Unveiling Schizophrenia: a study with generalized functional linear mixed model via the investigation of functional random effects

Previous studies have identified attenuated pre-speech activity and speech sound suppression in individuals with Schizophrenia, with similar patterns observed in basic tasks entailing button-pressing to perceive a tone. However, it remains unclear whether these patterns are uniform across individuals or vary from person to person. Motivated by electroencephalographic (EEG) data from a Schizophrenia study, we develop a generalized functional linear mixed model (GFLMM) for repeated measurements by incorporating subject-specific functional random effects associated with multiple functional predictors. To assess the significance of these functional effects, we employ two different multivariate functional principal component analysis methods, which transform the GFLMM into a conventional generalized linear mixed model, thereby facilitating its implementation with standard software. Furthermore, we introduce a cutting-edge testing approach utilizing working responses to detect both subject-specific and predictor-specific functional random effects. Monte Carlo simulation studies demonstrate the effectiveness of our proposed testing method. Application of the proposed methods to the Schizophrenia data reveals significant subject-specific effects of human brain activity in the frontal zone (Fz) and the central zone (Cz), providing valuable insights into the potential variations among individuals, from healthy controls to those diagnosed with Schizophrenia.