Choice of Order in Regression Strategy

Abstract

Regression analysis is viewed as a search through model space using data analytic functions. The desired models should satisfy several requirements, unimportant variables should be excluded, outliers identified, etc. The methods of regression data analysis such as variable selection, transformation and outlier detection, that address these concerns are characterized as functions acting on regression models and returning regression models. A model that is unchanged by the application of any of these methods is considered acceptable. A method for the generation of all acceptable models supported by all possible orderings of the choice of regression data analysis methods is described with a view to determining if two statisticians may reasonably hold differing views on the same data. The consideration of all possible orders of analysis generates a directed graph in which the vertices are regression models and the arcs are data-analytic methods. The structure of the graph is of statistical interest. The ideas are demonstrated using a LISP-based analysis package. The methods described are not intended for the entirely automatic analysis of data, rather to assist the statistician in examining regression data at a strategic level.