title: Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.
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.
authors.affiliation: The Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA, 16802 , USA. symiin@psu.edu.
authors.forename: Sy-Miin
authors.initials: SM
authors.lastname: Chow
authors.affiliation: University of North Carolina at Chapel Hill, Chapel Hill, USA.
authors.forename: Zhaohua
authors.initials: Z
authors.lastname: Lu
authors.affiliation: Duke University, Durham, USA.
authors.forename: Andrew
authors.initials: A
authors.lastname: Sherwood
authors.affiliation: University of North Carolina at Chapel Hill, Chapel Hill, USA.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D006801:Humans; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D011594:Psychometrics; D013269:Stochastic Processes
keywords: differential equation; dynamic; longitudinal; nonlinear; stochastic EM