Fixed-distance latent class models for the analysis of sets of two-way contingency tables

This paper develops and describes the application of modified latent class models for analyzing sets of two-way contingency tables. The proposed fixed-distance models differ from traditional latent class models in that the assumption of local stochastic independence is superseded by allowing interactions of the manifest variables within each class, which can be represented by a single association parameter. As an example, two data sets on eye color by hair color [collected in Caithness (N1 = 5,387) and Aberdeen (N2 = 22,361)] and fixed-distance models with up to six classes (three classes per data set) are considered, finally leading to satisfactory fit and rather simple interpretation.