A review of generalized linear mixed models
Geert Molenberghs; Didier Renard; Geert Verbeke
Journal de la société française de statistique (2002)
- Volume: 143, Issue: 1-2, page 53-78
- ISSN: 1962-5197
Access Full Article
topHow to cite
topMolenberghs, Geert, Renard, Didier, and Verbeke, Geert. "A review of generalized linear mixed models." Journal de la société française de statistique 143.1-2 (2002): 53-78. <http://eudml.org/doc/198501>.
@article{Molenberghs2002,
author = {Molenberghs, Geert, Renard, Didier, Verbeke, Geert},
journal = {Journal de la société française de statistique},
keywords = {sensitivity; local influence; marginal model; dropout; missing data; pattern mixture model; random effects; selection model},
language = {eng},
number = {1-2},
pages = {53-78},
publisher = {Société française de statistique},
title = {A review of generalized linear mixed models},
url = {http://eudml.org/doc/198501},
volume = {143},
year = {2002},
}
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
PB - Société française de statistique
VL - 143
IS - 1-2
SP - 53
EP - 78
LA - eng
KW - sensitivity; local influence; marginal model; dropout; missing data; pattern mixture model; random effects; selection model
UR - http://eudml.org/doc/198501
ER -
References
top- 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. Zbl1084.62513MR2022882
- ALTHAM P.M.E. (1978), Two generalizations of the binomial distribution, Applied Statistics, 27, 162-167. Zbl0438.62008MR506839
- 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. Zbl0103.36701MR121893
- BRESLOW N.E., CLAYTON D.G. (1993), Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9-25. Zbl0775.62195
- 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. Zbl1001.62004
- CONAWAY M. (1989), Analysis of repeated categorical measurements with conditional likelihood methods, Journal of the American Statistical Association, 84, 53-62. MR999664
- 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. Zbl0292.62022MR334376
- CRESSIE N.A.C. (1991), Statistics for Spatial Data, New York : John Wiley. Zbl0799.62002MR1127423
- 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. Zbl0940.62109MR1702681
- 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. Zbl0364.62022MR501537
- DIGGLE P.J. (1983), Statistical Analysis of Spatial Point Patterns, Mathematics in Biology, London : Academic Press. Zbl0559.62088MR743593
- DIGGLE P.J. (1990), Time Series : A Biostatistical Introduction, Oxford : Oxford University Press. Zbl0727.62083MR1055357
- DIGGLE P.J., LIANG K-Y., ZEGER S.L. (1994), Analysis of Longitudinal Data, New York : Oxford University Press. Zbl1031.62002
- EFRON B. (1986), Double exponential families and their use in generalized linear regression, Journal of the American Statistical Association, 81, 709-721. Zbl0611.62072MR860505
- FAHRMEIR L., TUTZ G. (1994), Multivariate Statistical Modelling Based on Generalized Linear Models, Heidelberg : Springer-Verlag. Zbl0980.62052MR1284203
- 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. Zbl0940.62065
- GEYS H., MOLENBERGHS G., RYAN L.M. (1997), Pseudo-likelihood inference for clustered binary data, Communications in Statistics : Theory and Methods, 26, 2743-2767. Zbl0954.62530MR1605596
- 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. Zbl0825.62407
- 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. MR817573
- GILULA Z., HABERMAN S. (1994), Conditional log-linear models for analyzing categorical panel data, Journal of the American Statistical Association, 89, 645-656. Zbl0801.62088MR1294088
- GLONEK G.F.V., MCCULLAGH P. (1995), Multivariate logistic models, Journal of the Royal Statistical Society, Series B, 57, 533-546. Zbl0827.62059
- GOLDSTEIN H. (1986), Multilevel mixed linear model analysis using iterative generalized least squares, Biometrika, 73, 43-56. Zbl0587.62143MR836433
- GOLDSTEIN H. (1991), Nonlinear multilevel models, with an application to discrete response data, Biometrika, 73, 43-56. MR1118229
- GOLDSTEIN H. (1995), Multilevel Statistical Models (2nd edition), London : Edward Arnold. Zbl1014.62126
- GOLDSTEIN H., RASBASH J. (1996), Improved approximations for multilevel models with binary responses, Journal of the Royal Statistical Society A, 159, 505-513. Zbl1001.62518MR1413664
- 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. Zbl0826.62049
- 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. Zbl0813.62064MR1323346
- 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. Zbl0421.62080
- 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. Zbl0799.62063
- 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. Zbl0825.62509
- 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. Zbl1112.62307MR1856328
- LIANG K.-Y., ZEGER S.L. (1986), Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22. Zbl0595.62110MR836430
- 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. Zbl0775.62172MR1157713
- 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. Zbl0882.62059MR1424603
- LITTLE R.J.A., RUBIN D.B. (1987), Statistical Analysis with Missing Data, New York : John Wiley. Zbl1011.62004MR890519
- LONGFORD N.T. (1993), Random Coefficient Models, London : Oxford University Press. Zbl0859.62064MR1271143
- MCCULLAGH P., NELDER J.A. (1989), Generalized Linear Models, London : Chapman & Hall. Zbl0588.62104MR727836
- MOLENBERGHS G., DECLERCK L., AERTS M. (1998), Misspecifying the likelihood for clustered binary data, Computational Statistics and Data Analysis, 26, 327-349. Zbl1042.62620
- 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. Zbl0802.62063
- 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. Zbl0569.62094MR775399
- 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. Zbl0113.35101MR152062
- PINHEIRO J.C., BATES D.M. (2000), Mixed effects models in S and S-Plus, New-York : Springer-Verlag. Zbl0953.62065
- PLACKETT R.L. (1965), A class of bivariate distributions, Journal of the American Statistical Association, 60, 516-522. MR183042
- RIPLEY B.D. (1981), Spatial Statistics, New York : John Wiley. Zbl0583.62087MR624436
- 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. Zbl0702.62005MR1019836
- SCHALL R. (1991), Estimation in generalised linear models with random effects, Biometrika, 78, 719-727. Zbl0850.62561
- 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. Zbl0032.41903MR28539
- 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. Zbl0956.62055MR1880596
- WILLIAMS D.A. (1975), The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity, Biometrics, 31, 949-952. Zbl0333.62069
- WOLFINGER R., O'CONNELL M. (1993), Generalized linear mixed models : A pseudo-likelihood approach, Journal of Statistical Computing and Simulation 48, 233-243. Zbl0833.62067
- 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. MR1137101
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.