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ERP averaging is an extraordinarily successful method, but can only be applied to a limited range of experimental designs. We introduce the regression-based rERP framework, which extends ERP averaging to handle arbitrary combinations of categorical and continuous covariates, partial confounding, nonlinear effects, and overlapping responses to distinct events, all within a single unified system. rERPs enable a richer variety of paradigms (including high-N naturalistic designs) while preserving the advantages of traditional ERPs. This article provides an accessible introduction to what rERPs are, why they are useful, how they are computed, and when we should expect them to be effective, particularly in cases of partial confounding. A companion article discusses how nonlinear effects and overlap correction can be handled within this framework, as well as practical considerations around baselining, filtering, statistical testing, and artifact rejection. Free software implementing these techniques is available.
Smith et al. (Thu,) studied this question.