Simplex mixed-effects models for longitudinal proportional data

Scandinavian Journal of Statistics

Volumn 35, Issue 4, 2008, Pages 577-596

  Qiu, Zhenguo ^a   Song, Peter X K ^b,d   Tan, Ming ^c  

^a Alberta Cancer Board   (Canada)

^b UNIVERSITY OF WATERLOO   (Canada)

^c UNIVERSITY OF MARYLAND   (United States)

^d UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Bias correction; Dispersion model; Laplace approximation; Overdispersion; Penalized quasi likelihood; Restricted maximum likelihood; Robustness; Simplex distribution

Indexed keywords

EID: 55849104326     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2008.00603.x     Document Type: Article

References (34)

1. Aitchison, J. (1986). The statistical analysis of compositional data. Chapman & Hall, London.
2. Bard, Y. (1970). Comparison of gradient methods for the solution of nonlinear parameter estimation problems. SIAM J. Numer. Anal. 7, 157 186.
3. Barndorff-Nielsen, O. E. Jørgensen, B. (1991). Some parametric models on the simplex. J. Multivar. Anal. 39, 106 116.
4. Breslow, N. E. Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. J. Amer. Statist. Assoc. 88, 9 25.
5. Breslow, N. E. Lin, X. (1995). Bias correction in generalized linear mixed models with a single component of dispersion. Biometrika 82, 81 91.
6. Fitzmaurice, G. M., Laird, N. M. Ware, J. H. (2004). Applied longitudinal analysis. Wiley, New York.
7. Geyer, C. J. Thompson, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data. J. Roy. Statist. Soc. Ser. B 54, 657 699.
8. Goldfeld, S. M., Quandt, R. E. Trotter, H. F. (1966). Maximization by quadratic hill-climbing. Econometrica 34, 541 551.
9. Green, P. J. (1987). Penalized likelihood for general semi-parametric regression models. Int. Statist. Rev. 55, 245 259.
10. Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. J. Amer. Statist. Assoc. 72, 320 340.
11. Jensen, W. A. Birch, J. B. (2008). Profile monitoring via nonlinear mixed models. J. Qual. Tech. (accepted for publication).
12. Jørgensen, B. (1997). The theory of dispersion models. Chapman & Hall, London.
13. Jørgensen, B. Knudsen, S. J. (2004). Parameter orthogonality and bias adjustment for estimating functions. Scand. J. Statist. 31, 93 114.
14. Kuk, A. Y. C. (1995). Asymptotically unbiased estimation in generalized linear models with random effects. J. Roy. Statist. Soc. Ser B 57, 395 407.
15. Lin, X. Breslow, N. E. (1996). Bias correction in GLMM with multiple components of dispersion. J. Amer. Statist. Assoc. 91, 1007 1016.
16. Lindstrom, M. J. Bates, D. M. (1988). Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data. J. Amer. Statist. Assoc. 83, 1014 1022.
17. Magnus, J. R. Neudecker, H. (1988). Matrix differential calculus with applications in statistics and econometrics. Wiley, New York.
18. Marquardt, D. W. (1963). An algorithm for least squares estimation of nonlinear parameters. SIAM J. 11, 431 441.
19. McCullagh, P. Nelder, J. A. (1989). Generalized Linear Models, 2nd edn. Chapman & Hall, London.
20. McCullagh, P. Tibshirani, R. (1990). A simple method for the adjustment of profile likelihoods. J. Roy. Statist. Soc. Ser. B 52, 325 344.
21. McCulloch, C. E. (1997). Maximum likelihood algorithms for generalized linear mixed models. J. Amer. Statist. Assoc. 92, 162 170.
22. Meyers, S. M., Ambler, J. S., Tan, M., Werner, J. C. Huang, S. S. (1992). Variation of perfluorpropane disappearance after vitrectomy. Retina 12, 359 363.
23. Pinheiro, J. C. Bates, D. M. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model. J. Comp. Graph. Statist. 4, 12 24.
24. Pinheiro, J. C., Liu, C. Wu, Y. N. (2001). Efficient algorithms for robust estimation in linear mixed-effects models using the multivariate t distribution. J. Comp. Graph. Statist. 10, 249 276.
25. Qiu, Z. (2001). PhD Dissertation, Department of Mathematics and Statistics, York University, Toronto, Canada.
26. Raudenbush, S. W., Yang, M.-L. Yosef, M. (2000). Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. J. Comp. Graph. Statist. 9, 141 157.
27. Ruppert, D. (2005). Discussion of ''maximization by parts in likelihood inference'' by Song, Fan, and Kalbfleisch. J. Amer. Statist. Assoc. 100, 1161 1163.
28. Shun, Z. (1997). Another look at the salamander mating data. J. Amer. Statist. Assoc. 92, 341 349.
29. Shun, Z. McCullagh, P. (1995). Laplace approximation of high dimensional integrals. J. Roy. Statist. Soc. Ser. B 57, 749 760.
30. Song, P. X.-K. Tan, M. (2000). Marginal models for longitudinal continuous proportional data. Biometrics 56, 496 502.
31. Song, P. X.-K., Qiu, Z. Tan, M. (2004). Modelling heterogeneous dispersion in marginal models for longitudinal proportional data. Biom. J. 46, 540 553.
32. Song, P. X.-K., Zhang, P. Qu, A. (2007). Maximum likelihood inference in robust linear mixed-effects models using multivariate t distributions. Statist. Sinica 17, 929 943.
33. 2 statistic based on the successive differences estimator. J. Qual. Tech. 38, 217 229.
34. Zeger, S. L. Karim, M. R. (1991). Generalized linear models with random effects; a Gibbs sampling approach. J. Amer. Statist. Assoc. 86, 79 86.