Normative Data Accounting for a Quantitative Independent Variable

This chapter focuses on the derivation of regression-based normative data that account for a quantitative independent variable (i.e., an independent variable that can have many possible outcome values, such as Age). The use of linear, quadratic, and cubic polynomial functions to model the mean structure is discussed, and the importance of having well-formulated models (i.e., models that include all lower-order parameters of the highest-order parameter) is stressed. It is further explained why it is useful to center quantitative independent variables and how continuous variance prediction functions can be used to account for heteroscedasticity (i.e., unequal error variances) in the derivation of the norms. The methodology is illustrated based on two case studies in which Age-corrected normative data are derived for the Letter Digit Substitution Test and the Total Recall Verbal Learning Test scores using the NormData package in the R software.