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-level variability. Although multilevel models such as heterogeneous variance models (HVMs) and Mixed-Effects Location-Scale models have been used to capture these dynamics, they typically rely on linear assumptions and restrict temporal changes in variability to a single level. Recent calls for nonlinear approaches in psychology highlight the need for more flexible models that can better account for complex, dynamic processes. This article introduces the use of Gaussian processes (GPs) within the framework of HVMs to address these limitations. By incorporating GPs in HVMs, 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 provides an improved model fit compared with 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.