Goodness-of-fit in generalized nonlinear mixed-effects models

Biometrics

Volumn 52, Issue 2, 1996, Pages 572-587

  Vonesh, Edward F ^a   Chinchilli, Vernon M ^b   Pu, Kewei ^a  

^a BAXTER HEALTHCARE CORPORATION   (United States)

^b PENN STATE COLLEGE OF MEDICINE   (United States)

Author keywords

Concordance correlation; Longitudinal data; Mixed effects models; Pseudo likelihood ratio test

Indexed keywords

CONCORDANCE CORRELATION; COVARIANCE STRUCTURES; GOODNESS OF FIT; LIKELIHOOD RATIO TESTS; LONGITUDINAL DATA; MIXED EFFECTS MODELS; NONLINEAR MIXED EFFECTS; PSEUDO- LIKELIHOOD RATIO TEST; PSEUDO-LIKELIHOOD; VARIANCE-COVARIANCE;

ARTICLE; BAYES THEOREM; DATA ANALYSIS; HYPOTHESIS; LONGITUDINAL STUDY; REGRESSION ANALYSIS; SIMULATION;

EID: 0029887528     PISSN: 0006341X     EISSN: None     Source Type: Journal    
DOI: 10.2307/2532896     Document Type: Article

References (37)

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716-723.
2. Beal, S. L. and Sheiner, L. B. (eds). (1992). NONMEM Users Guides. University of California at San Francisco, San Francisco: NONMEM Project Group.
3. Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9-25.
4. Carter, R. L., Resnick, M. B., Ariet, M., Shieh, G., and Vonesh, E. F. (1992). A random coefficient growth curve analysis of mental development in low-birth-weight infants. Statistics in Medicine 11, 243-256.
5. Cox, D. R. and Wermuth, N. (1992). A comment on the coefficient of determination for binary responses. The American Statistician 46, 1-4.
6. Davidian, M. and Gallant, A. R. (1993). The nonlinear mixed effects model with a smooth random effects density. Biometrika 80, 475-488.
7. Davidian, M. and Giltinan, D. M. (1993). Some general estimation methods for nonlinear mixed effects models. Journal of Biopharmaceutical Statistics 3, 23-55.
8. Diggle, P. J. (1988). An approach to the analysis of repeated measurements. Biometrics 40, 959-971.
9. Efron, B. (1978). Regression and ANOVA with zero-one data: Measures of residual variation. Journal of the American Statistical Association 73, 113-121.
10. Hirst, K., Zerbe, G. O., Boyle, D. W., and Wilkening, R. B. (1991). On nonlinear random effects models for repeated measurements. Communications in Statistics - Simulations 20, 463-478.
11. Jennrich, R. I. and Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42, 805-820.
12. Korn, E. L. and Simon, R. (1991). Explained residual variation, explained risk, and goodness of fit. The American Statistician 45, 201-206.
13. 2. The American Statistician 39, 279-285.
14. Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963-974.
15. Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73, 13-22.
16. Lindstrom, M. J. and Bates, D. M. (1990). Nonlinear mixed effects models for repeated measures data. Biometrics 46, 673-687.
17. Lin, L. I.-K. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45, 255-268.
18. 2 measures based on Wald and likelihood ratio joint significance tests. The American Statistician 44, 250-253.
19. Pinheiro, J. C. and Bates, D. M. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics 4, 12-35.
20. Potthoff, R. F. and Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika 51, 313-326.
21. Prentice, R. L. and Zhao, L. P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics 47, 825-840.
22. Rao, C. R. (1965). The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. Biometrika 52, 447-458.
23. Satorra, A. and Bentler, P. M. (1986). Some robustness properties of goodness of fit statistics in covariance structure analysis. Proceedings of the American Statistical Association, Business and Economic Statistics Section, 549-554. Washington, D.C.: American Statistical Association.
24. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6, 461-464.
25. Sheiner, L. B. and Beal, S. L. (1982). Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-Menten model: Routine clinical pharmacokinetic data. Journal of Pharmacokinetics and Biopharmaceutics 8, 553-571.
26. Solomon, P. J. and Cox, D. R. (1992). Nonlinear component of variance models. Biometrika 79, 1-11.
27. Steimer, J. L., Mallet, A., Golmard, J., and Boisieux, J. (1984). Alternative approaches to estimation of population pharmacokinetic parameters: Comparison with the nonlinear mixed effects model. Drug Metabolism Reviews 15, 265-292.
28. Thall, P. F. and Vail, S. C. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics 46, 657-671.
29. Vonesh, E. F. and Carter, R. L. (1987). Efficient inference for a random coefficient growth curve model with unbalanced data. Biometrics 43, 617-628.
30. Vonesh, E. F. and Carter, R. L. (1992). Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17.
31. Vonesh, E. F. (1992). Nonlinear models for the analysis of longitudinal data. Statistics in Medicine 11, 1929-1954.
32. Vonesh, E. F. (1996). A note on the use of Laplace's approximation for nonlinear mixed-effects models. Biometrika, in press.
33. 2: Its use in weighted least-squares regression analysis. The American Statistician 42, 236-238.
34. Wolfinger, R. (1993). Laplace's approximation for nonlinear mixed models. Biometrika 80, 791-795.
35. Young, D. A., Zerbe, G. O., and Hay, W. W. (1992). Application of a nonlinear random-effects model for comparing X-intercepts of linear regression lines. Statistics in Medicine 11, 2039-2040.
36. Zeger, S. L., Liang. K. Y., and Albert, P. S. (1988). Models for longitudinal data: A generalized estimating equation approach. Biometrics 44, 1049-1060.
37. Zhao, L. P. and Prentice, R. L. (1990). Correlated binary regression using a quadratic exponential model. Biometrika 77, 642-648.