Statistical Applications for Environmental Analysis and Risk Assessment

Chapter 14Robust Regression

14.1 Introduction and Overview

The term “robust” can be defined or interpreted in a broader sense as low sensitivity or resistance to deviations from the assumptions imposed on data by a model. In other words, a robust or resistant model is one for which moderate violations of model assumptions will not substantially invalidate the results obtained from the model. In a narrower context, robustness is defined as resistance or low sensitivity to unusual or extreme observations (i.e., outliers), but for practical purposes, the former definition is assumed to encompass the latter. As described in Chapter 12, ordinary least squares (OLS) regression imposes many assumptions on the data, including the assumptions that the relationship between the predictor (i.e., X) and the response (i.e., Y) variables is linear, and that the variability or random errors of the Y variable are homoscedastic (i.e., have constant variance), independent, and normally distributed. These assumptions are rarely fully satisfied by real-world environmental or other data types.

Various potential transformations of the data such as the logarithmic and the reciprocal transformations intended to “force” compliance with the assumptions of conventional regression are described in Chapter 13. These transformations are not always fully effective, that is, achieve compliance with all of the regression assumptions such that conventional OLS regression would be valid. For instance, a transformation ...