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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

Institution:
1Pennsylvania State University, University Park, PA, USA. symiin@psu.edu.
2University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
3Duke University, Durham, NC, USA.
Publication Date:
Mar-2016
Journal:
Psychometrika
Volume Number:
81
Issue Number:
1
Pages:
102-34
Citation:
Psychometrika. 2016 Mar;81(1):102-34.
PubMed ID:
25416456
PMCID:
PMC4441616
Keywords:
differential equation, dynamic, longitudinal, nonlinear, stochastic EM
Appears in Collections:
NA-MIC
Sponsors:
R21 AG033387/AG/NIA NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
R01 MH086633/MH/NIMH NIH HHS/United States
P01 CA142538/CA/NCI NIH HHS/United States
R01 GM105004/GM/NIGMS NIH HHS/United States
UL1 RR025747/RR/NCRR NIH HHS/United States
Generated Citation:
Chow S-M., Lu Z., Sherwood A., Zhu H. Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm. Psychometrika. 2016 Mar;81(1):102-34. PMID: 25416456. PMCID: PMC4441616.
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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.

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