Refer to the cumulative logit model for Table 7.8.

a. Compare the estimated income effect β̂₁ = €“0.510 to the estimate after collapsing the response to three categories by combining categories (i) very satisfied and moderately satisfied, and (ii) very dissatisfied and a little satisfied. What property of the model does this reflect?

b. Consider β̂₁/SE using the full scale to β̂₁/SE for the collapsing in part (a(i)). Usually, a disadvantage of collapsing multinomial responses is that the significance of effects diminishes.

Table 7.8:

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Job Satisfaction and Income, Controlling for Gender Job Satisfaction A Little Moderately Income Very Dissatisfied Very Satisfied Gender (dollars) Satisfied Satisfied < 5000 5000-15,000 15,000-25,000 > 25,000 < 5000 Female 11 2 17 3 Male 5000-15,000 15,000-25,000 > 25,000 3