Logistic Regression Models for Categorical Outcome Variables

Analysis of crime and criminal justice data often requires the researcher to deal with a categorical outcome variable that may be ordered or unordered. Our focus in this chapter is a discussion on the type of logistic regression model best suited to an analysis of categorical outcome variables. We review binary logistic regression models for situations where the dependent variable has only two categories, and then build on this material to illustrate the application and interpretation of multinomial and two different ordinal logistic regression models (proportional odds and partial proportional odds) for situations where the dependent variable has at least three unordered or ordered categories, respectively. Our general approach in the discussion of each model will be to highlight some of the key technical details of the model, and then to emphasize the application and the interpretation of the model. We conclude by noting some alternative logistic regression models that extend the models discussed in this chapter and which may have interesting applications in the study of crime and criminal justice.