Research using the event-related potential (ERP) method to investigate cognitive processes has usually focused on the analysis of either individual peaks or the area under the curve as components of interest. These approaches, however, cannot analyse the substantial variation in size and shape across individual waveforms.
The aim of my thesis is thus to introduce the gamma model analysis (GMA). The GMA addresses these specific restrictions of the usually applied methods and enables the analysis of additional time-dependent and shape-related information on ERP components by fitting mathematically computed gamma probability density function (PDF) waveforms to an ERP.
The advantage of the GMA is demonstrated in a simulation study and a digit flanker task, as well as a force production task. The data of the digit flanker task is also used to examine a potential limitation of the GMA, namely the inability of the gamma PDF to execute a sign change. Finally, the gamma PDF was compared with three other PDFs concerning their goodness of fit.
The different gamma model parameters were sensitive to various experimental manipulations across the empirical studies. Moreover, the GMA revealed several additional interrelated but non-redundant parameters compared to the classical methods, which were predictive of different aspects of behaviour, allowing for a more nuanced analysis of the cognitive processes. The GMA provides an elegant method for extracting easily interpretable indices for the rise and decline of the components that complement the classical parameters. This approach, therefore, provides a novel toolset to better understand the exact relationship between ERP components, behaviour, and cognition
