Advances in the analysis of event-related potential data with factor analytic methods

Researchers are often interested in comparing brain activity between experimental contexts. Event-related potentials (ERPs) are a common electrophysiological measure of brain activity that is time-locked to an event (e.g., a stimulus presented to the participant). A variety of decomposition methods has been used for ERP data among them temporal exploratory factor analysis (EFA). Essentially, temporal EFA decomposes the ERP waveform into a set of latent factors where the factor loadings reflect the time courses of the latent factors, and the amplitudes are represented by the factor scores. An important methodological concern is to ensure the estimates of the condition effects are unbiased and the term variance misallocation has been introduced in reference to the case of biased estimates. The aim of the present thesis was to explore how exploratory factor analytic methods can be made less prone to variance misallocation. These efforts resulted in a series of three publications in which variance misallocation in EFA was described as a consequence of the properties of ERP data, ESEM was proposed as an extension of EFA that acknowledges the structure of ERP data sets, and regularized estimation was suggested as an alternative to simple structure rotation with desirable properties. The presence of multiple sources of (co-)variance, the factor scoring step, and high temporal overlap of the factors were identified as major causes of variance misallocation in EFA for ERP data. It was shown that ESEM is capable of separating the (co-)variance sources and that it avoids biases due to factor scoring. Further, regularized estimation was shown to be a suitable alternative for factor rotation that is able to recover factor loading patterns in which only a subset of the variables follow a simple structure. Based on these results, regSEMs and ESEMs with ERP-specific rotation have been proposed as promising extensions of the EFA approach that might be less prone to variance misallocation. Future research should provide a direct comparison of regSEM and ESEM, and conduct simulation studies with more physiologically motivated data generation algorithms