General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

Parallel analysis has been shown to be suitable for dimensionality assessment in factor analysis of continuous variables. There have also been attempts to demonstrate that it may be used to uncover the factorial structure of binary variables conforming to the unidimensional normal ogive model. This article provides both theoretical and empirical…

This paper presents a new hierarchical classes model, called Tucker2-HICLAS, for binary three-way three-mode data. As any three-way hierarchical classes model, the Tucker2-HICLAS model includes a representation of the association relation among the three modes and a hierarchical classification of the elements of each mode. A distinctive feature of…

This paper proposes a multidimensional generalization of Coombs' (1964) parallelogram model for "pick any/'n'" data, which result from each of a number of subjects having selected a number of objects (s)he likes most from a prespecified set of "n" objects. In the model, persons and objects are represented in a low dimensional space defined by a…

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…

A method of comparing one-step M-estimates of location for heavy tailed distributions is proposed and investigated. Simulations indicate that the new procedure provides good control over Type I errors and has more power than do some other methods for dealing with heavy tailed distributions. (SLD)

The theoretical differences between the traditional definition of dimensionality and the more recently defined notion of essential dimensionality are presented. Monte Carlo simulations are used to demonstrate the utility of W. F. Stout's procedure to assess the essential unidimensionality of the latent space underlying a set of terms. The…

Binary or graded disagree-agree responses to attitude items are often collected for the purpose of attitude measurement. Although such data are sometimes analyzed with cumulative measurement models, recent investigations suggest that unfolding models are more appropriate (J. S. Roberts, 1995; W. H. Van Schuur and H. A. L. Kiers, 1994). Advances in…

Learning hierarchies are networks of prerequisite relationships of instructional objectives. Seven measures of the validity of learning hierarchies were compared for their ability to identify correctly- and incorrectly-ordered hierarchies. A computer simulation model was used to generate stochastic data of known underlying structure. Analysis of…

Simultaneous estimation of many parameters can often be improved, sometimes dramatically so, if it is reasonable to consider one or more subsets of parameters as exchangeable members of corresponding populations. While each observation may provide limited information about the parameters it is modeled directly in terms of, it also contributes…

This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the…

Three test-analysis models were used to analyze three types of simulated test score data plus the results of eight achievement tests. Chi-square goodness-of-fit statistics were used to evaluate the appropriateness of the models to the four kinds of data. Data were generated to simulate the responses of 1,000 students to 36 pseudo-items by…