6 - Regression Methods

Summary

Introduction

Regression is probably one of the most powerful tools in the data analysis package of the biologist, particularly when considered within the very broad framework of general linear models. Nevertheless, there are a number of problems with the approach that can be resolved by the use of computer-intensive methods. The most difficult problem, and that which is the focus of the present chapter, is the problem of determining which variables to include in a regression and how to include them. For example, should a predictor variable, X, be entered simply as X or would a better fit be obtained using a polynomial form such as X², or even a more general function, which we might not have any a priori reason to formulate? With a single predictor the problem is not very acute, because one can plot the data and visually inspect the pattern of covariation with the response variable, Y. But suppose the pattern is clearly non-linear and none of the usual transformation methods (e.g., log, square-root, arcsine, etc.) linearizes the data: the computer intensive methods outlined in this chapter can be used to both describe the pattern of covariation and to test its fit relative to other models. With multiple predictors the situation can be very problematic if the predictors are complex functions or there are non-linear interactions between predictors.