Open AccessFitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm
Author(s) -
Sy Miin Chow,
Zhaohua Lu,
Andrew Sherwood,
Hongtu Zhu
Publication year - 2014
Publication title -
psychometrika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.375
H-Index - 76
eISSN - 1860-0980
pISSN - 0033-3123
DOI - 10.1007/s11336-014-9431-z
Subject(s) - nonlinear system , stochastic approximation , maximization , benchmark (surveying) , mathematics , dynamical systems theory , stochastic differential equation , ordinary differential equation , expectation–maximization algorithm , computer science , mathematical optimization , algorithm , differential equation , statistics , maximum likelihood , mathematical analysis , physics , geodesy , quantum mechanics , key (lock) , computer security , geography
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.