the computer printout mean. (I use SPSS GENLOG as my example program, but if you
have a different program, just apply it to the example data and note the parallels in the
printout. But don’t be put off if your answers are slightly different. Different programs use
different algorithms, which come to slightly different answers. That’s not nice, but it is the
way things are.)Symmetric and Asymmetric Models
In general, log-linear analysis treats independent and dependent variables alike, ignoring
the distinction between them. We as experimenters, however, build our interpretation of the
data in part on whether a variable is seen, by us, as independent or dependent.
To take a simple example, suppose that we have developed a scale of myths related to
rape (“If a woman is raped she was probably partly responsible”) and myths related to
spouse abuse (“An abused wife is always free to leave her abuser”). Suppose further that
our subjects have responded Agree, Neutral, or Disagree with the terms on both scales. If
we want to look at the relation between the rape myths and spouse abuse myths, neither
variable would be dependent relative to the other. This would remain so if we added yet an-
other dimension and categorized subjects in terms of other sorts of beliefs (e.g., just-world
beliefs). Relations of this sort, in which all the variables are treated alike as dependent vari-
ables, are classed as symmetric relationships.
Now suppose that we take another variable (Gender) and look to see whether there are
differences in rape myths between males and females. Here most people would see Gender
as an independent variable and Rape myth as a dependent variable. We would account for
Rape myth as a function of Gender, but would be unlikely to account for Gender on the
basis of Rape myth. This is an asymmetric relationship.
Log-linear models apply to both symmetric and asymmetric models. The difference comes
more in the interpretation than in the mathematics. When you have an asymmetric model, you
will focus more on the dependent variable and its relations with independent variables. When
the model is symmetric, you will spread your interest more widely. In addition, with asymmet-
ric models you may choose to keep certain nonsignificant variables in the model on the basis
of their role in the study. With symmetric models we are more even-handed.17.1 Two-Way Contingency Tables
We will begin with the simplest example of a 2 3 2 contingency table. Although log-linear
analysis does not have a great deal more to offer than the standard Pearson chi-square ap-
proach in this situation, it will allow us to examine a number of important concepts in a
simple setting. Agresti (2002) suggests that with a single categorical response (dependent)
variable, it is simpler to use logistic regression. As we move to more complex situations we
will leave more and more of the actual calculations to computer software, because such
computations can become extremely cumbersome.
As an example we will use a study by Pugh (1983) on the “blaming-the-victim” issue
in prosecutions for rape. Pugh’s paper is an excellent example of how to use log-linear
analysis to establish a statistical model to explain experimental results. But we will, at first,
simplify the underlying experiment to create an example that is more useful for our pur-
poses. The simplification involves collapsing over, and thereby ignoring, some experimen-
tal variables. (In general, we would not collapse across variables unless we were confident
that they did not play a role or we were not interested in any role they did play.)
Pugh designed a study to examine what many have seen to be the disposition of jurors
to base their judgments of defendants on the alleged behavior of the victim. Defense attorneysSection 17.1 Two-Way Contingency Tables 631symmetric
relationships
asymmetric
relationship