Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of K dichotomous items. The two algorithms, stepwise forward selection and backward elimination, incorporate statistical criteria for selecting (or deleting) 0-1 response pattern vectors to form the subset of the total possible 2k vectors that uniquely describe the hierarchy. The performances of the algorithms are compared, using computer-constructed data, with those of three competing deterministic approaches based on ordering theory and the calculation of Phi/Phi-max coefficients. The discovery algorithms are also demonstrated on real data sets investigated in the literature.

Several articles in the past fifteen years have suggested various models for analyzing dichotomous test or questionnaire items which were constructed to reflect an assumed underlying structure. This paper shows that many models are special cases of latent class analysis. A currently available computer program for latent class analysis allows parameter estimates and goodness-of-fit tests not only for the models suggested by previous authors, but also for many models which they could not test with the more specialized computer programs they developed. Several examples are given of the variety of models which may be generated and tested. In addition, a general framework for conceptualizing all such models is given. This framework should be useful for generating models and for comparing various models.

In this note, we describe the iterative procedure introduced earlier by Goodman to calculate the maximum likelihood estimates of the parameters in latent structure analysis, and we provide here a simple and direct proof of the fact that the parameter estimates obtained with the iterative procedure cannot lie outside the allowed interval. Formann recently stated that Goodman's algorithm can yield parameter estimates that lie outside the allowed interval, and we prove in the present note that Formann's contention is incorrect.

A model for longitudinal latent structure analysis is proposed. We assume that test scores for a given mental or attitudinal test are observed for the same individuals at two different points in time. The purpose of the analysis is to fit a model that combines the values of the latent variable at the two time points in a two-dimensional latent density. The correlation coefficient between the two values of the latent variable can then be estimated. The theory and methods are illustrated by a Danish dataset concerning psychic vulnerability.

This paper provides a description of a new adaptive testing algorithm based on a latent class modeling framework. The algorithm incorporates a four-stage iterative procedure that conditionally minimizes expected loss in classification of respondents across different content domains. The classification decisions relate to the membership of a person in a category of a latent variable for each of the separate domains considered. The algorithm appears to be particularly effective when latent class membership is related across the various domains of interest, since classification decisions on domains assessed early in the process are used to revise the probabilities for latent class membership on domains for which classification decisions have not yet been made. To assess the effectiveness of the proposed algorithm, a simulation based upon real data was conducted. For this example, the algorithm proved to be relatively efficient, requiring only 40% of the number of items needed under a nonadaptive approach. In addition, the algorithm provided classification decisions which, in 96% of the cases, were consistent with decisions based upon all available items when the maximum acceptable classification error rate was set at 5%.

The algorithms for the demonstration of shared phenomenology of psychiatric syndromes in DSM-III are resistant to quantification. In contrast, the rating scale approach quantifies clinical target syndromes in psychiatry. The two most useful statistical models for quantifying shared phenomenology by symptom rating scales have been reviewed; namely factor analysis and latent structure analysis. Results have shown that factor analysis has demonstrated dimensions of dementia, delirium, schizophrenia, mania, outward aggression, depression and anxiety. Latent structure analysis has confirmed that the items of brief rating scales (such as the Melancholia Scale) are additively related implying that their total scores are sufficient statistics for the measurement of these factors or dimensions. Latent structure analysis should be considered as a psychometric “glasnost” compared to algorithm-resistant logic of quantification in DSM-III.

With the introduction of major tranquillizers more than three decades ago symptom rating scales were soon accepted as the method of evaluating their clinical effects. The Mini-compendium is a collection of rating scales for measuring outcome of antianxiety drugs, antidepressants, antimanics, and anti-psychotics. The scales have been selected by their “cash values”, i.e. the scales most frequently used for the respective dimensions. These scales have been further developed in terms of strict item definitions. The simple sum of the individual scale items has been considered as a sufficient statistic if they fulfilled latent structure analysis of shared phenomenology.

We consider representations of a joint distribution law of a family of categorical randomvariables (i.e., a multivariate categorical variable) as a mixture ofindependent distribution laws (i.e. distribution laws according to whichrandom variables are mutually independent). For infinite families of random variables, wedescribe a class of mixtures with identifiable mixing measure. This class is interestingfrom a practical point of view as well, as its structure clarifies principles of selectinga “good” finite family of random variables to be used in applied research. For finitefamilies of random variables, the mixing measure is never identifiable; however, it alwayspossesses a number of identifiable invariants, which provide substantial informationregarding the distribution under consideration.

If class theory has explanatory and descriptive power it should be possible to provide evidence that social classes exist as phenomena generic to modern industrial societies. This paper addresses this issue by examining the structure of class situations, as defined by job attributes, in two central European, post-communist societies – Hungary and Poland – and then comparing them with a benchmark Western society, Britain. Classes are identified through a latent structure analysis of job attributes and by assessing the correspondence between the latent classes estimated through this procedure and positions on two alternative indicators of class position – the Goldthorpe class schema and self-rated class identity. The structure of latent classes is found to be generally similar across all three societies, as is the correspondence between these latent classes and positions in the Goldthorpe schema in the two societies in which it is measured, and class identification. The main exceptions to this shared pattern relate to variations in the size and organisation of the agricultural sector and the distinctiveness of ‘intermediate’ class positions. The evidence indicates the presence of a considerable degree of cross-national consistency in the structure of class situations across diverse social and political contexts.