ABSTRACT
Partial models are ordered regression models that relax the parallel regression assumption for one subset of variables. Relaxing the parallel assumption allows the coefficients in this group to vary across the cutpoint equations. In other words, some variables will have coefficients that change depending on the level of the dependent variable. The parallel regression assumption ensures that the model is “ordinal” in the strictest sense (see McCullagh 1980, pp. 115-116). Therefore, partial models are only strictly ordinal with respect to the set of independent variables with the parallel assumption. Ordinal patterns may emerge for the nonparallel subset, but there is no guarantee that they will. As a result, partial models are often a mix of ordinal and more complex, nonordinal relationships. Models that allow for more complex relationships may be particularly useful in the social and behavioral sciences given that many of the response variables are “assessed” ordinal variables with observed responses that are the result of the judgments of assessors (e.g., survey respondents) often using several different criteria (Anderson 1984, p. 2). For this type of ordinal variable, it is not necessarily clear whether the ordering of outcome categories is important for the relationships with the independent variables in the model (Anderson 1984, p. 1; Long 1997, p. 115). Partial models are flexible enough to allow some variables in the model to have effects that do not maintain a strict stochastic ordering.
