The procedure uses the negative binomial probability distribution in making its parameter estimates. Stage 2 uses the estimates from stage 1 to define a transformation that corrects for problems in the residuals. In many ways similar to logistic regression except that the dependent variable can take on more than two values. Curvilinear regression makes use of various transformations of variables to achieve its fit. See polynomial regression.
Quantile regression is a generalization of median regression in which any quantile can be selected.