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Original Articles

Extensions of multiple linear regression

&
Pages 2033-2053 | Received 01 May 1999, Published online: 27 Jun 2007

References

  • Aitkin , M. , Anderson , D. , Francis , B. and Hinde , J. 1989 . Statistical Modelling in GLIM , Oxford : Oxford University Press .
  • Aitkin , M. 1999 . “A general maximum likelihood analysis of variance components in genefalized linear models” . Biometrics , 55 : 117 – 128 .
  • Breslow , N.E. and Clayton , D.G. 1993 . “Approximate inference in generalized linear models” . J. Amer. Statist. Assoc , 88 : 9 – 25 .
  • Candy , S.G. 1985 . “Using factors in composite link function models” . GLIM Newsletter , 11 : 24 – 27 .
  • Candy , S.G. 1997 . “Estimation in forest yield models using composite link functions with random effects” . Biometrics , 53 : 146 – 160 .
  • Carey , V.C. , Zeger , S.L. and Diggle , P.J. 1993 . “Modelling multivariate binary data with alternating logistic regressions” . Biometrika , 80 : 517 – 526 .
  • Chiou , J.M. and Müller , H.G. 1998 . “Quasi–likelihood regression with unknown link and variance functions” . J. Amer. Statist. Assoc , 93 : 1376 – 1387 .
  • Clayton , D.G. . Repeated ordinal measurements: a generalized estimating equation approach . Technical report . 24-27 1995 . Cambridge, UK : Medical Research Council Biostatiostics Unit .
  • Clayton , D.G. 1996 . “Generalized Linear Mixed Models” . In Markov Chain Monte Carlo Methods in Practice , Edited by: Gilks , W.R. , Richardson , S. and Spiegelhalter , D.J. London : Chapman and Hall .
  • Cnann , A. , Laird , N.M. and Slasor , P. 1997 . “Using the general linear mixed modie to analyse unbalanced repeated measures and longitudinal data” . Statist. Med , 16 : 2349 – 2380 .
  • Cox , C. 1984 . “Generalized linear models – the missing link” . Appl. Statist , 33 : 18 – 24 .
  • Cox , D.A. and Snell , E.J. 1989 . Analysis of Binary Data , London : Chapman and Hall .
  • Crowder , M.J. 1985 . “Gaussian estimation for correlated binomial data” . J.R.Statist.Soc.(B) , 47 : 229 – 237 .
  • Crowder , M.J. 1987 . “On linear and quadratic estimating functions” . Biometrika , 74 : 591 – 597 .
  • Crowder , M.J. 1992 . “Contribution to the discussion of Liang, Zeger and Qaqish” . J.R.Statist. Soc. (B) , 53 : 3 – 40 .
  • Crowder , M.J. 1995 . “On the use of a working correlation; matrix in using generalized linear models for repeated measures” . Biometrika , 82 : 407 – 410 .
  • Dempster , A.P. , Laird , N.M. and Rubin , D.B. 1977 . “Maximurn likelihood from incomplete data” . J.R. Statist, Soc. (B) , 39 : 1 – 38 .
  • Diggle , P.J. , Liang , K.Y. and Zeger , S.L. 1994 . Analysis of Longitudinal Data , Oxford : Oxford University Press .
  • Dobson , A.J. 1990 . Am Introduction to Generalzed Linear Models , London : Chapman and Hall .
  • Draper , N. and Smith , H. 1998 . Applied Regression Analysis , New York : Wiley .
  • Dunlop , D, . 1994 . “Regression for longitudinal data: a bridge from least squares regression” . Am. Statist , 48 : 299 – 303 .
  • Engel , B. and Keen , A. 1994 . “A simple approach for the analysis of generalized linear mixed models” . Statistica Nederlandica , 48 : 1 – 22 .
  • Fabrmeir , L. and Tutz , G. 1994 . Multivariate Statistical Modelling Based on Generalized Linear Models , New York : Springer–Verlag .
  • Firth , D. 1987 . “On the efficiency of quasi–likelihood estimation” . Biometrika , 74 : 233 – 245 .
  • Firth , D. 1991 . “Generalized Linear Models” . In Statistical Theory and Modelling: In Honour of Sir David Cox , Edited by: Hinkley , D. , Reid , N. and Snell , E. London : Chapman and Hall .
  • Fitzmaurice , G.M. , Laird , N.M. and Rotnitzky , A.G. 1993 . “Regression models for discrete longitudinal responses” . Statistical Science , 8 : 284 – 309 .
  • Gilmour , A.R. , Thompson , R. and Cullis , B,R. 1995 . “Average information REML an efficient algorithm for variance parameter estimation in linear mixed models” . Biometrics , 51 : 1440 – 1450 .
  • Goldstein , H. 1995 . Multilevel Statistical Models , London : Edward Arnold .
  • Green , P.J. 1984 . “Iterative reweighted least squares for maximum likelihood estimation and some robusst alternatives” . J.R.Statist. Soc. (B) , 46 : 149 – 192 .
