Modeling nonlinear relationships in ERP data using mixed-effects regression with R examples.

In the analysis of psychological and psychophysiological data, the relationship between two variables is often assumed to be a straight line. This may be due to the prevalence of the general linear model in data analysis in these fields, which makes this assumption implicitly. However, there are many problems for which this assumption does not hold. In this paper, we show that, in the analysis of event-related potential (ERP) data, the assumption of linearity comes at a cost and may significantly affect the inferences drawn from the data. We demonstrate why the assumption of linearity should be relaxed and how to model nonlinear relationships between ERP amplitudes and predictor variables within the familiar framework of generalized linear models, using regression splines and mixed-effects modeling.