Tree-structured logistic models for over-dispersed binomial data with application to modeling developmental effects

This article proposes tree-structured logistic regression modeling for over-dispersed binomial data. Recursive partitioning is performed using a combination of statistical tests and residual analysis. The splitting criterion in cross-validation is based on the deviance function. A nested grid algorithm to estimate the bootstrap parameters is developed. The regression tree procedure provides a new approach for exploring in detail the relationship between the binomial response and explanatory variables. The proposed procedure is used to model the relationship between the incidence of malformation and dose and fetal weight using data from a developmental experiment conducted at the National Center for Toxicological Research. A conditional Gaussian chain model is used to account for the effect of fetal weight by dose.