Logistic Regression Using SAS®: Theory and Application

6.6. Adjacent Categories Model

Another general model for ordered categorical data is the adjacent categories model. As before, we let p_ij be the probability that individual i falls into category j of the dependent variable, and we assume that the categories are ordered in the sequence j=1, ..., J. Now take any pair of categories that are adjacent, such as j and j+1. We can write a logit model for the contrast between these two categories as a function of explanatory variables:

Equation 6.5

where β_jx_i = β_jix_il +...+ β_jkx_ik. There are J–1 of these paired contrasts. It turns out that this is just another way of writing the multinomial logit ...