In this lesson, we extended the binary logistic regression model to account for response variables with more than two levels. These may be nominal or ordinal, and the proportional odds model allows us to utilize that ordinal nature to reduce the number of parameters involved and to simplify the model. Each reduces to the binary logistic regression model we had seen earlier in the event of two response categories.
One challenge that comes with the increased generality of multinomial responses is the way that odds can be defined and interpreted. In the case of nominal categories, we choose one category, in particular, to serve as the baseline, and other categories have odds defined relative to that. In the case of ordinal data, we can either define the odds of an event relative to an adjacent event or as cumulative odds, which effectively combines all events equal to or less than one, relative to all events greater. Keeping track of these events is no easy feat!
In the next lesson, we move away from categorical response variables that fall necessarily within a certain range and consider counting the number of events that occur, as a quantitative, whole number. For this, we'll need the Poisson distribution. Fortunately, much of the basic principles that we've dealt with in binary and multinomial logistic regression will carry over.