Modeling and Multivariate Methods - SAS

220 Performing Logistic Regression on Nominal and Ordinal Responses Chapter 7
Example of an Ordinal Logistic Model
Figure 7.20 Ordinal Logistic Fit
The model in this example reduces the –LogLikelihood of 429.9 to 355.67. This reduction yields a
likelihood-ratio Chi-square for the whole model of 148.45 with 3 degrees of freedom, showing the
difference in perceived cheese taste to be highly significant.
The Lack of Fit test happens to be testing the ordinal response model compared to the nominal model. This
is because the model is saturated if the response is treated as nominal rather than ordinal, giving 21
additional parameters, which is the Lack of Fit degrees of freedom. The nonsignificance of Lack of Fit leads
one to believe that the ordinal model is reasonable.
There are eight intercept parameters because there are nine response categories. There are only three
structural parameters. As a nominal problem, there are 8× 3 = 24 structural parameters.
When there is only one effect, its test is equivalent to the Likelihood-ratio test for the whole model. The
Likelihood-ratio Chi-square is 148.45, different from the Wald Chi-square of 115.15, which illustrates the
point that Wald tests are to be regarded with some skepticism.
To see whether a cheese additive is preferred, look for the most negative values of the parameters (Cheese D’s
effect is the negative sum of the others, shown in Figure 7.1.).