Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate, Multi-Subject Time-Series Data

In the study of human dynamics, the behavior under study is often operationalized by tallying the frequencies and intensities of a collection of lower-order processes. For instance, the higher-order construct of negative affect may be indicated by the occurrence of crying, frowning, and other verbal and nonverbal expressions of distress, fear, anger, and other negative feelings. However, because of idiosyncratic differences in how negative affect is expressed, some of the lower-order processes may be characterized by sparse occurrences in some individuals. To aid the recovery of the true dynamics of a system in cases where there may be an inflation of such “zero responses,” we propose adding a regime (unobserved phase) of “non-occurrence” to a bivariate Ornstein–Uhlenbeck (OU) model to account for the high instances of non-occurrence in some individuals while simultaneously allowing for multivariate dynamic representation of the processes of interest under nonzero responses. The transition between the occurrence (i.e., active) and non-occurrence (i.e., inactive) regimes is represented using a novel latent Markovian transition model with dependencies on latent variables and person-specific covariates to account for inter-individual heterogeneity of the processes. Bayesian estimation and inference are based on Markov chain Monte Carlo algorithms implemented using the JAGS software. We demonstrate the utility of the proposed zero-inflated regime-switching OU model to a study of young children’s self-regulation at 36 and 48 months.