The negative binomial regression model

Another useful approach to discrete regression is the log-linear negative binomial regression model, which uses the negative binomial probability distribution. At a high level, negative binomial regression is useful with over-dispersed count data where the conditional mean of the count is smaller than the conditional variance of the count. Model over-dispersion is where the variance of the target variable is greater than the mean assumed by the model. In a regression model, the mean is the regression line. We make the determination of using the negative binomial model based on target variable counts analysis (mean versus variance) and supply a measure of model over-dispersion to the negative binomial model to adjust for the over-dispersion, which we will discuss here.

It is important to note that the negative binomial model is not for modeling simply discrete data, but specifically count data associated with a fixed number of random trials...