Chapter 10In Chapter 9 we discussed the multinomial logit model as well as the conditional logit model, and in this chapter we discussed the ordinal logit model. These are all models of discrete dependent variables, but each has its special features. In MLM the dependent variable is nominal, but the nominal outcome is determined by characteristics that are specific to the individual. In CLM the nominal outcome depends on the characteristics of the choices rather than on the characteristics of the individual. In OLM we deal with discrete variables that can be ordered or ranked.
We discussed the limitations of MLM and CLM in the previous chapters. The assumption of proportional odds in OLM is often violated in many an application. But if this assumption is valid, and if the data are truly ordinal, OLM is preferred to MLM because we estimate a single regression for each ordered category; the only difference is that the intercepts differ between categories. Therefore OLM is more economical than MLM in terms of the number of parameters estimated.
Even then, we need to test explicitly the assumption of proportionality in any concrete application by applying tests, such as Omodel or Brant.