Ordinal regression models: Problems, solutions, and problems with the solutions

Ordered logit/probit models are among the most popular ordinal regression techniques. However, these models often have serious problems. The proportional odds/parallel lines assumptions made by these methods are often violated. Further, because of the way these models are identified, they have many of the same limitations as are encountered when analyzing standardized coefficients in OLS regression, e.g., interaction terms and crosspopulation comparisons of effects can be highly misleading. This paper shows how generalized ordered logit/probit models (estimated via gologit2) and heterogeneous choice/location scale models (estimated via oglm) can often address these concerns in ways that are more parsimonious and easier to interpret than is the case with other suggested alternatives. At the same time, the paper cautions that these methods sometimes raise their own concerns that researchers need to be aware of and know how to deal with. First, misspecified models can create worse problems than the ones these methods were designed to solve. Second, estimates are sometimes implausible, suggesting that the data are being spread too thin and/or yet another method is needed. Third, multiple and very different interpretations of the same results are often possible and plausible. I will present guidelines for identifying and dealing with each of these problems.