Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate,...

Area of Science:

• Human Dynamics
• Developmental Psychology
• Behavioral Science

Background:

• Human behavior is often studied by measuring lower-order processes.
• Individual differences can lead to sparse occurrences of certain behaviors, complicating analysis.
• Existing models may not adequately account for high instances of non-occurrence.

Purpose of the Study:

• To propose a novel statistical model for analyzing human dynamics with sparse data.
• To address the challenge of "zero responses" in behavioral studies.
• To improve the recovery of true system dynamics in the presence of non-occurrence.

Main Methods:

• Developed a bivariate Ornstein-Uhlenbeck (OU) model with an added "non-occurrence" regime.
• Incorporated a latent Markovian transition model to handle regime switching.
• Accounted for inter-individual heterogeneity using latent variables and person-specific covariates.
• Employed Bayesian estimation via Markov chain Monte Carlo (MCMC) algorithms in JAGS.

Main Results:

• The proposed zero-inflated regime-switching OU model effectively accounts for high instances of non-occurrence.
• The model allows for multivariate dynamic representation of processes under both occurrence and non-occurrence.
• Demonstrated utility in analyzing young children's self-regulation at 36 and 48 months.

Conclusions:

• The novel model enhances the analysis of human dynamics, particularly in cases with significant "zero responses."
• This approach provides a more accurate representation of individual behavioral processes.
• Applicable to developmental studies and understanding self-regulation in children.