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Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm

Published online by Cambridge University Press:  01 January 2025

Sy-Miin Chow ,
Zhaohua Lu ,
Hongtu Zhu  and
Andrew Sherwood
Sy-Miin Chow*
Affiliation:
The Pennsylvania State University
Zhaohua Lu
Affiliation:
University of North Carolina at Chapel Hill
Hongtu Zhu
Affiliation:
University of North Carolina at Chapel Hill
Andrew Sherwood
Affiliation:
Duke University
*
Correspondence should be made to Sy-Miin Chow, The Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA 16802 USA. Email: symiin@psu.edu
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Abstract

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

Keywords

differential equationdynamicnonlinearstochastic EMlongitudinal

Information

Type
Original paper
Information
Psychometrika , Volume 81 , Issue 1 , March 2016 , pp. 102 - 134
Copyright
Copyright © 2014 The Psychometric Society

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