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)

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)

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…

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)

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)

Developed a Bayesian approach for a general multigroup nonlinear factor analysis model that simultaneously obtains joint Bayesian estimates of the factor scores and the structural parameters subjected to some constraints across different groups. (SLD)

The Gibbs sampling algorithms presented by M. H. Seltzer (1993) are fully generalized to a broad range of settings in which vectors of random regression parameters in the hierarchical model are assumed multivariate normally or multivariate "t" distributed across groups. The use of a fully Bayesian approach is discussed. (SLD)

A framework is described for exploiting auxiliary information about test items within item response theory models to enhance parameter estimates. The method also provides diagnostic information about items' operating characteristics. An empirical Bayesian estimation of Rasch item difficulty is used to illustrate the principles involved. (TJH)

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.…