Logistic Regression Using SAS®: Theory and Application

5.6. General Form of the Model

To this point, we’ve been dealing with just three categories for the dependent variable. Now let’s generalize the model to J categories, with the running index j= 1, ..., J. Let p_ij be the probability that individual i falls into category j. The model is then

Equation 5.1

where x_i is a column vector of variables describing individual i and β_j is a row vector of coefficients for category j. Note that each category is compared with the highest category J. These equations can be solved to yield

Equation 5.2