A review of generalized linear mixed models
Journal de la Société française de statistique, Tome 143 (2002) no. 1-2, pp. 53-78. 
@article{JSFS_2002__143_1-2_53_0,
     author = {Molenberghs, Geert and Renard, Didier and Verbeke, Geert},
     title = {A review of generalized linear mixed models},
     journal = {Journal de la Soci\'et\'e fran\c{c}aise de statistique},
     pages = {53--78},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {143},
     number = {1-2},
     year = {2002},
     language = {en},
     url = {http://archive.numdam.org/item/JSFS_2002__143_1-2_53_0/}
}
TY  - JOUR
AU  - Molenberghs, Geert
AU  - Renard, Didier
AU  - Verbeke, Geert
TI  - A review of generalized linear mixed models
JO  - Journal de la Société française de statistique
PY  - 2002
SP  - 53
EP  - 78
VL  - 143
IS  - 1-2
PB  - Société française de statistique
UR  - http://archive.numdam.org/item/JSFS_2002__143_1-2_53_0/
LA  - en
ID  - JSFS_2002__143_1-2_53_0
ER  - 
%0 Journal Article
%A Molenberghs, Geert
%A Renard, Didier
%A Verbeke, Geert
%T A review of generalized linear mixed models
%J Journal de la Société française de statistique
%D 2002
%P 53-78
%V 143
%N 1-2
%I Société française de statistique
%U http://archive.numdam.org/item/JSFS_2002__143_1-2_53_0/
%G en
%F JSFS_2002__143_1-2_53_0
Molenberghs, Geert; Renard, Didier; Verbeke, Geert. A review of generalized linear mixed models. Journal de la Société française de statistique, Tome 143 (2002) no. 1-2, pp. 53-78. http://archive.numdam.org/item/JSFS_2002__143_1-2_53_0/

Aerts M., Declerck L., Molenberghs G. (1997), Likelihood misspecification and safe dose determination for clustered binary data, Environmetrics, 8, 613-627.

Aerts M., Geys H., Molenberghs G., Ryan L.M. (2002), Topics in Modelling of Clustered Binary Data, London : Chapman & Hall. | MR | Zbl

Altham P.M.E. (1978), Two generalizations of the binomial distribution, Applied Statistics, 27, 162-167. | MR | Zbl

Bahadur R.R. (1961), A representation of the joint distribution of responses of n dichotomous items, In : Studies in item analysis and prediction, H. Solomon (ed.), Stanford Mathematical Studies in the Social Sciences VI. Stanford, California, Stanford University Press. | MR | Zbl

Breslow N.E., Clayton D.G. (1993), Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9-25. | Zbl

Breslow N.E., Day N.E. (1987), Statistical Methods in Cancer Research, Volume II, Oxford : Oxford University Press.

Bryk A.S., Raudenbush S.W. (1992), Hierarchical Linear Models : Applications and Data Analysis Methods, Newbury Park : Sage Publications. | Zbl

Conaway M. (1989), Analysis of repeated categorical measurements with conditional likelihood methods, Journal of the American Statistical Association, 84, 53-62. | MR

Cox D.R. (1972), The analysis of multivariate binary data, Applied Statistics, 21, 113-120.

Cox N.R. (1974), Estimation of the correlation between a continuous and a discrete variable, Biometrics, 30, 171-178. | MR | Zbl

Cressie N.A.C. (1991), Statistics for Spatial Data, New York : John Wiley. | MR | Zbl

Dale J.R. (1986), Global cross-ratio models for bivariate, discrete, ordered responses, Biometrics, 42, 909-917.

