Constrained and Unconstrained Partial Adjacent Category Logit Models for Ordinal Response Variables

Adjacent category logit models are ordered regression models that focus on comparisons of adjacent categories. These models are particularly useful for ordinal response variables with categories that are of substantive interest. In this article, we consider unconstrained and constrained versions of the partial adjacent category logit model, which is an extension of the traditional model that relaxes the proportional odds assumption for a subset of independent variables. In the unconstrained partial model, the variables without proportional odds have coefficients that freely vary across cutpoint equations, whereas in the constrained partial model two or more of these variables have coefficients that vary by common factors. We improve upon an earlier formulation of the constrained partial adjacent category model by introducing a new estimation method and conceptual justification for the model. Additionally, we discuss the connections between partial adjacent category models and other models within the adjacent approach, including stereotype logit and multinomial logit. We show that the constrained and unconstrained partial models differ only in terms of the number of dimensions required to describe the effects of variables with nonproportional odds. Finally, we illustrate the partial adjacent category logit models with empirical examples using data from the international social survey program and the general social survey.