MOST OF THIS BOOKhas been concerned with variables that are measured on a more or less
continuous scale and for which the mean, or a related sample statistic, would be a typical
measure of interest. However, many variables we deal with are measured categorically,
such as the classic study by Geller, Witmer, and Orebaugh (1976), discussed in Chapter 6,
in which a supermarket flier on “daily specials” was categorized both in terms of whether
it contained a message about littering and where it was found at the end of the day (trash
can, litter, removed from store). In that particular example we were able to show that where
a notice was left depended on whether it contained a message about littering. In other
words, the two variables are not independent—they interact.
Experimenters faced with multiple categorical variables have often dealt with them
two at a time, creating two-way contingency tables and computing the standard Pearson
chi-square test statistic to check for independence. Recently, however, major efforts to de-
velop procedures that deal with multiple categorical variables simultaneously have been
undertaken. (I say “recently” because even though the important work in this field started
with Leo Goodman at the University of Chicago in the 1960s, it generally takes at least 20
to 30 years for statistical procedures to work their way from initial development in the sta-
tistical journals, to occasional appearance in the experimental literature, to widespread ac-
ceptance. Log-linear modelsare just beginning to make it to the latter stage.)
The presentation of log-linear models presents several challenges. In the first place
such models are much easier to understand when presented as simple contingency tables
with two dimensions (variables). However, the two-dimensional case is not handled appre-
ciably better by log-linear models than by the standard approach, and the reader can easily
be left wondering “So what?” Log-linear models come into their own with three-, four-, or
higher-dimensional cases, but the explanation can become unpleasantly tortuous and
opaque. For this reason we will start with the two-dimensional case, lay out most of the
reasoning, and then move on to higher dimensions.
A second problem with log-linear models is that each author views them from a differ-
ent perspective. If you skim several of the excellent books on such models, you might
almost think that they were talking about different topics. Some authors are interested pri-
marily in hypothesis testing, whereas others are interested primarily in model building.
Some concentrate on examining individual effects, whereas others mention individual
effects only in passing. Some concentrate on models in which all of the variables are
treated as independent variables, whereas others focus on cases in which one or more vari-
ables are thought of as dependent variables and the others as independent variables. This
chapter will try to steer a middle course, focusing on those aspects of the models that apply
most directly to psychology and related disciplines. I recommend that the first time through
you concentrate on the hypothesis testing aspects of log-linear models. Then go back and
pay more serious attention to estimating treatment effects.
A number of excellent references on this subject are available. Some of the clearest are
Agresti (1984, 1990—especially the former), Green (1988), Kennedy (1983), Marascuilo
and Serlin (1990), and Wickens (1989), which is very complete and readable. An excellent
presentation of the applications of standard computer software is given in Tabachnick and
Fidell (2007). I have borrowed heavily from all of these sources.
My motivation in writing this chapter is a little different from the motivation for other
chapters. There is a great deal of technical information here that I would not expect my stu-
dents to grapple with until they had a particular need for the material. I think that this
chapter is most likely to be read by someone who has found herself with a set of data on
categorical variables and knows (or has been told) that log-linear models might be the way
to go. This chapter was written primarily from the point of view of helping that person
wade through complex and confusing material on the topic. I try to explain what those
terms are all about, and why you would care. I also try to explain what various sections of630 Chapter 17 Log-Linear Analysis
log-linear models