Title | Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm. |
Publication Type | Journal Article |
Year of Publication | 2016 |
Authors | Chow, Sy-Miin, Zhaohua Lu, Andrew Sherwood, and Hongtu Zhu |
Journal | Psychometrika |
Volume | 81 |
Issue | 1 |
Pagination | 102-34 |
Date Published | 2016 Mar |
ISSN | 1860-0980 |
Keywords | Algorithms, Humans, Models, Theoretical, Nonlinear Dynamics, Psychometrics, Stochastic Processes |
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. |
DOI | 10.1007/s11336-014-9431-z |
Alternate Journal | Psychometrika |
Original Publication | Fitting nonlinear ordinary differential equation models with random effects and unknown initial conditions using the stochastic approximation expectation-maximization (SAEM) algorithm. |
PubMed ID | 25416456 |
PubMed Central ID | PMC4441616 |
Grant List | AG033387 / AG / NIA NIH HHS / United States R01GM105004 / GM / NIGMS NIH HHS / United States U54 EB005149 / EB / NIBIB NIH HHS / United States P01CA142538-01 / CA / NCI NIH HHS / United States R01 MH086633 / MH / NIMH NIH HHS / United States EB005149-01 / EB / NIBIB NIH HHS / United States R01 GM105004 / GM / NIGMS NIH HHS / United States RR025747-01 / RR / NCRR NIH HHS / United States MH086633 / MH / NIMH NIH HHS / United States UL1 RR025747 / RR / NCRR NIH HHS / United States P01 CA142538 / CA / NCI NIH HHS / United States R21 AG033387 / AG / NIA NIH HHS / United States |
Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.
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