Regression by Parts: Fitting Visually Interpretable Models with GUIDE

A regression model is best interpreted visually. Because we are limited to 2D displays, one way that we can fit a non-trivial model involving several predictor variables and still visually display it, is to partition the data and fit a simple model to each partition. We show how this can be achieved with a recursive partitioning algorithm called GUIDE. Further, we use examples to demonstrate how GUIDE can (i) explain ambiguities from multiple linear regression, (ii) reveal the effect of a categorical variable hidden from a sliced inverse regression model, (iii) identify outliers in data from a large and complex but poorly designed experiment, and (iv) fit an interpretable Poisson regression model to data containing categorical predictor variables.