A Growth of Hierarchical Autoregression Model for Capturing Individual Differences in Changes of Dynamic Characteristics of Psychological Processes

Several methodological innovations have been advanced in the past decades that combine growth curve models (GCMs) with models of autoregressive (AR) processes. However, most of these approaches do not effectively capitalize on known (e.g., study design-related) information to structure the growth curves into meaningful between- and within-phase changes, while simultaneously accommodating interindividual differences in these intraindividual changes. We propose a Bayesian growth of hierarchical autoregression (GoHiAR) model, which combines AR and GCM to evaluate phase-to-phase changes in multifaceted dynamic characteristics (e.g., baseline, variability, and inertia) as well as individual differences in these changes. This approach allows for drawing conclusions in a way that the proposed data generating mechanisms are in line with the theoretical insights about psychological change and dynamics. Our Bayesian implementation of the GoHiAR model allows for all parameters to be estimated simultaneously. First, we evaluated GoHiAR's overall estimation accuracy and sampling efficiency, effects of model misspecifications, and sensitivity to effect sizes via a simulation study. Results showed reasonable performance. Then, we applied GoHiAR to an ecological momentary assessment (EMA) study that comprised data from pre-, during, and following an intervention, and investigated changes in the dynamic characteristics of individuals' psychological well-being (specifically in meaning of life) within and across phases.