Stepwise Regressor Selection for Interdependence Analysis and Multivariate Multiple Regression

The SWEEP operator in SAS/IML software is used to solve two classes of multivariate problems, namely stepwise predictor selection in (1) interdependence analysis as defined by Beale, Kendall, and Mann (1967), and (2) multivariate, multiple regression. Though both problems have lain quiescent, they are resurrected here because of their relevance to analysis of massive data sets. In both cases, each forward selection step is followed by a “look back”, where the latter involves switching 1-tuples, 2-tuples, or higher k-tuples of previously selected predictors. In this sense, both algorithms resemble SELECTION=MAXR in procedure REG, but with the capability of simultaneously switching more than single predictor variables in and out of the current model, and with the added important provision of a multivariate response. Examples of interdependence analysis are drawn from electrical engineering, yielding subsets of fundamental parameters which are used to characterize general purpose IC chips. Selection in multivariate, multiple regression is illustrated by two examples focusing on sources of variation for dioxin and furan yields in municipal waste incineration. The paper will be of interest to those who are proficient in regression-based model building techniques