Abstract
Qualitative variables with ordinal categories often arise in social research. In this paper we consider a special class of log-linear models for analysis of these variables (viz., latent structure of latent class models) which take account of (a) the actual distributional properties corresponding to the sampled cross-classification of the variables, (b) the ordinal character of the variables, and (c) the status of the observed variables as indicators of unobservable or latent variables. Parameters are estimated by the method of maximum likelihood, using an iterative proportional scaling algorithm appropriate for latent structure analysis. Asymptotic tests of various models, assignment of individuals into latent classes, and indexes appropriate for measuring model adequacy are discussed. An example with a 3 × 3 × 3 cross-classification illustrates the application of these models.
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