zbMATH — the first resource for mathematics

Conditional and marginal models: another view (with comments and rejoinder). (English) Zbl 1100.62591
Summary: There has existed controversy about the use of marginal and conditional models, particularly in the analysis of data from longitudinal studies. We show that alleged differences in the behavior of parameters in so-called marginal and conditional models are based on a failure to compare like with like. In particular, these seemingly apparent differences are meaningless because they are mainly caused by preimposed unidentifiable constraints on the random effects in models. We discuss the advantages of conditional models over marginal models. We regard the conditional model as fundamental, from which marginal predictions can be made.

62J12 Generalized linear models (logistic models)
Full Text: DOI
[1] Crowder, M. J. (1995). On the use of a working correlation matrix in using generalised linear models for repeated measures. Biometrika 82 407–410. · Zbl 0823.62060
[2] Crowder, M. J. and Hand, D. J. (1990). Analysis of Repeated Measures. Chapman and Hall, London. · Zbl 0745.62064
[3] Diggle, P. J., Liang, K. Y. and Zeger, S. L. (1994). Analysis of Longitudinal Data . Clarendon Press, Oxford. · Zbl 1031.62002
[4] Galbraith, R. F. and Laslett, G. M. (1993). Statistical models for mixed fission track ages. Nuclear Tracks and Radiation Measurements 21 459–470.
[5] Goldstein, H. (1995). Multilevel Statistical Models . Arnold, London. · Zbl 1014.62126
[6] Goldstein, H. and Rasbash, J. (1996). Improved approximations for multilevel models with binary responses. J. Roy. Statist. Soc. Ser. A 159 505–513. · Zbl 1001.62518
[7] Ha, I. D., Lee, Y. and Song, J. K. (2001). Hierarchical likelihood approach for frailty models. Biometrika 88 233–243. · Zbl 1033.62096
[8] Heagerty, P. J. and Zeger, S. L. (2000). Marginalized multilevel models and likelihood inference (with discussion). Statist. Sci. 15 1–26.
[9] Kent, J. T. (1982). Robust properties of likelihood ratio tests. Biometrika 69 19–27. · Zbl 0485.62031
[10] Laird, N. M. (1978). Nonparametric maximum likelihood estimation of a mixing distribution. J. Amer. Statist. Assoc . 73 805–811. · Zbl 0391.62029
[11] Lee, Y. (2002). Robust variance estimators for fixed-effect estimates with hierarchical-likelihood. Statist. Comput. 12 201–207.
[12] Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion). J. Roy. Statist. Soc. Ser. B 58 619–678. · Zbl 0880.62076
[13] Lee, Y. and Nelder, J. A. (1999). Robustness of the quasilikelihood estimator. Canad. J. Statist. 27 321–327. · Zbl 0941.62082
[14] Lee, Y. and Nelder, J. A. (2000). Two ways of modelling overdispersion in non-normal data. Appl. Statist. 49 591–598. · Zbl 04561702
[15] Lee, Y. and Nelder, J. A. (2001a). Hierarchical generalised linear models: A synthesis of generalised linear models, random effect models and structured dispersions. Biometrika 88 987–1006. · Zbl 0995.62066
[16] Lee, Y. and Nelder, J. A. (2001b). Modelling and analysing correlated non-normal data. Statist. Model. 1 3–16. · Zbl 1004.62080
[17] Lee, Y. and Nelder, J. A. (2002). Analysis of the ulcer data using hierarchical generalized linear models. Statistics in Medicine 21 191–202.
[18] Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73 13–22. · Zbl 0595.62110
[19] Lindsey, J. K. and Lambert, P. (1998). On the appropriateness of marginal models for repeated measurements in clinical trials. Statistics in Medicine 17 447–469.
[20] McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models , 2nd ed. Chapman and Hall, London. · Zbl 0588.62104
[21] Nelder, J. A. (1994). The statistics of linear models: Back to basics. Statist. Comput. 4 221–234.
[22] Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects (with discussion). Statist. Sci. 6 15–51. JSTOR: · Zbl 0955.62500
[23] Seely, J. and Hogg, R. V. (1982). Symmetrically distributed and unbiased estimators in linear models. Comm. Statist. A—Theory Methods 11 721–729. · Zbl 0516.62053
[24] Simpson, E. H. (1952). The interpretation of interaction in contingency tables. J. Roy. Statist. Soc. Ser. B 13 238–241. · Zbl 0045.08802
[25] Wedderburn, R. W. M. (1974). Quasilikelihood functions, generalized linear models and the Gauss–Newton method. Biometrika 61 439–447. · Zbl 0292.62050
[26] Weil, C. S. (1970). Selection of the valid number of sampling units and a consideration of their combination in toxicological studies involving reproduction, teratogenesis or carcino-genesis. Food and Cosmetics Toxicology 8 177–182.
[27] Zeger, S. L. and Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42 121–130.
[28] Zeger, S. L., Liang, K. Y. and Albert, P. S. (1988). Models for longitudinal data: A generalized estimating equation approach. Biometrics 44 1049–1060. · Zbl 0715.62136
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.