Semi-parametric marginal models for hierarchical data and their corresponding full models

Computational Statistics and Data Analysis

Volumn 54, Issue 2, 2010, Pages 585-597

  Molenberghs, Geert ^a,b   Kenward, Michael G ^c  

^a HASSELT UNIVERSITY   (Belgium)

^b UNIVERSITY OF LEUVEN   (Belgium)

^c LONDON SCHOOL OF HYGIENE AND TROPICAL MEDICINE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY DATA; CONDITIONAL MODELS; CORRELATION STRUCTURE; COVARIATES; DEVELOPMENTAL TOXICITY STUDIES; EXPONENTIAL FAMILY; FULL MODEL; GENERALIZED ESTIMATING EQUATIONS; HIERARCHICAL DATA; MULTI-LEVEL; NON-GAUSSIAN; RANDOM EFFECTS; SEMIPARAMETRIC; TRIVARIATE;

EID: 70350570533     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2009.09.040     Document Type: Article

References (42)

1. Aerts M., Geys H., Molenberghs G., and Ryan L.M. Topics in Modeling of Clustered Data (2002), Chapman & Hall/CRC, London
2. Autian J. Toxicity and health threats of phthalate esters: Review of the literature. Environmental Health Perspectives 4 (1973) 3-26
3. Bahadur R.R. A representation of the joint distribution of responses to n dichotomous items. In: Solomon H. (Ed). Studies in Item Analysis and Prediction. Stanford Mathematical Studies in the Social Sciences vol. VI (1961), Stanford University Press, Stanford, CA
4. Barndorff-Nielsen O.E. Information and Exponential Families in Statistical Theory (1978), John Wiley, Chichester
5. Carey V.C., Zeger S.L., and Diggle P.J. Modelling multivariate binary data with alternating logistic regressions. Biometrika 80 (1993) 517-526
6. Cox D.R. The analysis of multivariate binary data. Applied Statistics 21 (1972) 113-120
7. Cox D.R., and Reid N. On the stability of maximum-likelihood estimators of orthogonal parameters. Canadian Journal of Statistics 49 (1987) 1-39
8. Dale J.R. Global cross-ratio models for bivariate, discrete, ordered responses. Biometrics 42 (1986) 909-917
9. Declerck L., Aerts M., and Molenberghs G. Behaviour of the likelihood ratio test statistic under a Bahadur model for exchangeable binary data. Journal of Statistical Computation and Simulation 61 (1998) 15-38
10. Diggle P.J., Heagerty P.J., Liang K.-Y., and Zeger S.L. Analysis of Longitudinal Data. 2nd ed. Oxford Science Publications (2002), Clarendon Press, Oxford
11. Fitzmaurice G.M., and Laird N.M. A likelihood-based method for analysing longitudinal binary responses. Biometrika 80 (1993) 141-151
12. Fitzmaurice G.M., Laird N.M., and Rotnitzky A. Regression models for discrete longitudinal responses. Statistical Science 8 (1993) 284-309
13. Fréchet M. Sur les tableaux de corrélation dont les marges sont données. Annals Université Lyon, Section A, Series 3 14 (1951) 53-77
14. Glonek G.F.V. A class of regression models for multivariate categorical responses. Biometrika 83 (1996) 15-28
15. Glonek G.F.V., and McCullagh P. Multivariate logistic models. Journal of the Royal Statistical Society, Series B 81 (1995) 477-482
16. Heagerty P.J. Marginalized transition models and likelihood inference for longitudinal categorical data. Biometrics 58 (2002) 342-351
17. Heagerty P.J., and Zeger S.L. Marginal regression models for clustered ordinal measurements. Journal of the American Statistical Association 91 (1996) 1024-1036
18. Ilk O., and Daniels M.J. Marginalized transition random effects models for multivariate longitudinal binary data. The Canadian Journal of Statistics 35 (2007) 105-123
19. Kleinman J. Proportions with extraneous variance: single and independent samples. Journal of the American Statistical Association 68 (1973) 46-54
