Assumptions of the Normal Error Regression Model

This chapter describes the main assumptions that are made in the derivation of regression-based normative data, i.e., equality of the error variances, normality of the (standardized) errors, independence of errors, and the absence of outliers. Graphical tools and formal testing procedures to examine these assumptions are described. Further, the impact of model assumption violations in the specific context where it is of interest to derive regression-based normative data is discussed, and remedial strategies to deal with potential model violations are proposed (e.g., the use of sandwich-estimators of the standard errors to account for unequal error variances). A simulation study is done to examine the impact of such model violations on the obtained norms. It is shown that the use of the proposed remedial strategies to deal with the model violations leads to essentially unbiased norms. The same case studies as those that were analyzed in Chap. 3 are used to illustrate how the model assumptions can be tested in practice using the NormData package in the R software. It is also shown how violations of the model assumptions can be accounted for in the construction of the norms.