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

The di erential e ects 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 e ect 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 e ects are generally described using smoothing splines. Eilers and Marx proposed to work
with P-splines, a combination of B-splines and di erence penalties on coe cients. We de ne a Psplines
model for ERPs curves combined with random e ects. In particular, we show that it is a useful
alternative to classical strategies requiring the visual and usually imprecise localization of speci c ERP
peaks from curves with a low signal-to-noise ratio.