10.1. Introduction

In Chapter 4, we saw how to analyze contingency tables that included a dichotomous variable treated as dependent on the other variables. The strategy was to directly estimate a logit model in PROC LOGISTIC or PROC GENMOD. We extended that approach in Chapter 5 to handle dependent variables with more than two categories by estimating a multinomial logit model with PROC CATMOD. In this chapter, we see how to estimate loglinear models for contingency tables. What distinguishes loglinear models from logit models is that loglinear models do not have an explicit dependent variable, at least not one that corresponds to any conceptual variable. As I’ve mentioned previously, every logit model for a contingency table has a loglinear model that is exactly equivalent. But the class of loglinear models also includes models that don’t correspond to any logit models, so we are dealing with a much wider class of models.

Why do we need loglinear models? When loglinear analysis was first developed in the late 1960s and early 1970s, there wasn’t much software available for logit analysis. And what was available wasn’t very suitable for analyzing contingency tables. By contrast, loglinear models were easily estimated with widely available software. Now, however, you’re usually better off estimating a logit model directly. Logit models are simpler and correspond more directly to substantive theory. However, there are some situations, when a logit model just doesn’t do the job. For example, you might want to explore the relationships among several attitude measures that have no obvious causal ordering. But a logit model requires that you choose one variable as the dependent variable and the others as independent variables.

Even if you do have a clear-cut dependent variable, the particular logit model you want to estimate may be awkward for conventional software. For example, the adjacent-categories model described in Chapter 6 is a special case of the multinomial logit model. But the maximum likelihood algorithm in CATMOD will not impose the necessary constraints to get this model. As we shall see, the adjacent-categories model is easily estimated as a loglinear model when the data comes in the form of a contingency table. Loglinear models are particularly well suited to the analysis of two-way tables in which the row variable has the same categories as the column variables (a square table). For example, there is a large literature on loglinear models for mobility tables in which the row variable represents parent’s occupation and the column variable represents child’s occupation (for example, Hout 1983).

The treatment of loglinear analysis in this book is far from comprehensive. The topic is so vast that I can do no more than scratch the surface here. My goals are, first, to give you some idea of what loglinear models are like and how they are related to logit models. Second, I will show you how to estimate fairly conventional loglinear models by using the GENMOD procedure. Third, I will present some examples in which a loglinear model has significant advantages over a logit model.