ABSTRACT
Parallel ordered regression models share a common assumption, which is that the effects of independent variables do not vary across cutpoint equations. We refer to this as the parallel regression assumption, and for logit models it is also known as the “proportional odds” assumption (McCullagh 1980). We provide an illustration of the parallel regression assumption for cumulative models in Figure 5.1. In the graph on the left, the cumulative probability curves are parallel, whereas in the graph on the right they are not. The parallel regression assumption is very useful because it produces a relatively parsimonious model and restricts the coefficients to ensure ordinality in the relationships. However, the assumption is often violated in practice.