20. Kupper L.L., and Haseman J.K. The use of a correlated binomial model for the analysis of certain toxicology experiments. Biometrics 34 (1978) 69-76
21. Lang J.B., and Agresti A. Simultaneously modelling joint and marginal distributions of multivariate categorical responses. Journal of the American Statistical Association 89 (1994) 625-632
22. Liang K.-Y., and Zeger S.L. Longitudinal data analysis using generalized linear models. Biometrika 73 (1986) 13-22
23. Liang K.-Y., Zeger S.L., and Qaqish B. Multivariate regression analyses for categorical data. Journal of the Royal Statistical Society, Series B 54 (1992) 3-40
24. Lipsitz S.R., Laird N.M., and Harrington D.P. Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika 78 (1991) 153-160
25. Little R.J.A., and Rubin D.B. Statistical Analysis with Missing Data. 2nd ed (2002), John Wiley, New York
26. McCullagh P., and Nelder J.A. Generalized Linear Models (1989), Chapman & Hall/CRC, London
27. Molenberghs, G., Danielson, L., 1999. Simple methods for the analysis of multivariate and longitudinal categorical data. In: Grigelionis, B. et al. (Eds.), Proceedings of the 7th International Conference on Probability Theory and Mathematical Statistics and Vilnius Conference (1998). TEV, Vilnius/VSP, Utrecht, pp. 499-514
28. Molenberghs G., and Kenward M.G. Missing Data in Clinical Studies (2007), John Wiley, Chichester
29. Molenberghs G., and Lesaffre E. Marginal modelling of correlated ordinal data using a multivariate Plackett distribution. Journal of the American Statistical Association 89 (1994) 633-644
30. Molenberghs G., and Lesaffre E. Marginal modelling of multivariate categorical data. Statistics in Medicine 18 (1999) 2237-2255
31. Molenberghs G., and Ritter L. Likelihood and quasi-likelihood based methods for analysing multivariate categorical data, with the association between outcomes of interest. Biometrics 52 (1996) 1121-1133
32. Molenberghs G., and Verbeke G. Models for Discrete Longitudinal Data (2005), Springer, New York
33. Nelder J.A., and Wedderburn R.W.M. Generalized linear models. Journal of the Royal Statistical Society, Series B 135 (1972) 370-384
34. Palmgren, J., 1989. Regression Models for Bivariate Responses. Technical Report 101, Department of Biostatistics, Seattle, WA
35. Plackett R.L. A class of bivariate distributions. Journal of the American Statistical Association 60 (1965) 516-522
36. Prentice R.L. Correlated binary regression with covariates specific to each binary observation. Biometrics 44 (1988) 1033-1048
37. Shiota K., Chou M.J., and Nishimura H. Embryotoxic effects of di-2-ethylhexyl phthalate (DEHP) and di-n-butyl phthalate (DBP) in mice. Environmental Research 22 (1980) 245-253
38. Skellam J.G. A probability distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials. Journal of the Royal Statistical Society, Series B 10 (1948) 257-261
39. Tyl R.W., Price C.J., Marr M.C., and Kimmel C.A. Developmental toxicity evaluation of dietary di(2-ethylhexyl)phthalate in Fischer 344 rats and CD-1 mice. Fundamental and Applied Toxicology 10 (1988) 395-412
40. Windholz M. The Merck Index: An Encyclopedia of Chemicals, Drugs, and Biologicals. 10th ed (1983), Merck and Co, Rahway, NJ
41. Zeger S.L., Liang K.-Y., and Albert P.S. Models for longitudinal data: a generalized estimating equation approach. Biometrics 44 (1988) 1049-1060
42. Zhao L.P., and Prentice R.L. Correlated binary regression using a quadratic exponential model. Biometrika 77 (1990) 642-648