Typically, nonlinear models such as those used in the analysis of covariance structures, are not globally identifiable. Investigations of local identifiability must either yield a mapping onto the entire parameter space, or be confined to points of special interest such as the maximum likelihood point. (Author/JKS)

The authors examine the asymptotic effect of omitting a random coefficient in the multilevel model and derive expressions for the change in (a) the variance components estimator and (b) the estimated variance of the fixed effects estimator. They apply the method of moments, which yields a closed form expression for the omission effect. In…

When the results of a series of independent studies are combined, it is useful to quantitatively estimate the magnitude of the effects. Several methods for estimating effect size are compared in this paper. Glass' estimator and the uniformly minimum variance unbiased estimator are based on the ratio of the sample mean difference and the pooled…

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. An example is presented to demonstrate potential problems in other approaches to maximum likelihood factor analysis. (Author/JKS)

Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called "unconditional" and the "conditional" maximum-likelihood estimation equations in the dichotomous Rasch model are given. It is shown how to apply the results in practical uses of the Rasch model. (Author/JKS)

In Bayesian statistics, the choice of the prior distribution is often controversial. Different rules for selecting priors have been suggested in the literature, which, sometimes, produce priors that are difficult for the students to understand intuitively. In this article, we use a simple heuristic to illustrate to the students the rather…

It is common to assume during statistical analysis of a multiscale assessment that the assessment has simple structure or that it is composed of several unidimensional subtests. Under this assumption, both the unidimensional and multidimensional approaches can be used to estimate item parameters. This paper theoretically demonstrates that these…

An iterative procedure to obtain maximum likelihood estimates of latent structure analysis parameters is described. The procedure is defended against a critic (EJ 187 975) who contended that it would permit unacceptable estimates. (JKS)

Misspecification of mean and covariance structures for metric endogenous variables is considered. Maximum likelihood estimation of model parameters and the asymptotic covariance matrix of the estimates are discussed. A Haussman test for misspecification is developed, which is sensitive to misspecification not detected by the test statistics…

Less than optimum strategies for missing values can produce biased estimates, distorted statistical power, and invalid conclusions. After reviewing traditional approaches (listwise, pairwise, and mean substitution), selected alternatives are covered including single imputation, multiple imputation, and full information maximum likelihood…

This paper is concerned with estimation and hypothesis testing of treatment effects in nonequivalent control group designs with the assumption that in the absence of treatment effects, natural growth conforms to a particular class of continuous growth models. Point estimation, interval estimation, and hypothesis testing procedures were developed…

Technical problems in achievement testing associated with using latent structure models to estimate the probability of guessing correct responses by examinees is studied; also the lack of problems associated with using Wilcox's formula score. Maximum likelihood estimates are derived which may be applied when items are hierarchically related.…

Through a large-scale simulation study, this article compares item parameter estimates obtained by the marginal maximum likelihood estimation (MMLE) and marginal Bayes modal estimation (MBME) procedures in the 3-parameter logistic model. The impact of different prior specifications on the MBME estimates is also investigated using carefully…

This article illustrates a method for fitting straight lines to data that is resistant to outliers and might therefore sometimes be preferred to the customary least squares procedure.

Item response theory (IRT) has proven to be a very powerful and useful measurement tool. However, most of the IRT models that have been proposed, and all of the models commonly used, require the assumption of unidimensionality, which prevents their application to a wide range of tests. The few models that have been proposed for use with…