Logistic Regression Using SAS®: Theory and Application

5.3. A Model for Three Categories

First, some notation. Define

p_i1 = the probability that WALLET=1 for person i,

p_i2 = the probability that WALLET=2 for person i,

p_i3 = the probability that WALLET=3 for person i.

Let x_i be a column vector of explanatory variables for person i:

x_i = [1 x_i1 x_i2 x_i3 x_i4]’

If this is unfamiliar, you can just think of x_i as a single explanatory variable. In order to generalize the logit model to this three-category case, it’s tempting to consider writing three binary logit models, one for each outcome:

where the β’s are row vectors of coefficients. This turns out to be an unworkable approach, however. Because ...