Premium
Fitting Nonlinear and Constrained Generalized Estimating Equations with Optimization Software
Author(s) -
Contreras Martha,
Ryan Louise M.
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.01268.x
Subject(s) - nonlinear system , matlab , nonlinear programming , nonparametric statistics , binary number , mathematics , software , confidence interval , mathematical optimization , nonlinear regression , computer science , statistics , regression analysis , physics , arithmetic , quantum mechanics , programming language , operating system
Summary. In this article, we present an estimation approach for solving nonlinear constrained generalized estimating equations that can be implemented using object‐oriented software for nonlinear programming, such as nlminb in Splus or fmincon and lsqnonlin in Matlab. We show how standard estimating equation theory includes this method as a special case so that our estimates, when unconstrained, will remain consistent and asymptotically normal. To illustrate this method, we fit a nonlinear dose‐response model with nonnegative mixed bound constraints to clustered binary data from a developmental toxicity study. Satisfactory confidence intervals are found using a nonparametric bootstrap method when a common correlation coefficient is assumed for all the dose groups and for some of the dose‐specific groups.