  • Grizzle , J.E. , Starmer , C.F. and Koch , G.G. 1969 . “Analysis of categorical data by linear models” . Biometrics , 25 : 489 – 504 .
  • Härdle , W. , Manmmen , E. and Müller , M. 1998 . “Testing parametric Versus semiparametric modeling in generalized linear models” . J. Amer. Statist. Assoc , 93 : 1461 – 1474 .
  • Harville , D. 1977 . “Maximum likelihood approaches to variance components estimation and to related probles” . J. Amer. Statist. Assoc , 72 : 320 – 340 .
  • Henderson , C.R. 1975 . “Best linear unbiased estimation and prediction under a selection models” . Biometrics , 31 : 423 – 447 .
  • Heyde , C.C. 1997 . Quasi–Likelihood and Its Application: a General Approach to Optimal Parameter Estimation , New York : Springer–Verlag .
  • Hinde , J. 1982 . “Compound Poisson regression models” . In GLIM 82 Proceedings of the International Conference on Generalized Linear Models , Edited by: Gilchrist , R. 109 – 121 . New York : Springer–Verlag .
  • Ibrahim , J.G. and Land , P.W. 1991 . “On Bayesian analysis of generalized linear models using Jeffrey's prior” . J. Amer. Statist. Assoc , 86 : 981 – 986 .
  • Jennrich , R. 1984 . “Contribution to the discussion of Green” . J.R. Statist. Soc (B) , 46 : 182 – 182 .
  • Jorgensoen , B. 1997 . The Theory of Dispersion Models , London : Chapman and Hall .
  • Kenward , M.G. , Lesaffre , E. and Molenbertglis , G. 1994 . “An application of maximum likelihood and generalized estimating equation to the analyssi of ordinal data from a longitudinal study with cases missing at random” . Biometrics , 50 : 945 – 953 .
  • Koch , G.G. , Landis , J.R. , Freeman , J.L. , Freeman , D.H. and Lahnen , R.G. 1977 . “A general methodology for the analyusis of repeated measurements of categorical data” . Biometrics , 33 : 133 – 158 .
  • Laird , N.M. and Ware , J.H. 1982 . “Random–effects models for longitudinal data” . Biometrics , 38 : 963 – 974 .
  • Laird , N.M. 1996 . “Longitudinal pancl data: an overview of current methodology” . In Time Series Models in Econometrics, Finance and Other Fields , Edited by: Cox , D.A. , Hinkeley , D. and Barndorff , O. London : Champman and Hall .
  • Lee , Y. and Nelder , J.A. 1996 . “Hierarchical generalized linear models” . J,.R. Statists. Soc. (B) , 58 : 619 – 678 .
  • Li , B. 1998 . “An optimal estimating equation based on the first three cumulants” . Biometrika , 85 : 103 – 114 .
  • Liang , K.Y. and Zeger , S.L. 1986 . “Longitudinal data analysis using generalized linear models” . Biometrika , 73 : 13 – 22 .
  • Liang , K.Y. , Zeger , S.L. and Qaqish , B. 1992 . “Multivariate regression analyses for categorical data” . J.R. Statist. Soc. (B) , 53 : 3 – 40 .
  • Lindsey , J.K. 1996 . Parametric Statistical Inference , Oxford : Oxford University Press .
  • Lindsey , J.K. 1997 . Applying Generalized Linear Models , New York : Springer–Verlag .
  • Longford , N.T. 1993 . Random Coeffiecient Models , Oxford : Oxford University Press .
  • Mallick , B.K. and Gelfamd , A.E. 1994 . Generalized linear models with unknown link functions . Biometrika , 81 : 109 – 142 .
  • Mccullagh , P. 1980 . “Regression models for ordinal data” . J.R. Statist. Soc. (B) , 42 : 109 – 142 .
  • Mccullagh , P. and Nelder , J.A. 1989 . Generalized Linear Models , London : Chapman and Hall .
  • Mcgilghrist , C.A. and Yau , K. 1995 . “The derivation of BLUP, ML, REML estimation methods for generalized linear models” . Commun. Statist.–Theory Meth , 24 : 2963 – 2980 .
  • Nelder , J.A. 1998 . “A large class of models derived from generalized linear models” . Statist. Med , 17 : 2747 – 2753 .
  • Nelder , J.A. and Pregibon , D. 1987 . “An extended quasi–likelihood function” . Biometrika , 74 : 221 – 232 .
  • Nelder , J.A. and Wedderburn , R.W.M. 1972 . “Generalized linear models” . J.R. Statist. Soc. (A) , 135 : 370 – 383 .
  • Paik , M.C. 1992 . “Parametric variance funtion estimation for nonnormal repeated measurements data” . Biometrics , 48 : 19 – 30 .
  • Patterson , H.D. and Thompson , R. 1971 . “Recovery of inter–block infromation when the block sizes are unequal” . Biometrika , 58 : 545 – 554 .
