Use Nominal Logistic Regression when your response is nominal or when the response is ordinal, but you do not wish to assume the effect of the predictor is constant across all response categories, as required by ordinal logistic regression.

In nominal logistic regression, the fitted model includes a logit functions for the number of response categories minus one (for the reference event). For example, if the response has 4 levels, Minitab calculates 3 logit equations. Each equation has a unique constant and a unique parameter for each predictor. Nominal logistic regression assumes that the effect of the predictor is different for each response value. Each logit function evaluates how the covariates affect the likelihood of observing the reference level of the response versus observing another level of the response. The slope for each covariate describes how the likelihood is affected.

Betting on horse races is based on the pari-mutuel system, in which bettors determine the odds for horses through their wagers. The more money bet on a particular horse, the lower the odds are for that horse. In theory, the lower the odds, the more likely it is that the horse will win the race.

You follow a horse called DegreesofFreedom and have tracked her race odds and order of finish for her 199 career races. You can use ordinal logistic regression to predict the probability that DegreesofFreedom finishes 1st , 2nd ... , 8th using her odds at race time. Your nominal logistic regression model includes:

·    Finish - the response variable. It is the order in which your horse finished in the race. The reference event is 1st place.

·    RaceOdds - the predictor (covariate). It is the horse's odds for the race.

Although the response is ordinal, the investigators are not certain that the effect of the predictor RaceOdds is constant across all response categories, so they use nominal logistic regression.

Data: HorseRacing.MTW (available in the Sample Data folder).