8.7. For a sample of 40 subjects, Table 8.10 relates Y = mental impairment. (1 == None, 2 Mild, 3 Moderate, 4 Impaired) to socioeconomic status (SES 1, high; SES = 0, low) and a life events index, which is a com- posite measure of both the number and severity of important life events (such as loss of job, divorce, death in family) that the subject experienced within the past three years.

a. Fit a proportional odds model, and interpret effects.

b. Add an interaction term between the predictors. Interpret this model by describing the impact of life events on mental impairment separately at each level of SES. Check whether this model provides an improved fit.

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Subject Responses Table 8.10 Responses on (Mental impairment, SES, Life events) Subject Responses Subject Responses Subject Responses 1 (1, 1, 1) 11 (1,0,1) 21 (2,1,9) 31 (3,0,3) 2 (1, 1,9) 12 (1,0,2) 22 (2,0,3) 32 (4,1,8) (1,1,4) 13 (2,1,5) 23 (2,1,3) 33 (4,1,2) 4 (1,1,3) 14 (2,0,6) 24 (2,1,1) 34 (4,1,7) 5 (1,0,2) 15 (2,1,3) 25 (3,0,0) 35 (4,0,5) 6 (1,1,0) 16 (2,0,1) 26 (3,1,4) 36 (4,0,4) 7 (1,0,1) 17 (2,1,8) 27 (3,0,3) 37 (4,0,4) 8 (1,1,3) 18 (2,1,2) 28 (3,0,9) 38 (4,1,8) 9 (1,1,3) 19 (2,0,5) 29 (3,1,6) 39 (4,0,8) 10 (1,1,7) 20 (2,1,5) 30 (3,0,4) 40 (4,0.9)