Declerck L., Aerts M., Molenberghs G. (1998), Behaviour of the likelihood ratio test statistic under a Bahadur model for exchangeable binary data, Journal of Statistical Computations and Simulations, 61, 15-38. | MR | Zbl

Dempster A.P., Laird N.M., Rubin D. B. (1977), Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society, Series B, 39, 1-38. | MR | Zbl

Diggle P.J. (1983), Statistical Analysis of Spatial Point Patterns, Mathematics in Biology, London : Academic Press. | MR | Zbl

Diggle P.J. (1990), Time Series : A Biostatistical Introduction, Oxford : Oxford University Press. | MR | Zbl

Diggle P.J., Liang K-Y., Zeger S.L. (1994), Analysis of Longitudinal Data, New York : Oxford University Press. | Zbl

Efron B. (1986), Double exponential families and their use in generalized linear regression, Journal of the American Statistical Association, 81, 709-721. | MR | Zbl

Fahrmeir L., Tutz G. (1994), Multivariate Statistical Modelling Based on Generalized Linear Models, Heidelberg : Springer-Verlag. | MR | Zbl

Geys H., Molenberghs G., Lipsitz S.R. (1998), A note on the comparison of pseudo-likelihood and generalized estimating equations for marginal odds ratio models, Journal of Statistical Computation and Simulation, 62, 45-72. | Zbl

Geys H., Molenberghs G., Ryan L.M. (1997), Pseudo-likelihood inference for clustered binary data, Communications in Statistics : Theory and Methods, 26, 2743-2767. | MR | Zbl

Geys H., Molenberghs G., Ryan L. (1999), Pseudo-likelihood modelling of multivariate outcomes in developmental toxicology, Journal of the American Statistical Association, 94, 34-745.

Gilks W.R., Wlld P. (1992), Adaptive rejection sampling for Gibbs sampling, Applied Statistics, 4, 337-348. | Zbl

Gilmour A.R., Anderson R.D., Rae A.L. (1985), The analysis of binomial data by a generalized linear mixed model, Biometrika, 72, 593-599. | MR

Gilula Z., Haberman S. (1994), Conditional log-linear models for analyzing categorical panel data, Journal of the American Statistical Association, 89, 645-656. | MR | Zbl

Glonek G.F.V., Mccullagh P. (1995), Multivariate logistic models, Journal of the Royal Statistical Society, Series B, 57, 533-546. | Zbl

Goldstein H. (1986), Multilevel mixed linear model analysis using iterative generalized least squares, Biometrika, 73, 43-56. | MR | Zbl

Goldstein H. (1991), Nonlinear multilevel models, with an application to discrete response data, Biometrika, 73, 43-56. | MR

Goldstein H. (1995), Multilevel Statistical Models (2nd edition), London : Edward Arnold. | Zbl

Goldstein H., Rasbash J. (1996), Improved approximations for multilevel models with binary responses, Journal of the Royal Statistical Society A, 159, 505-513. | MR | Zbl

Hedeker D., Gibbons R.D. (1993), MIXOR : a Computer Program for Mixed Effects Ordinal Probit and Logistic Regression, Chicago : University of Illinois.

Hedeker D., Gibbons R.D. (1994), A random-effects ordinal regression model for multilevel analysis, Biometrics, 50, 933-944. | Zbl

Hedeker D., Gibbons R.D. (1996), MIXOR : A computer program for mixed-effects ordinal regression analysis, Computer Methods and Programs in Biomedicine, 49, 157-176.

Kleinman J. (1973), Proportions with extraneous variance : single and independent samples, Journal of the American Statistical Association, 68, 46-54.

Kreft I., De Leeuw J. (1998), Introducing Multilevel Modeling, London : Sage Publications.

Kuk A.Y.C. (1995), Asymptotically unbiased estimation in generalised linear models with random effects, Journal of the Royal Statistical Society B, 57, 395-407. | MR | Zbl

Kupper L.L., Haseman J.K. (1978), The use of a correlated binomial model for the analysis of certain toxicology experiments, Biometrics, 34, 69-76. | Zbl

Lang J.B., Agresti A. (1994), Simultaneously modeling joint and marginal distributions of multivariate categorical responses, Journal of the American Statistical Association, 89, 625-632. | Zbl

Lavergne C., Trottier C. (2000), Sur l'estimation dans les modèles linéaires généralisés à effets aléatoires, Revue de Statistique Appliquée, 48, 49-67.

