The accuracy of Gibbs sampling, a Markov chain Monte Carlo procedure, was considered for estimation of item and ability parameters under the two-parameter logistic model. Memory test data were analyzed to illustrate the Gibbs sampling procedure. Simulated data sets were analyzed using Gibbs sampling and the marginal Bayesian method. The marginal…

A class of two-stage models is developed to accommodate three common characteristics of behavioral data: (1) its multivariate nature; (2) the typical small sample size; and (3) the possibility of missing observations. The model, as illustrated, permits estimation of the full spectrum of plausible measurement error structures. (SLD)

Introduces a new technique for estimating the parameters of models with continuous latent data. To streamline presentation of this Markov Chain Monte Carlo (MCMC) method, the Rasch model is used. Also introduces a new sampling-based Bayesian technique, the DA-T-Gibbs sampler. (SLD)

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…

This paper suggests several item selection criteria for adaptive testing that are all based on the use of the true posterior. Some of the ability estimators produced by these criteria are discussed and empirically criticized. (SLD)

Imposed a two-level regression model on the ability parameters in an item response theory (IRT) model. Uses a simulation study and an empirical data set to show that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. (SLD)

The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization to a model with multidimensional ability parameters are discussed. The procedure is a generalization of a procedure by J. Albert (1992) for estimating the two-parameter normal ogive model. The procedure will support multiple samples from multiple…

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)

To better describe individual behavior within a system, this paper uses a sample of longitudinal test scores from a large urban school system to consider hierarchical Bayes estimation of a multilevel linear regression model in which each individual regression slope of test score on time switches at some unknown point in time, "kj."…

Developed a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data that obtains joint Bayesian estimates of thresholds, structural parameters, and latent factor scores simultaneously. Illustrated the approach through analysis of a real data set of 20 patterns of condom use in the Philippines. (SLD)

Pseudo-Bayesian and joint maximum likelihood procedures were compared for their ability to estimate item parameters for item response theory's (IRT's) three-parameter logistic model. Item responses were generated for sample sizes of 2,000 and 500; test lengths of 35 and 15; and examinees of high, medium, and low ability. (TJH)

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.…

Used simulations of computerized adaptive tests to evaluate results yielded by four commonly used ability estimation methods: maximum likelihood estimation (MLE) and three Bayesian approaches. Results show clear distinctions between MLE and Bayesian methods. (SLD)