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)

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)

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)

This paper reviews various procedures for constructing an interval for an individual's true score given the assumption that errors of measurement are distributed as binomial. This paper also presents two general interval estimation procedures (i.e., normal approximation and endpoints conversion methods) for an individual's true scale score;…

A study was conducted to investigate whether augmenting the calibration of items using computerized adaptive test (CAT) data matrices produced estimates that were unbiased and improved the stability of existing item parameter estimates. Item parameter estimates from four pools of items constructed for operational use were used in the study to…

Studied whether ordered latent class models can be used as nonparametric item response theory (NIRT) models to scale polytomous models. Simulation findings show that the Bayesian estimation method presented can handle the inequality restrictions on the parameters and the sparseness of the data quite well. (SLD)

This paper investigates methods that avoid using multiple groups to represent the missing data patterns in covariance structure modeling, attempting instead to do a single-group analysis where the only action the analyst has to take is to indicate that data is missing. A new covariance structure approach developed by B. Muthen and G. Arminger is…

A structural multilevel model is presented in which some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal politicos response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel…

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…

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)

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…

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)