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

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Chow, S-M; Lu, Z; Sherwood, A; Zhu, H

Published Date

  • March 2016

Published In

Volume / Issue

  • 81 / 1

Start / End Page

  • 102 - 134

PubMed ID

  • 25416456

Pubmed Central ID

  • 25416456

Electronic International Standard Serial Number (EISSN)

  • 1860-0980

Digital Object Identifier (DOI)

  • 10.1007/s11336-014-9431-z

Language

  • eng

Conference Location

  • United States