Heterogeneous Variance Models with Gaussian Processes

Understanding variability is a key focus in many areas of psychological research, with growing interest in modeling individual and group variability. While multilevel models such as heterogeneous variance models and Mixed-Effect Location Scale (MELS) models have been used to capture these dynamics, they typically rely on linear assumptions and temporal change of the variability is restricted to one level. Recent calls for nonlinear approaches in psychology highlight the need for more flexible models that can better account for complex, dynamic processes. This paper introduces the use of Gaussian Processes (GPs) within the framework of heterogeneous variance models to address these limitations. By incorporating GPs, we allow for the modeling of nonlinear variability across multiple levels, including temporal dynamics at both the individual and group levels. We demonstrate the benefits of this approach in two empirical applications. Our findings show that using GPs provide an improved model fit compared to traditional linear methods and highlight the utility of GPs in variance modeling, offering new possibilities for studying dynamic and emergent processes in psychological and social science research.