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

Sy-Miin Chow, Zhaohua Lu, Andrew Sherwood, Hongtu Zhu

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)102-134
Number of pages33
JournalPsychometrika
Volume81
Issue number1
DOIs
StatePublished - Mar 1 2016

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Benchmarking
Social Sciences
Stochastic Approximation
Expectation-maximization Algorithm
Approximation algorithms
Nonlinear Ordinary Differential Equations
Random Effects
Ordinary differential equations
Approximation Algorithms
Initial conditions
Research Personnel
Unknown
Nonlinear dynamical systems
Social sciences
Dynamic models
Differential equations
Van Der Pol Oscillator
Nonlinear Dynamical Systems
Longitudinal Data
Model

All Science Journal Classification (ASJC) codes

  • Psychology(all)
  • Applied Mathematics

Cite this

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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. / Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu.

In: Psychometrika, Vol. 81, No. 1, 01.03.2016, p. 102-134.

Research output: Contribution to journalArticle

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