Capturing heterogeneity in levels, variability, and couplings across persons and time with a hierarchical time-varying coefficient formulation of the multivariate normal

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 levels and associations among variables in intensive longitudinal data. However, conventional TVCM remains limited to investigating directional effects across individuals. By introducing a TVCM formulation of the multivariate normal distribution, the present study extends TVCM to explore temporal dynamics in undirected associations (couplings) and variability, thereby broadening its utility for psychological research. We discuss three versions of this approach: an aggregate-level model and two hierarchical versions capturing interindividual differences in temporal dynamics, either via person-specific intercepts accounting for onset differences or through fully person-specific coefficient functions smoothed via partial pooling. To illustrate the proposed developments, we apply them to six weeks of intensive longitudinal data from 16 anxiety patients undergoing therapy, and examine unfolding changes in the level and volatility of nervousness and threat monitoring, the temporal dynamics of their coupling, as well as between-person heterogeneity in each of these. We further show how inspecting first-order derivatives of the coefficient functions supports identifying periods of stability and change. Finally, we discuss extensions incorporating person-level characteristics to explain heterogeneity in temporal dynamics and predict outcomes.