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

Published online by Cambridge University Press:  01 January 2025

Zhao-Hua Lu Open the ORCID record for Zhao-Hua Lu [Opens in a new window] ,
Sy-Miin Chow ,
Nilam Ram  and
Pamela M. Cole
Zhao-Hua Lu*
Affiliation:
St. Jude Children’s Research Hospital
Sy-Miin Chow
Affiliation:
The Pennsylvania State University
Nilam Ram
Affiliation:
The Pennsylvania State University
Pamela M. Cole
Affiliation:
The Pennsylvania State University
*
Correspondence should be made to Zhao-Hua Lu, St. Jude Children’s Research Hospital, MS 768, Room R6006, 262 Danny Thomas Place, Memphis, TN 38105-3678, USA. Email: zhaohua.lu@stjude.org
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Abstract

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.

Keywords

stochastic differential equationsOrnstein–UhlenbeckMarkov switching transitionregime switchingBayesian methodsMarkov chain Monte Carlo algorithms
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 2 , June 2019 , pp. 611 - 645
Copyright
Copyright © 2019 The Psychometric Society

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Footnotes

Zhao-Hua Lu and Sy-Miin Chow have contributed equally to this work.

Funding for this study was provided by NSF Grant SES-1357666, NIH Grants R01MH61388, R01HD07699, R01GM105004, U24EB026436, Penn State Quantitative Social Sciences Initiative and UL TR000127 from the National Center for Advancing Translational Sciences. The article is partly done when Zhao-Hua Lu was in the Pennsylvania State University.

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