ABSTRACT
This chapter presents regression models for response variables (Y) that are modeled using discrete conditional distributions. Binary, nominal, and ordinal Y have conditional distributions that are allowed to “morph” continuously as a function of the X variable(s). These distributions, as in previous chapters, provide maximum likelihood estimates for the model parameters. The necessity of using maximum likelihood is shown to be especially clear with these models, as there are no other obvious choices. First, logistic regression is presented for the analysis of binary Y data, then multinomial logistic regression for the analysis of nominal Y data, then ordinal logistic (and probit) regression for the analysis of ordinal Y data. A final caution is given as regards comparing continuous and discrete models for the same data when using maximum likelihood.
