With tree-structured regression modeling, the response data are stratified according to particular covariate values, and separate regression models are fit to each stratum. Stratification is performed recursively, using a combination of statistical tests and residual analysis. At the National Ccenter for Toxicological Research, I worked on over-dispersed binomial regression tree models with James Chen. In teratology studies, a dose-response model is often fit to bioassay data to provide a relationship between the probability of a developmental defect and the level of exposure. The regression tree approach can be applied to dose response modeling of a developmental effect.
Softwares are available for the tree-structured regression models.