An analytic expression is derived for the posterior distribution of the bivariate correlation given a data set that contains missing values on both variables. Interval estimates of the unknown correlation are then computed in terms of the highest posterior density regions. A sampling study illustrates the procedure. (SLD)

Presents a Bayesian method for obtaining an interval estimate of the population squared multiple correlation from an incomplete multivariate normal data set. Estimates were constructed using Gibbs sampling. Simulation studies indicate that the method can yield accurate interval estimates of the population squared multiple correlation. (SLD)

In intervention studies, it is important to assess whether one program might be more effective for individuals with extreme initial difficulties, while another might be more effective for individuals with less extreme initial difficulties. In setting in which time-series data are obtained for each person, this entails examining interactions…

Explains how the Gibbs sampler can be applied to obtain a sample from the posterior distribution over the parameters of a structural equation model. Presents statistics to use to summarize marginal posterior densities and model checks using posterior predictive p-values. (SLD)

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)

It is not unusual for several tests measuring different abilities to be given in one test administration. A common practice is to estimate these abilities independently of each other, but this paper proposes a more efficient method of estimating these abilities that takes into account the correlational structure of the abilities. The method uses a…

Implemented a Bayesian factor analysis model to formulate estimators of the hyper-parameters. Simulation results lead to the proposal of new bias-corrected estimates of factor loadings. (SLD)

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…

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)

The ability estimates of Gibbs sampling and the magnitudes of the posterior standard deviations were investigated. Item parameters of the Q-E intelligence test (J. Fraenkel and N. Wallen, 2000) for 44 examinees were obtained using Gibbs sampling, marginal Bayesian estimation, and BILOG. Two normal priors were used in item parameter estimation.…

An analysis of repeated measures designs is proposed that uses an empirical Bayes estimator of the covariance matrix. The proposed analysis behaves like a univariate analysis when sample size is small or sphericity nearly satisfied, but behaves like multivariate analysis when sample size is large or sphericity is strongly violated. (SLD)

Explores posterior analysis in estimating factor score in a confirmatory factor analysis model with polytomous, censored or truncated data, and studies the accuracy of Bayesian estimates through simulation. Results support these Bayesian estimates for statistical inference. (SLD)