A Monte Carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions, improper solutions and the distribution of goodness-of-fit indices in maximum likelihood confirmatory factor analysis. Nonconvergent and improper solutions occurred more frequently for smaller sample sizes and for models with fewer indicators of each factor. Effects of practical significance due to sample size, the number of indicators per factor and the number of factors were found for GFI, AGFI, and RMR, whereas no practical effects were found for the probability values associated with the chi-square likelihood ratio test.

The purpose of the current paper is to propose a general multicomponent latent trait model (GLTM) for response processes. The proposed model combines the linear logistic latent trait (LLTM) with the multicomponent latent trait model (MLTM). As with both LLTM and MLTM, the general multicomponent latent trait model can be used to (1) test hypotheses about the theoretical variables that underlie response difficulty and (2) estimate parameters that describe test items by basic substantive properties. However, GLTM contains both component outcomes and complexity factors in a single model and may be applied to data that neither LLTM nor MLTM can handle. Joint maximum likelihood estimators are presented for the parameters of GLTM and an application to cognitive test items is described.

In many classification problems, one often possesses external and/or internal information concerning the objects or units to be analyzed which makes it appropriate to impose constraints on the set of allowable classifications and their characteristics. CONCLUS, or CONstrained CLUStering, is a new methodology devised to perform constrained classification in either an overlapping or nonoverlapping (hierarchical or nonhierarchial) manner. This paper initially reviews the related classification literature. A discussion of the use of constraints in clustering problems is then presented. The CONCLUS model and algorithm are described in detail, as well as their flexibility for use in various applications. Monte Carlo results are presented for two synthetic data sets with appropriate discussion of the resulting implications. An illustration of CONCLUS is presented with respect to a sales territory design problem where the objects classified are various Forbes-500 companies. Finally, the discussion section highlights the main contribution of the paper and offers some areas for future research.

A general class of differentiation indices is introduced for profiles of scores. Their ordinal properties and an application to Holland's classification system are examined. Comparison with other suggested indices is performed both theoretically and empirically.

Existing statistical tests for the fit of the Rasch model have been criticized, because they are only sensitive to specific violations of its assumptions. Contingency table methods using loglinear models have been used to test various psychometric models. In this paper, the assumptions of the Rasch model are discussed and the Rasch model is reformulated as a quasi-independence model. The model is a quasi-loglinear model for the incomplete subgroup × score × item 1 × item 2 × ... × item k contingency table. Using ordinary contingency table methods the Rasch model can be tested generally or against less restrictive quasi-loglinear models to investigate specific violations of its assumptions.

A computer-interactive preference ordering procedure that is based on assumed transitivity of relations is described. The procedure includes features that are designed to make it robust in the presence of inconsistency. With errorless data, the method will find the underlying order in close to log2n! comparisons. Two simulation studies are described where the responses are assumed to follow the Thurstone Case V model. It was found that the method produces orders that are more valid than does a considerably larger preselected subset of pairs.

The locally best invariant test statistic for testing sphericity of normal distributions is shown to be a simple function of the Box/Geisser-Greenhouse degrees of freedom correction factor in a repeated measures design. Because of this relationship it provides a more intuitively appealing test of the necessary and sufficient conditions for valid F-tests in repeated measures analysis of variance than the likelihood ratio test. The properties of the two tests are compared and tables of the critical values of the Box/Geisser-Greenhouse correction factor are given.

In maximum likelihood estimation the standard error of the location parameter of the three parameter logistic model can be large, due to inaccurate estimation of the lower asymptote. Thissen and Wainer who demonstrated this effect, suggested that the introduction of a prior distribution for the lower asymptote might alleviate the problems. Here it is demonstrated in some detail that the standard error of the location parameter can be made acceptably small in this way.

A test for multisample sphericity based on the efficient scores criterion is obtained as an alternative to the likelihood ratio test developed by Mendoza.