In many surveys, the data comprise a large number of categorical variables that suffer from item nonresponse. Standard methods for multiple imputation, like log-linear models or sequential regression imputation, can fail to capture complex dependencies and can be difficult to implement effectively in high dimensions. We present a fully Bayesian,…

The purpose of this study was to explore the degree of grain size of the attributes and the sample sizes that can support accurate parameter recovery with the General Diagnostic Model (GDM) for a large-scale international assessment. In this resampling study, bootstrap samples were obtained from the 2003 Grade 8 TIMSS in Mathematics at varying…

In the modern world information has become the new power. An increasing amount of efforts are being made to gather data, resources being allocated, time being invested and tools being developed. Data collection is no longer a myth; however, it remains a great challenge to create value out of the enormous data that is being collected. Data modeling…

During the last decade the use of Bayesian statistical method has become quite prevalent in the educational community. Yet, like most statistical techniques, little has been written concerning the application of these methods to the classroom setting. The purpose of this paper is to help correct such a deficiency in the literature by developing a…

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.…

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 Libby-Novick class of three-parameter generalized beta distributions is shown to provide a rich class of prior distributions for the binomial model that removes some restrictions of the standard beta class. A numerical example indicates the desirability of using these wider classes of densities for binomial models. (Author/BW)

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)

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…

A model developed by G. Rasch that assumes scores on some attainment tests can be realizations of a Poisson process is explained and expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. How additional between-subject and within-subject factors can be incorporated is discussed. (SLD)

Hierarchical Bayes procedures were compared for estimating item and ability parameters in item response theory. Simulated data sets from the two-parameter logistic model were analyzed using three different hierarchical Bayes procedures: (1) the joint Bayesian with known hyperparameters (JB1); (2) the joint Bayesian with information hyperpriors…

The focus of this study is on the estimation procedures implemented in BILOG, a computer program. One purpose is to compare the item parameter estimates produced by various procedures available in BILOG. Four different models are used: the one, two, and three parameter model and a three parameter model with common guessing parameters. The results…