Investigating different aspects of heterogeneity in temporal dynamics with a hierarchical time-varying coefficient formulation of the multivariate normal distribution

Time-varying coefficient modeling (TVCM), which represents regression coefficients as smooth functions of continuous time, provides a flexible framework for uncovering complex patterns of change in the levels and associations among variables measured in intensive longitudinal data. However, conventional TVCM remains limited to investigating directional effects that are aggregated across individuals. The present study broadens the applicability of TVCM in two ways. First, we introduce a TVCM formulation of the multivariate normal distribution to explore temporal dynamics in both undirected associations (or couplings) and the variability of variables of interest. Second, we integrate TVCM with hierarchical modeling, thereby extending inference from average coefficient functions across persons to their individual-level counterparts. Specifically, we explore (a) the inclusion of person-specific intercepts in time-varying coefficient functions to investigate interindividual differences at the onset of the period of interest, and (b) modeling fully person-specific coefficient functions to capture heterogeneity across the entire period, with partial pooling stabilizing individual-level estimates. To illustrate the model extensions, we apply them to six weeks of intensive longitudinal data from 16 patients with anxiety disorders participating in an attention training intervention, examining interindividual differences in changes in both the level and volatility of nervousness and threat monitoring, as well as in the temporal dynamics of their coupling. Finally, we discuss model extensions that incorporate person-level characteristics to explain interindividual differences in temporal dynamics and use these differences to predict outcomes of interest.