Le Cessie S., Van Houwelingen J.C. (1994), Logistic regression for correlated binary data, Applied Statistics, 43, 95-108. | Zbl

Lesaffre E., Spiessens B. (2001), On the effect of the number of quadrature points in a logistic random-effects model : an example, Applied Statistics, 50, 325-336. | MR | Zbl

Liang K.-Y., Zeger S.L. (1986), Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22. | MR | Zbl

Liang K.Y., Zeger S.L., Qaqish B. (1992), Multivariate regression analyses for categorical data, Journal of the Royal Statistical Society, Series B, 54, 3-40. | MR | Zbl

Lin X., Breslow N.E. (1996), Bias correction in generalized linear mixed models with multiple components of dispersion, Journal of the American Statistical Association, 91, 1007-1016. | MR | Zbl

Little R.J.A., Rubin D.B. (1987), Statistical Analysis with Missing Data, New York : John Wiley. | MR | Zbl

Longford N.T. (1993), Random Coefficient Models, London : Oxford University Press. | MR | Zbl

Mccullagh P., Nelder J.A. (1989), Generalized Linear Models, London : Chapman & Hall. | MR | Zbl

Molenberghs G., Declerck L., Aerts M. (1998), Misspecifying the likelihood for clustered binary data, Computational Statistics and Data Analysis, 26, 327-349. | Zbl

Molenberghs G., Lesaffre E. (1994), Marginal modelling of correlated ordinal data using a multivariate Plackett distribution, Journal of the American Statistical Association, 89, 633-644. | Zbl

Molenberghs G., Lesaffre E. (1999), Marginal modelling of multivariate categorical data, Statistics in Medicine, 18, 2237-2255.

Molenberghs G., Ryan L.M. (1999), Likelihood inference for clustered multivariate binary data, Environmetrics, 10, 279-300.

Nelder J.A., Wedderburn R.W.M. (1972), Generalized linear models, Journal of the Royal Statistical Society, Series B, 135, 370-384.

Neuhaus J.M. (1992), Statistical methods for longitudinal and clustered designs with binary responses, Statistical Methods in Medical Research, 1, 249-273.

Neuhaus J.M., Kalbfleisch J.D., Hauck W.W. (1991), A comparison of clusterspecific and population-averaged approaches for analyzing correlated binary data, International Statistical Review, 59, 25-35.

Ochi Y., Prentice R.L. (1984), Likelihood inference in a correlated probit regression model, Biometrika, 71, 531-543. | MR | Zbl

Olkin I., Tate R.F. (1961), Multivariate correlation models with mixed discrete and continuous variables, Annals of Mathematical Statistics, 32, 448-465 (with correction in 36, 343-344. | MR | Zbl

Pinheiro J.C., Bates D.M. (2000), Mixed effects models in S and S-Plus, New-York : Springer-Verlag. | Zbl

Plackett R.L. (1965), A class of bivariate distributions, Journal of the American Statistical Association, 60, 516-522. | MR

Ripley B.D. (1981), Spatial Statistics, New York : John Wiley. | MR | Zbl

Rodriguez G., Goldman N. (1995), An assessment of estimation procedures for multilevel models with binary responses, Journal of the Royal Statistical Society A, 158, 73-89.

Rosner B. (1984), Multivariate methods in opthalmology with applications to other paired-data, Biometrics, 40, 1025-1035.

Santner T.J., Duffy D.E. (1989), The Statistical Analysis of Discrete Data, New York : Springer-Verlag. | MR | Zbl

Schall R. (1991), Estimation in generalised linear models with random effects, Biometrika, 78, 719-727. | Zbl

Skellam J.G. (1948), 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, 257-261. | MR | Zbl

Stiratelli R., Laird N., Ware J.H. (1984), Random-effects model for serial observations with binary response, Biometrics, 40, 961-971.

Ten Have T.R., Landis R., Weaver S.L. (1995), Association models for periodontal disease progression : A comparison of methods for clustered binary data, Statistics in Medicine, 14, 413-429.

Verbeke G., Molenberghs G. (2000), Linear Mixed Models for Longitudinal Data, New York : Springer-Verlag. | MR | Zbl

Williams D.A. (1975), The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity, Biometrics, 31, 949-952. | Zbl

Wolfinger R., O'Connell M. (1993), Generalized linear mixed models : A pseudo-likelihood approach, Journal of Statistical Computing and Simulation 48, 233-243. | Zbl

Zeger S.L., Karim M.R. (1991), Generalised linear models with random effects : a Gibbs sampling approach, Journal of the American Statistical Association, 86, 79-102. | MR