ABSTRACT
Nonparallel models are ordered regression models that relax the parallel regression assumption for every independent variable in the model. The slopes for every variable are allowed to freely vary across the binary cutpoint equations. Nonparallel models are not ordinal models in the strictest sense because they do not impose constraints to maintain a strict stochastic ordering. However, ordinal patterns may emerge without the use of the parallel constraints. The nonparallel cumulative and continuation ratio models are ordinal in a weaker sense because reordering the outcome categories (e.g., 1,2,3,4 → 3,1,4,2) affects the coefficients and significance tests. In other words, the models are not “permutation invariant” (McCullagh 1980, p. 116). The nonparallel adjacent category model, however, does display permutation invariance. It is equivalent to multinomial logit, which is a model designed for nominal outcomes. Therefore, it is not an ordinal method even in the weaker sense.
