MODELING MANIFEST AND LATENT DIMENSIONS OF ASSOCIATION IN 2-WAY CROSS-CLASSIFICATIONS

In this article, the author develops a model that combines the RC(M) a ssociation model with the linear-by-linear association model for the a nalysis of two-way contingency tables. This combination provides a use ful extension of both models that is applicable under many research co nditions. A primary advantage of the model is that it allows the resea rcher to assess the influence of manifest factors on the row/column as sociation while controlling for significant latent effects. The model also enables a partitioning of the association into that percentage du e to the manifest component(s) and that percentage due to the latent c omponent(s). Data from the 1991 General Social Survey are used to cons truct a cross-classification of occupations by job-related responsibil ities which, in turn, is used to develop and illustrate (a) interpreta tion of parameter estimates, (b) row/column distance measures and plot s in oblique space, and (c) a partitioning of the explained associatio n in the table.