Modeling and Multivariate Methods - SAS

396 Performing Categorical Response Analysis Chapter 15
Categorical Reports
The test is the chi-square test for marginal homogeneity of response patterns, testing that the response
probabilities are the same across samples. This is equivalent to a test for independence when the sample
category is like a response. There are two versions of this test, the Pearson form and the Likelihood Ratio
form, both with chi-square statistics. The Test Options menu is used to show or hide the Likelihood Ratio
or Pearson tests.
As an example, open Car Poll.jmp and launch the Categorical platform. Choose country as a Separate
Response and marital status as an X, Grouping Category. When the report appears, select Test Reponse
Homogeneity from the platform menu.
The Share Chart seems to indicate that the married group has higher probability to buy American cars, and
the single group has higher probability to buy Japanese cars, but the statistical test only shows a significance
of 0.08. Therefore, the difference in response probabilities across marital status is not statistically significant
at an alpha level of 0.05.
Test Each Response
When there are multiple responses, each response category can be modeled separately. The question is
whether the response rates are the same across samples. For each response category, we assume the frequency
count has a random Poisson distribution. The rate test is obtained using a Poisson regression (through
generalized linear models) of the frequency per unit modeled by the sample categorical variable. The result is
a likelihood ratio chi-square test of whether the rates are different across samples.