Modeling Manifest and Latent Dimensions of Association in Two-Way Cross-Classifications

In this article, the author develops a model that combines the RC(M) association model with the linear-by-linear association model for the analysis of two-way contingency tables. This combination provides a useful extension of both models that is applicable under many research conditions. A primary advantage of the model is that it allows the researcher to assess the influence of manifest factors on the row/column association while controlling for significant latent effects. The model also enables a partitioning of the association into that percentage due to the manifest component(s) and that percentage due to the latent component(s). Data from the 1991 General Social Survey are used to construct a cross-classification of occupations by job-related responsibilities which, in turn, is used to develop and illustrate (a) interpretation of parameter estimates, (b) row/column distance measures and plots in oblique space, and (c) a partitioning of the explained association in the table.