This paper presents an expository development of James-Stein estimation with substantial emphasis on exact results for nonnormal location models. The themes of the paper are: (1) the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives; (2) the amount of…

Compared approaches to determining the precision of gain scores: (1) the asymptotic normal distribution of the maximum likelihood estimator of the person parameter; and (2) the exact conditional distribution of the gain score. Use of three data sets illustrates that these methods yield more relevant and more detailed information than traditional…

A constrained quadratic spline is proposed as an estimator of the hazard function of a random variable. A maximum penalized likelihood procedure is used to fit the estimator to a sample of psychological response times. (Author/LMO)

In order to obtain conditional maximum likelihood estimates, the so-called conditioning estimates have to be calculated. In this paper a method is examined that does not calculate these constants exactly, but approximates them using Monte Carlo Markov Chains. As an example, the method is applied to the conditional estimation of both item and…

The utility of the three-form design coupled with maximum likelihood methods for estimation of missing values was evaluated. Simulation studies demonstrate that maximum likelihood estimation and multiple imputation methods produce the most efficient and least biased estimates of variances and covariances for normally distributed and slightly…

The extent to which properties of the ability scale and the form of the latent trait distribution influence the estimated item parameters of item response theory (IRT) was investigated using real and simulated data. Simulated data included 5,000 ability values randomly drawn from the standard normal distribution. Real data included the results for…

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)

Asymptotic distributions of H. Brogden's and F. Lord's modified sample biserial correlation coefficients (SBCCs) are derived. Asymptotic variances of these estimators are evaluated for bivariate normal populations and compared to the maximum likelihood estimator's asymptotic variance. These estimators are less variable than ordinary SBCCs when the…

Alternative models for a large dataset were analyzed by asymptotically distribution-free, generalized least squares, maximum likelihood, and ordinary least squares estimation methods, comparing incremental and nonincremental fit indexes. Incremental methods were quite unstable across estimation methods. This phenomenon is explained. (SLD)

The accuracy of estimation procedures in item response theory was studied using Monte Carlo methods and varying sample size, number of subjects, and distribution of ability parameters for: (1) joint maximum likelihood as implemented in the computer program LOGIST; (2) marginal maximum likelihood; and (3) marginal Bayesian procedures as implemented…

Two simple empirical approximate Bayes estimators are introduced for estimating domain scores under binomial and hypergeometric distributions respectively. Criteria are established regarding use of these functions over maximum likelihood estimation counterparts. (SLD)

This study was designed to compare the accuracy of three commonly used ability estimation procedures under the graded response model. The three methods, maximum likelihood (ML), expected a posteriori (EAP), and maximum a posteriori (MAP), were compared using a recovery study design for two sample sizes, two underlying ability distributions, and…

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)

This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…

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)