Statistical Applications for Environmental Analysis and Risk Assessment

Chapter 13Data Transformation versus Generalized Linear Model

13.1 Introduction and Overview

The basic components of simple linear regression (SLR) were described in Chapter 12. In that chapter, data that reasonably satisfy the assumptions of linear regression without requiring any modifications were used to illustrate the principles and methods of conventional ordinary least squares (OLS) regression. This chapter extends the concepts of Chapter 12 to data that do not satisfy some or all of the regression assumptions, thereby requiring data modifications to render the data suitable for OLS regression, or use of other regression methods besides OLS. As described in Section 12.4, the assumptions of OLS regression include linearity of the X–Y relationship, homoscedasticity, independence and normality of the Y errors, absence of outliers, and absence of error or variability in the predictor variable, X. Although environmental data frequently violate these assumptions, use of conventional linear regression is nevertheless desirable because the methods are well developed, computer programs for its computation widely available, and interpretation of the regression results fairly straightforward.

As discussed in Section 13.2, data transformation is a commonly used approach for modifying data to satisfy the regression assumptions, typically the assumptions of linearity of the X–Y relationship, homoscedasticity (i.e., constancy of the Y error variance), normality of the errors, and the ...