Latent Structure Analysis

The structure of a log-linear model can be described on an association diagram by the lines connecting the points. Especially for higher order contingency tables the structure on an assocition diagram can be very complicated, implicating a complicated interpretation of the model. Adding to the interpretation problems for a multi-dimensional contingency table is the fact, that the decision to exclude or include a given interaction in the model can be based on conflicting significance levels depending on the order in which the statistical tests are carried out. These decisions are thus based on the intuition and experience of the data analyst rather than on objective criteria. Hence a good deal of arbitrariness is often involved, when a model is selected to describe the data. We recall for example from several of the examples in the previous chapters that the log-linear model often gave an adequate description of the data judged by a direct test of the model against the saturated model, while among the sequence of successive tests leading to the model, there were cases of significant levels.