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Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime Switching

Published online by Cambridge University Press:  01 January 2025

Sy-Miin Chow Open the ORCID record for Sy-Miin Chow [Opens in a new window] ,
Lu Ou ,
Arridhana Ciptadi ,
Emily B. Prince ,
Dongjun You ,
Michael D. Hunter ,
James M. Rehg ,
Agata Rozga  and
Daniel S. Messinger
Sy-Miin Chow*
Affiliation:
Pennsylvania State University
Lu Ou
Affiliation:
Pennsylvania State University
Arridhana Ciptadi
Affiliation:
Georgia Institute of Technology
Emily B. Prince
Affiliation:
University of Miami
Dongjun You
Affiliation:
Pennsylvania State University
Michael D. Hunter
Affiliation:
University of Oklahoma Health Sciences Center
James M. Rehg
Affiliation:
Georgia Institute of Technology
Agata Rozga
Affiliation:
Georgia Institute of Technology
Daniel S. Messinger
Affiliation:
University of Miami
*
Correspondence should be made to Sy-Miin Chow, Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA16802, USA. Email: [email protected]
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Abstract

A growing number of social scientists have turned to differential equations as a tool for capturing the dynamic interdependence among a system of variables. Current tools for fitting differential equation models do not provide a straightforward mechanism for diagnosing evidence for qualitative shifts in dynamics, nor do they provide ways of identifying the timing and possible determinants of such shifts. In this paper, we discuss regime-switching differential equation models, a novel modeling framework for representing abrupt changes in a system of differential equation models. Estimation was performed by combining the Kim filter (Kim and Nelson State-space models with regime switching: classical and Gibbs-sampling approaches with applications, MIT Press, Cambridge, 1999) and a numerical differential equation solver that can handle both ordinary and stochastic differential equations. The proposed approach was motivated by the need to represent discrete shifts in the movement dynamics of n=29\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n= 29$$\end{document} mother–infant dyads during the Strange Situation Procedure (SSP), a behavioral assessment where the infant is separated from and reunited with the mother twice. We illustrate the utility of a novel regime-switching differential equation model in representing children’s tendency to exhibit shifts between the goal of staying close to their mothers and intermittent interest in moving away from their mothers to explore the room during the SSP. Results from empirical model fitting were supplemented with a Monte Carlo simulation study to evaluate the use of information criterion measures to diagnose sudden shifts in dynamics.

Keywords

differential equationregime switchinghidden Markovdynamicdyadicstrange situation
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 2 , June 2018 , pp. 476 - 510
Copyright
Copyright © 2018 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-9605-1) contains supplementary material, which is available to authorized users.

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