Maximum likelihood and least-squares estimates of parameters from the logistic regression model are derived from an iteratively reweighted linear regression algorithm. Empirical Bayes estimates are derived using an m-group regression model to regress the within-group estimates toward common values. The m-group regression model assumes that the…

The quality of approximations to first- and second-order moments based on latent ability estimates is discussed. The ability estimates are based on the Rasch or the two-parameter logistic model, and true score theory is used to account for the fact that the basic quantities are estimates. (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)

The real problems of contextual analysis concern the conceptualization of contextual effects, the kinds of data with which to estimate them, and the selection and implementation of appropriate statistical techniques. This paper focuses on detection; specifically, an approach to contextual analysis based on the estimation and interpretation of a…

Methods for predicting specific college course grades, based on small numbers of observations, were investigated. These methods use collateral information across potentially diverse institutions to obtain refined within-group parameter estimates. One method, referred to as pooled least squares with adjusted intercepts, assumes that slopes and…

Two methods of using collateral information from similar institutions to predict college freshman grade average were investigated. One central prediction model, referred to as pooled least squares with adjusted intercepts, assumes that slopes and residual variances are homogeneous across selected colleges. The second model, referred to as Bayesian…

Thissen and Wainer (EJ 284 848) suggested that the introduction of a prior distribution for the lower asymptote may alleviate problems of a large standard error of the location parameter of the three parameter logistic model. The correctness of this suggestion is demonstrated in detail. (Author/BW)

This paper considers the application of Bayesian techniques for simultaneous estimation to the specification of regression weights for selection tests used in various technical training courses in the Marine Corps. It concludes that a hypothesis of complete generalization of the predictor-criterion relationship would only be retained for selected…

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 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)

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)

Standard procedures for estimating item parameters in Item Response Theory models make no use of auxiliary information about test items, such as their format or content, or the skills they require for solution. This paper describes a framework for exploiting this information, thereby enhancing the precision and stability of item parameter…

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…

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)

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)