1990 NonlinearMixedEffectsModels
- (Lindstrom & Bates, 1990) ⇒ Mary J. Lindstrom, and Douglas M. Bates. (1990). “Nonlinear Mixed Effects Models for Repeated Measures Data.” In: Biometrics, 46(3).
Subject Headings: Nonlinear Mixed Effects Models.
Notes
- Stable URL: http://www.jstor.org/stable/2532087
Cited By
Quotes
Author Keywords
Longitudinal data; Newton- — Raphson; Nonlinear least squares; Nonlinear models; Random effects.
Abstract
We propose a general, nonlinear mixed effects model for repeated measures data and define estimators for its parameters. The proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood (or restricted maximum likelihood) estimators for [[linear mixed effects model]]s. We implement Newton — Raphson estimation using previously developed computational methods for nonlinear fixed effects models and for [[linear mixed effects model]]s. Two examples are presented and the connections between this work and recent work on generalized [[linear mixed effects model]]s are discussed.
REFERENCES
- Bates, D. M. and Watts, D. G. (1980). Relative curvature measures of nonlinearity (with Discussion). Journal 0f the Royal Statistical S0ciety, Series B 42, 1-25.
- Bates, D. M. and Watts, D. G. (1981). A relative offset orthogonality convergence criterion for nonlinear least squares. T echnometrics 23, 179-183.
- Bates, D. M. and Watts, D. G. (1988). Nonlinear Regression Analysis and Its Applications. New York: Wiley.
- Berkey, C. S. (1982). Bayesian approach for a nonlinear growth model. Biometrics 38, 953-961.
- Chi, E. M. and Reinsel, G. C. (1989). Models for longitudinal data with random effects and AR(1) errors. Journal ofthe American Statistical Association 84, 452-459.
- Draper, N. R. and Smith, H. (1981). Applied Regression Analysis, 2nd edition. New York: Wiley.
- Harville, D. A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika 61, 383-385.
- Jennrich, R. I. and Schluchter, M. D. (1986). Unbalanced repeated measures models with structural covariance matrices. Biometrics 42, 805-820.
- Johansen, S. (1984). Functional Relations, Random Coejicients, and Nonlinear Regression with Application to Kinetic Data. New York; Springer-Verlag.
- Laird, N., Lange, N., and Stram, D. (1987). Maximum likelihood computations with repeated measures: Application of the EM algorithm. Journal ofthe American Statistical Association 82, 97-105.
- Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963-974.
- Liang, K. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73, 13-22.
- Lindstrom, M. J. and Bates, D. M. (1988). Newton — Raphson and EM algorithms for [[linear
mixed effects model]]s for repeated measures data. Journal of the American Statistical Association 83, 1014-1022.
- Racine-Poon, A. (1985). Bayesian approach to nonlinear random effects models. Biometrics 41, 1015-1023.
- Sheiner, L. B. and Beal, S. L. (1980). Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-Menten model: Routine clinical pharmacokinetic data. Journal of Pharmacokinetics and Biopharmaceutics 8, 553-571.
- Soo, Y. and Bates, D. M. Loosely coupled nonlinear least squares. Computational Statistics and Data Analysis (in press).
- Stiratelli, R., Laird, N., and Ware, J. H. (1984). Random-effects models for serial observations with binary response. Biometrics 40, 961-971.
- Zeger, S. L., Liang, K., and Albert, P. (1988). Models for longitudinal data: A generalized estimating equation approach. Biometrics 44, 1049-1060.
,
| Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1990 NonlinearMixedEffectsModels | Mary J. Lindstrom Douglas M. Bates | Nonlinear Mixed Effects Models for Repeated Measures Data | Biometrics Subject Area | ftp://ftp.biostat.wisc.edu/pub/lindstrom/papers/biometrics.1990.ps | 1990 |