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Approximations to the Loglikelihood Function in the Nonlinear Mixed Effects Model (1995)
| Venue: | Journal of Computational and Graphical Statistics |
| Citations: | 148 - 4 self |
BibTeX
@ARTICLE{Pinheiro95approximationsto,
author = {José C. Pinheiro and Douglas M. Bates},
title = {Approximations to the Loglikelihood Function in the Nonlinear Mixed Effects Model},
journal = {Journal of Computational and Graphical Statistics},
year = {1995},
volume = {4},
pages = {12--35}
}
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Abstract
Introduction. Several different nonlinear mixed effects models and estimation methods for their parameters have been proposed in recent years (Sheiner and Beal, 1980; Mallet, Mentre, Steimer and Lokiek, 1988; Lindstrom and Bates, 1990; Vonesh and Carter, 1992; Davidian and Gallant, 1992; Wakefield, Smith, Racine-Poon and Gelfand, 1994). We consider here a slightly modified version of the model proposed in Lindstrom and Bates (1990). This model can be viewed as a hierarchical model that in some ways generalizes both the linear mixed effects model of Laird and Ware (1982) and the usual nonlinear model for independent data (Bates and Watts, 1988). In the first stage the jth observation on the ith cluster is modeled as y ij = f(OE ij ; x ij ) + ffl ij ; i = 1; : : : ; M; j = 1; : : : ; n i<F
