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Using Threshold Autoregressive Models to Study Dyadic Interactions

Published online by Cambridge University Press:  01 January 2025

Ellen L. Hamaker ,
Zhiyong Zhang  and
Han L. J. van der Maas
Ellen L. Hamaker*
Affiliation:
Methodology and Statistics, Faculty of Social Sciences, Utrecht University
Zhiyong Zhang
Affiliation:
Quantitative Psychology, University of Notre Dame
Han L. J. van der Maas
Affiliation:
Psychological Methodology, University of Amsterdam
*
Requests for reprints should be sent to Ellen L. Hamaker, Methods and Statistics, Faculty of Social Sciences, Utrecht University, P.O. Box 80140, 3508 TC, Utrecht, The Netherlands. E-mail: [email protected]
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Abstract

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Considering a dyad as a dynamic system whose current state depends on its past state has allowed researchers to investigate whether and how partners influence each other. Some researchers have also focused on how differences between dyads in their interaction patterns are related to other differences between them. A promising approach in this area is the model that was proposed by Gottman and Murray, which is based on nonlinear coupled difference equations. In this paper, it is shown that their model is a special case of the threshold autoregressive (TAR) model. As a consequence, we can make use of existing knowledge about TAR models with respect to parameter estimation, model alternatives and model selection. We propose a new estimation procedure and perform a simulation study to compare it to the estimation procedure developed by Gottman and Murray. In addition, we include an empirical example based on interaction data of three dyads.

Keywords

dynamic systemTAR modelautoregressivedyadic interaction
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 4 , December 2009 , pp. 727 - 745
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This article distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2009 The Psychometric Society

Footnotes

This study was supported by the National Institute on Aging (Grant 5T32AG020500), and the Dutch Organization for Scientific Research (NWO; VENI Grant 451-05-012).

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