Conditions necessary and sufficient for the determination of LISREL model solutions are identified. The reasons for indeterminacy of LISREL solutions are discussed, and an index of determinacy is presented and related to the covariance matrix of latent variables. (SLD)

Problems of estimation and interpretation are discussed that arise when a statistical package, which does not incorporate a dedicated weighted least-squares (WLS) routine, performs WLS regression by misapplication of a case-weighting strategy. A strategy is offered for adjusting WLS regression estimates after a case weighting strategy has been…

Two methods of handling unequal variances in the two-way fixed effects analysis of variance (ANOVA) model are described. One is based on an improved Wilcox (1988) method for the one-way model, and the other is an extension of G. S. James' (1951) second order method. (TJH)

An algorithm based on the majorization theory of J. de Leeuw and W. J. Heiser is presented for fitting the slide-vector model. It views the model as a constrained version of the unfolding model. A three-way variant is proposed, and two examples from market structure analysis are presented. (SLD)

Reasons/methods for standardizing discriminant function coefficients are reviewed, and use of the pooled within-groups variance estimate is examined. Use of total or pooled within-groups estimates can be justified only on purely mathematical grounds. Total variance estimates offer a more consistent and parsimonious approach than do pooled…

Applications of the confirmatory factor analysis block-diagonal model to published data on 18 multitrait-multimethod matrices were reviewed to show widespread estimation problems. Possible causes of estimation difficulties were explored using computer simulations. These problems make the block-diagonal approach less useful than has generally been…

A general model for two-level multivariate data, with responses possibly missing at random, is described. The model combines regressions on fixed explanatory variables with structured residual covariance matrices. The likelihood function is reduced to a form enabling computational methods for estimating the model to be devised. (Author)

Discusses whether the tradition of accepting point-symmetric item characteristic curves is justified by uncovering the inconsistent relationship between the difficulties of items and the order of maximum likelihood estimates of ability. In this context, proposes a family of models, called the logistic positive exponent family, that provides…

This paper presents a detailed description of maximum parameter estimation for item response models using the general EM algorithm. In this paper the models are specified using a univariate discrete latent ability variable. When the latent ability variable is discrete the distribution of the observed item responses is a finite mixture, and the EM…

In many large-scale educational assessments it is of interest to compare the distribution of latent abilities of different subpopulations, and track these distributions over time to monitor educational progress. B. Junker, together with two colleagues, has developed a simple scheme, based on the proportion correct score, for smoothly approximating…

The probability integral of the multivariate normal distribution (ND) has received considerable attention since W. F. Sheppard's (1900) and K. Pearson's (1901) seminal work on the bivariate ND. This paper evaluates the formula that represents the "n x n" correlation matrix of the "chi(sub i)" and the standardized multivariate…

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.…

The purpose of this paper is to propose a general multicomponent latent trait model (LTM) for response processes. It combines the linear logistic LTM with the multicomponent LTM. Joint maximum likelihood estimators are presented for parameters of the general multicomponent LTM and an application to cognitive test items is described. (Author/BW)

This paper considers the following questions: (1) what is the relationship between the method of paired comparisons and Rasch measurement theory? (2) what is the relationship between the method of paired comparisons and graph theory? and (3) what can graph theory contribute to the understanding of Rasch measurement theory? It is specifically shown…

It has previously been shown that the Bock-Aitkin procedure (R. Bock and M. Aitkin, 1981) is an instance of the EM algorithm when trying to find the marginal maximum likelihood estimate for a discrete latent ability variable (latent trait). In this paper, it is shown that the Bock-Aitkin procedure is a numerical implementation of the EM algorithm…