Introduction to Categorical Data Analysis

200 MULTICATEGORY LOGIT MODELS
6.9 A cumulative logit model is fitted to data from the 2004 General Social
Survey, with Y = political ideology (extremely liberal or liberal, slightly
liberal, moderate, slightly conservative, extremely conservative or conservative)
and predictor religious preference (Protestant, Catholic, Jewish, None).
With indicator variables for the first three religion categories, the ML fit has
ˆα1 =−1.03, ˆα2 =−0.13, ˆα3 = 1.57, ˆα4 = 2.41, ˆβ1 =−1.27, ˆβ2 =−1.22,
ˆβ3 =−0.44.
a. Why are there four {ˆαj }?Whyis ˆα1 < ˆα2 < ˆα3 < ˆα4?
b. Which group is estimated to be the (i) most liberal, (ii) most conservative?
Why?
c. Estimate the probability of the most liberal response for the Protestant and
None groups.
d. Use an estimated odds ratio to compare political ideology for the (i) Protestant
and None groups, (ii) Protestant and Catholic groups.
6.10 Refer to the interpretations in Section 6.2.6 for the mental health data. Summarize
the SES effect by finding P(Y ≤ 2) for high SES and for low SES, at
the mean life events of 4.3.
6.11 Refer to Table 6.12. Treating job satisfaction as the response, analyze the data
using a cumulative logit model.
a. Describe the effect of income, using scores {3, 10, 20, 35}.
b. Compare the estimated income effect to the estimate obtained after combining
categories “Very dissatisfied” and “A little satisfied.” What property
of the model does this reflect?
c. Can you drop gender from the model in (a)?
6.12 Table 6.18 shows results from the 2000 General Social Survey relating happiness
and religious attendance (1 = at most several times a year, 2 = once a
month to several times a year, 3 = every week to several times a week).
a. Fit a multinomial model. Conduct descriptive and inferential analyses about
the association.
b. Analyze the model goodness of fit.
Table 6.18. GSS Data for Exercise 6.12 on Happiness
Happiness
Religion Not Too Happy Pretty Happy Very Happy
1 189 908 382
2 53 311 180
3 46 335 294