The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach

Models and methods for analyzing the relations among a set of polytomous variables, when some of the variables are posterior to others, are presented. The techniques proposed here yield ‘path diagrams’ that are somewhat analogous to those used in path analysis. Earlier path analysis models are not suited to the case where the variables are polytomous, or dichotomous, but the models proposed herein are. For each of our models, methods are presented for (a) testing whether the model fits the data, (b) partitioning the test statistic into components that can be used to test submodels within the overall model, and (c) estimating the parameters in the model. An illustrative application is also included.