Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variable as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The proposed estimation methods are illustrated by two simulation studies. (SLD)

The purpose of this paper is to demonstrate in detail how the Empirical Bayes (EB) statistical estimation strategy can be applied to an important class of educational research contexts. EB methods are tailored specifically to the analysis of data with a hierarchical structure. For instance, investigators may be interested in discovering how…

Latent trait test models for responses to dichotomously scored items are considered from the point of view of parameter estimation using a Bayesian statistical approach and the EM estimation algorithm. An example using the Rasch model is presented. (Author/JKS)

Estimation theory in educational statistics and the application of hierarchical linear models are reviewed. Observations within each group vary as a function of microparameters. Microparameters vary across the population of groups as a function of macroparameters. Bayes and empirical Bayes viewpoints review examples with two levels of hierarchy.…

The concept of consensus ordering is defined, and formulas for exact and approximate posterior probabilities for consensus ordering are developed under the assumption of a generalized Mallows' model with a diffuse conjugate prior. These methods are applied to a data set concerning 98 college students. (SLD)

A Bayes estimation procedure for Rasch-type model estimation that has statistical and computational advantages over existing methods is described. It involves constructing posterior distributions based on sample data and artificial data reflecting prior information. Its use for some Rasch-type cases, and how it can improve parameter estimation are…

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. (Author/LMO)

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.…

This proposal attempts to follow in Allan Birnbaum's tradition by using Bayesian ideas to show that his mental test model possesses even broader applicability than previously realized. Birnbaum's two significant contributions to the theories of statistics and educational testing are: (1) the proof that the sufficiency and conditionality principles…

There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated…

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data…

This article describes a Bayesian framework for estimation in item response models, with two-stage distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. (Author/LMO)

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.…

An empirical Bayes-maximum likelihood estimation procedure is presented for the application of fuzzy partition models in describing high dimensional discrete response data. The model describes individuals in terms of partial membership in multiple latent categories that represent bounded discrete spaces. (SLD)

A new computerized mastery test is described that builds on the Lewis and Sheehan procedure (sequential testlets) (1990), but uses fuzzy set decision theory to determine stopping rules and the Rasch model to calibrate items and estimate abilities. Differences between fuzzy set and Bayesian methods are illustrated through an example. (SLD)