  • Pepe , M.S. and Anderson , G.L. 1994 . “A cautionary note on inference for marginal regression models with logitudinal data and general correlated response data” . Commun. Statist.–Theory Meth , 23 : 939 – 951 .
  • Pregibon , D. 1980 . “Goodness of link tests for generalized linear models” . Appl. Statist , 29 : 15 – 24 .
  • Prentice , R.L. 1976 . “Generalization of the probit and logit methods for dose response curves” . Biometrics , 32 : 761 – 768 .
  • Prentice , R.L. 1988 . “Correlated binary regression with covariates specific to each binary observation” . Biometrics , 44 : 1033 – 1048 .
  • Rigby , R.A. and Stasinopoulos , D.M. 1996 . “Mean and Dispersion Additive Models” . In Statistical Theory and Computational Aspects of Smoothing , Edited by: Härdle , W. and Schimek , M.G. 215 – 230 . Heidelberg : Physica–Verlag .
  • Robinson , D. 1987 . “Estimation and use of variance components” . The Statistician , 36 : 3 – 14 .
  • Robinson , G.K. 1991 . “That BLUP is a good thing: the estimation of random effects” . Statistical Science , 6 : 15 – 51 .
  • Roger , J.H. 1985 . “Nearly linear models using general link functions” . In Generalized Linear Models, Proceedings, Lancaster 1985 , Edited by: Gilchrist , R. , Francis , B. and Whittaker , J. 147 – 159 . New York : Springer–Verlag .
  • Scallan , A.J. 1985 . “Maximum likelihood estimation for a Normal/Laplace mixture distribution” . Statistician , 41 : 227 – 231 .
  • Scallan , A.J. 1995 . “Fitting autoregressive processes in GLIM” . The GLIM Newsletter , 9 : 17 – 222 .
  • Schall , R. 1991 . “Estimation in generalized linear models with random effects” . Biometrika , 78 : 719 – 727 .
  • Seber , G.A.F. 1977 . Linear Regressin Analysis , New York : Wiley .
  • Sharples , K. and Breslow , N.E. 1992 . “Regression analysis fo correlated binary data: some small sample results for the estimating equation approach” . J. Statist. Comput. Simul , 42 : 1 – 20 .
  • Smith , D.M. and Morgan , B.J.T. 1989 . “Extended models for Wadley's problem” . GLIM Newsletter , 18 : 21 – 28 .
  • Smyth , G.K. 1989 . “Generalized linear models with varying dispersion” . J.R. Statisti. Soc (B) , 51 : 47 – 60 .
  • Styan, G.P.H. (1968). “Inference in multivariate normal populations with structure. Part 1: inference when correiations are known.” Teclinical report, Department of Statistics, University of Minnesota, USA.
  • Thompson , R. 1980 . “Maximum likelihood estimation of variance components” . Math. Operationsforsch. Statist., Series Statistics , 11 : 545 – 561 .
  • Thompson , R. and Baker , R.J. 1981 . “Composite link functins in generalized linear models” . Appl. Statist , 30 : 125 – 131 .
  • Tjur , T. 1998 . “Nonlinear regression quasi likelihood and overdispersion in generalized linear models” . Ann. Statist , 52 : 222 – 227 .
  • Verbyla , A.P. 1990 . “A conditional derivation of residual maximum likelihood” . Austral. J. Statist , 32 : 227 – 230 .
  • Verbyla , A.P. 1993 . “Modelling variance heterogeneity: residual maximum likelihood and diagnostics” . J.R. Statist. Soc. (B) , 55 : 493 – 508 .
  • Ware , J.H. 1985 . “Linear models for the analysis of longitudinal studies” . Am. Statist , 39 : 95 – 101 .
  • Wedderburn , R.W.M. 1974 . “Quasi–likelihood funtions generalized linear models and the Gauss–Newton method” . Biometrika , 61 : 439 – 447 .
  • West , M. , Harrison , P.J. and Migon , H.S. 1985 . “Dynamic generalized linear models and Bayesian forecasting” . J. Amer. Statist. Assoc , 80 : 73 – 97 .
  • Wolfinger , R.D. 1996 . “Heterogeneous variance–covariance structures for repeated measures” . J. Agr., Biol.Env.Statist , 1 : 205 – 230 .
  • Wolfinger , R.D. and Oconnell , M. 1993 . “Generalized linear mixed models: a pseudo–likelihood approach” . J. Statist. Comput. Simul , 48 : 233 – 243 .
  • Zeger , S.L. and Karim , M.R. 1991 . “Generalized linear models with random effects: a Gibbs sampling approach” . J. Amer. Statist. Assoc , 86 : 79 – 86 .
  • Zeger , S.L. and Liang , K.Y. 1986 . “Longitudinal data analysis for discrete and continuous outcomes” . Biometrics , 42 : 121 – 130 .
  • Zhao , L.P. and Prentice , R.L. 1990 . Correlated binary regression using a quadratic exponential model . Biometrika , 77 : 642 – 648 .

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