The proportional odds with partial proportionality constraints model for ordinal response variables

The proportional odds assumption in ordered logit models is a restrictive assumption that is often violated in practice. A violation of the assumption indicates that the effects of one or more independent variables significantly vary across cutpoint equations in the model. In order to relax this assumption for the cumulative odds model, researchers may use either a "partial" model that relaxes the assumption for a subset of variables or the "generalized" model that relaxes the assumption for every independent variable. In this paper, we propose a relatively new and under-utilized third alternative, the proportional odds with partial proportionality constraints (POPPC) model, which allows the effects of a subset of variables to vary across cutpoint equations by a common factor. We improve upon an earlier formulation of the POPPC model by offering an additional conceptual justification for the model and an estimation method that does not require the use of person-threshold data. We illustrate the POPPC model with two examples from the 2008 General Social Survey.