Introduction to Categorical Data Analysis

PROBLEMS 203
a. Show that the Pearson X 2 = 11.5 with df = 9(P = 0.24). Show that
the correlation statistic with equally-spaced scores is M 2 = 7.6 based on
df = 1(P = 0.006). Interpret.
b. Conduct an analysis with a model for which you would expect the test of
the income effect also to be powerful.
6.21 For the 2000 GSS, counts in the happiness categories (not too, pretty,
very) were (67, 650, 555) for those who were married and (65, 276, 93) for
those who were divorced. Analyze these data, preparing a one-page report
summarizing your descriptive and inferential analyses.
6.22 True, or false?
a. One reason it is usually wise to treat an ordinal variable with methods that
use the ordering is that in tests about effects, chi-squared statistics have
smaller df values, so it is easier for them to be farther out in the tail and
give small P -values; that is, the ordinal tests tend to be more powerful.
b. The cumulative logit model assumes that the response variable Y is ordinal;
it should not be used with nominal variables. By contrast, the baselinecategory
logit model treats Y as nominal. It can be used with ordinal Y ,but
it then ignores the ordering information.
c. If political ideology tends to be mainly in the moderate category in New
Zealand and mainly in the liberal and conservative categories in Australia,
then the cumulative logit model with proportional odds assumption should
fit well for comparing these countries.
d. Logistic regression for binary Y is a special case of the baseline-category
logit and cumulative logit model with J = 2.