Differential Effects: Are the Effects Studied by Psychologists Really Linear and Homogeneous?

Abstract

Linear regression and its variants like analysis of variance are arguably the most widely used statistical techniques in psychology. By using linear regression it is merely assumed rather than empirically tested that the effects of the predictor variables are linear and homogeneous across the distribution of the dependent variable. This is problematic because it biases a scientist’s reasoning and hinders possible practical and theoretical insights. Thus an important question to ask is: Are the effects studied by psychologists really linear and homogeneous? Generalized additive models (GAMs) and quantile regression can be used to pursue this question. Benefits of complementing linear regression with these approaches include the ability to tailor actions on the specific individual in practice and the opportunity to gain more advanced scientific knowledge, for example about non-linear effects. The use of GAMs and quantile regression is furthermore empirically demonstrated in an analysis of risk-seeking and criminal peer networks as predictors of violent crime in a representative sample of German youth (N = 44.610). Practical and theoretical consequences of the results are discussed. Psychological science could immensely benefit from studying non-linear and heterogeneous effects.