from the posterior distribution in terms of the highest density regions. (SLD)

Proposes a marginal Bayesian estimation procedure to improve item parameter estimates for the three parameter logistic model. Computer simulation suggests that implementing the marginal Bayesian estimation algorithm with four-parameter beta prior distributions and then updating the priors with empirical means of updated intermediate estimates can…

A flexible class of stochastic mixture models is introduced and illustrated for analysis and interpretation of individual differences in recurrent choice and other types of count data. These models are derived by specifying elements of the choice process at the individual level. An easy-to-implement algorithm is presented for parameter estimation.…

Investigates the BILOG computer program's ability to recover known item parameters for different numbers of items, examinees, and variances of the prior distributions of discrimination parameters for the two-parameter logistic item-response theory model. For samples of at least 250 examinees and 15 items, simulation results support using BILOG.…

Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classical test theory. Analogies are provided for use as approximations in work with item response theory (IRT). The following issues are addressed: (1) the relationship between the distribution of the latent…

Statistical methods are presented for studying "correlates of diversity," defined as characteristics of educational organizations that predict dispersion on the dependent variable. Strategies based on exact distribution theory and asymptotic normal approximation are considered. (TJH)

A Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model. Joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described. (Author/LMO)

The accuracy of estimation procedures in item response theory was studied using Monte Carlo methods and varying sample size, number of subjects, and distribution of ability parameters for: (1) joint maximum likelihood as implemented in the computer program LOGIST; (2) marginal maximum likelihood; and (3) marginal Bayesian procedures as implemented…

Two simple empirical approximate Bayes estimators are introduced for estimating domain scores under binomial and hypergeometric distributions respectively. Criteria are established regarding use of these functions over maximum likelihood estimation counterparts. (SLD)

The precision of the group-based item-response theory (IRT) model applied to school ability estimation is described, assuming use of Bayesian estimation with precision represented by the standard deviation of the posterior distribution. Similarities with and differences between the school-based model and the individual-level IRT are explored. (SLD)

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)

This paper describes a study, now in progress, of new methods for representing the sampling variability of Mantel-Haenszel differential item functioning (DIF) results, based on the system for categorizing the severity of DIF that is now in place at the Educational Testing Service. The methods, which involve a Bayesian elaboration of procedures…

A joint Bayesian estimation procedure for estimating parameters in the three-parameter logistic model is developed. Simulation studies show that the Bayesian procedure (1) ensures that the estimates stay in the parameter space and (2) produces better estimates than the joint maximum likelihood procedure. (Author/BS)

Assuming vectors of item responses depend on ability through a fully specified item response model, this paper presents maximum likelihood equations for estimating the population parameters without estimating an ability parameter for each subject. Asymptotic standard errors, tests of fit, computing approximations, and details of four special cases…

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)