Functional ANOVA with random functional effects: an application to event-related potentials modelling for electroencephalograms analysis

The differential effects of basic visual or auditory stimuli on electroencephalograms (EEG), named event related potentials (ERPs), are often used to evaluate the impact of treatments on brain performances. In the present paper, we propose a P-splines based model that can be used to evaluate treatment effect on the timing and the amplitude of some peaks of the ERPs curves. Functional ANOVA is an adaptation of linear model or analysis of variance to analyse functional observations. The changes in the functional of interest effects are generally described using smoothing splines. Eilers and Marx proposed to work with P-splines, a combination of B-splines and difference penalties on coefficients. We define a P-splines model for ERPs curves combined with random effects. In particular, we show that it is a useful alternative to classical strategies requiring the visual and usually imprecise localization of specific ERP peaks from curves with a low signal-to-noise ratio.