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Penalized Estimation and Forecasting of Multiple Subject Intensive Longitudinal Data

Published online by Cambridge University Press:  01 January 2025

Zachary F. Fisher Open the ORCID record for Zachary F. Fisher [Opens in a new window] ,
Younghoon Kim ,
Barbara L. Fredrickson  and
Vladas Pipiras
Zachary F. Fisher*
Affiliation:
The Pennsylvania State University
Younghoon Kim
Affiliation:
University of North Carolina at Chapel Hill
Barbara L. Fredrickson
Affiliation:
University of North Carolina at Chapel Hill
Vladas Pipiras
Affiliation:
University of North Carolina at Chapel Hill
*
Correspondence should be made to Zachary F. Fisher, The Pennsylvania State University, Pennsylvania, USA. Email: fish.zachary@gmail.com
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Abstract

Intensive longitudinal data (ILD) is an increasingly common data type in the social and behavioral sciences. Despite the many benefits these data provide, little work has been dedicated to realize the potential such data hold for forecasting dynamic processes at the individual level. To address this gap in the literature, we present the multi-VAR framework, a novel methodological approach allowing for penalized estimation of ILD collected from multiple individuals. Importantly, our approach estimates models for all individuals simultaneously and is capable of adaptively adjusting to the amount of heterogeneity present across individual dynamic processes. To accomplish this, we propose a novel proximal gradient descent algorithm for solving the multi-VAR problem and prove the consistency of the recovered transition matrices. We evaluate the forecasting performance of our method in comparison with a number of benchmark methods and provide an illustrative example involving the day-to-day emotional experiences of 16 individuals over an 11-week period.

Keywords

ILDforecastingtime seriesregularizationLASSOproximal gradient descentvector autoregression
Type
Theory and Methods
Information
Psychometrika , Volume 87 , Issue 2: Special Issue on Forecasting with Intensive Longitudinal Data , June 2022 , pp. 403 - 431
Copyright
copyright © 2021 The Author(s) under exclusive licence to The Psychometric Society

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