rERP: Estimating ERPs using statistical regression

The traditional approach to estimating event-related potential (ERP) signals is to use averaging. This works well, but places severe limitations on experimental design. The theory underlying ERP analyses requires that stimuli vary only in a small number of categorical variables, with all other properties balanced, and events well-separated in time. These restrictions rule out many potentially interesting paradigms, and are nearly impossible to satisfy properly when studying a domain like language, where our stimuli necessarily vary in many correlated dimensions. Here, I'll describe how we can recast the averaging method as a simple form of regression. For traditional experimental designs, this produces identical results -- but it opens the door to applying a large toolbox of "off the shelf" tricks from the regression literature. These allow us to compute ERPs for multifactorial experiments with partial confounding (controlling for confounding variables post hoc), non-categorical stimulus properties, and events that are closely spaced in time. It may also allow the use of high-powered statistics to detect effects within individual participants. None of these methods are new, exactly; most have even been proposed individually in the neurophysiological literature in some form or another, or are close cousins of techniques used for fMRI analysis. But the rERP approach provides a single unified framework for handling both simple and complex EEG analysis problems in a straightforward way, while preserving the results and much of the toolkit of traditional ERP techniques.