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Path and Directionality Discovery in Individual Dynamic Models: A Regularized Unified Structural Equation Modeling Approach for Hybrid Vector Autoregression

Published online by Cambridge University Press:  01 January 2025

Ai Ye Open the ORCID record for Ai Ye [Opens in a new window] ,
Kathleen M. Gates ,
Teague Rhine Henry  and
Lan Luo
Ai Ye*
Affiliation:
University of North Carolina at Chapel Hill
Kathleen M. Gates
Affiliation:
University of North Carolina at Chapel Hill
Teague Rhine Henry
Affiliation:
University of North Carolina at Chapel Hill
Lan Luo
Affiliation:
University of North Carolina at Chapel Hill
*
Correspondence should be made to Ai Ye, L. L. Thurstone Psychometric Lab, Department of Psychology and Neuroscience, University of North Carolina at Chapel Hill, 235 E. Cameron Avenue, Campus Box 3270 , Chapel Hill, NC 27599, USA. Email: [email protected]
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Abstract

There recently has been growing interest in the study of psychological and neurological processes at an individual level. One goal in such endeavors is to construct person-specific dynamic assessments using time series techniques such as Vector Autoregressive (VAR) models. However, two problems exist with current VAR specifications: (1) VAR models are restricted in that contemporaneous relations are typically modeled either as undirected relations among residuals or directed relations among observed variables, but not both; (2) current estimation frameworks are limited by the reliance on stepwise model building procedures. This study adopts a new modeling approach. We first extended the current unified SEM (uSEM) framework, a widely used structural VAR model, to a hybrid representation (i.e., “huSEM”) to include both undirected and directed contemporaneous effects, and then replaced the stepwise modeling with a LASSO-type regularization for a global search of the optimal sparse model. Our simulation study showed that regularized huSEM performed uniformly the best over alternative VAR representations and/or modeling approaches, with respect to accurately recovering the presence and directionality of hybrid relations and reliably removing false relations when the data are generated to have two types of contemporaneous relations. The present study to our knowledge is the first application of the recently developed regularized SEM technique to the estimation of huSEM, which points to a promising future for statistical learning in psychometric models.

Keywords

time series datastructural VARhybrid VARcontemporaneous relationsunified SEMgraphical VARregularized SEM
Type
Original Research
Information
Psychometrika , Volume 86 , Issue 2 , June 2021 , pp. 404 - 441
Copyright
Copyright © 2021 The Psychometric Society

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