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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.

Publication ,  Journal Article
Chow, S-M; Lu, Z; Sherwood, A; Zhu, H
Published in: Psychometrika
March 2016

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.

Duke Scholars

Published In

Psychometrika

DOI

EISSN

1860-0980

Publication Date

March 2016

Volume

81

Issue

1

Start / End Page

102 / 134

Location

United States

Related Subject Headings

  • Stochastic Processes
  • Social Sciences Methods
  • Psychometrics
  • Nonlinear Dynamics
  • Models, Theoretical
  • Humans
  • Algorithms
  • 5205 Social and personality psychology
  • 5201 Applied and developmental psychology
  • 4905 Statistics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Journal cover image

Published In

Psychometrika

DOI

EISSN

1860-0980

Publication Date

March 2016

Volume

81

Issue

1

Start / End Page

102 / 134

Location

United States

Related Subject Headings

  • Stochastic Processes
  • Social Sciences Methods
  • Psychometrics
  • Nonlinear Dynamics
  • Models, Theoretical
  • Humans
  • Algorithms
  • 5205 Social and personality psychology
  • 5201 Applied and developmental psychology
  • 4905 Statistics