frequencies. This test is easy to compute because the standard error of a residual is simply
the square root of the expected frequency. Thus,is conservatively a standard normal deviate (Agresti, 1990). Standardized residuals (z) in
excess of 1.96 should give cause for concern (the model did not fit that cell well), but be-
cause you are running a large number of such tests a Bonferroni correction would be in or-
der. To do this, treat the deviates as though they weretvalues on an infinite number of
degrees of freedom and use Appendix to adjust for the number of independent tests. For
our example we have no significant deviations. The sum of the squared entries in the
Deviance column will equal the log-likelihood.Interpreting the Model
From the analysis we have just gone through, we can say quite a bit about our data. Gener-
ally, statements about main effects are less interesting than statements about interactions,
but I will discuss both. In the first place, the frequencies were a function of the level of the
Moral variable, but because these frequencies were largely fixed by the experimenter, they
are of no great interest. Similarly, the data reflect small, but significant, differences in the
attribution of Fault to the victim, with slightly more subjects seeing the victim as high in
fault. This again was in part attributable to the experimenter’s sampling plan. What was not
under the direct control of the experimenter, and is of more interest, is a significantly
higher number of defendants judged guilty than judged not guilty. Collapsing across the
other dimensions, the odds in favor of a guilty judgment are 258/100 5 2.58.
When we look at the interactions we see that there is an interaction between Moral
and Verdict. A guilty verdict is more likely when the victim is seen as of high moral char-
acter than when she is seen as of low moral character. Put another way, the odds in favor
of a guilty verdict for the High, Neutral, and Low Moral conditions are 65/15 5 4.33,
144/53 5 2.72, and 49/32 5 1.53, respectively. Whether a defendant is seen as guilty ap-
pears to depend on events beyond the alleged crime itself.
Finally, there is an interaction between Fault and Verdict. When the victim is seen as
low in fault, the odds in favor of a guilty verdict are 153/24 5 6.38. In the high fault condi-
tion, those same odds are 105/76 5 1.38. (Thus, the odds ratio is 6.38/1.38 5 4.62, and the
log(odds ratio) 5 ln(4.62) 5 1.53, which is the parameter estimate for the Verdict 3 Fault
interaction). A judgment of guilty is clearly dependent on the degree to which the victim is
seen as being at fault. These data shed light on the tendency of defense attorneys to try to
put the blame on the victim, in that they show that juries’ judgments of guilt or innocence
are influenced by attributions of fault and low moral character to the victim.Ordinal Variables
In this chapter we have treated our variables as if they were measured on a nominal scale,
although Moral did have an ordinal scale of Low, Neutral, and High. If variables are meas-
ured on an ordinal scale, standard log-linear analysis, though legitimate, does not use that
information. Scrambling the levels of each variable would lead to the same statistical results.
Recently attention has focused on alternative treatments that allow us to use ordinal
scaling of variables where it is available. Discussions of log-linear models with ordinal
variables can be found in Green (1988) and Agresti (1984, 1990). SPSS can accommodate
such analyses.x^2t¿6
z=Observed 2 Expected
1 Expected654 Chapter 17 Log-Linear Analysis