Extended-REML estimators

Restricted likelihood was originally introduced as the criterion for the estimation of dispersion components in normal mixed linear models. Lee & Nelder (2001a) showed that it can be extended to a much wider class of models via double extended quasi-likelihood. We give a detailed description of the new method and show that it gives an efficient estimation procedure for dispersion components.

[1]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[2]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[3]  John A. Nelder,et al.  Generalized linear models for the analysis of quality‐improvement experiments , 1998 .

[4]  John A. Nelder,et al.  Generalized linear models for the analysis of Taguchi-type experiments , 1991 .

[5]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[6]  P. McCullagh,et al.  Bias Correction in Generalized Linear Models , 1991 .

[7]  J. Nelder,et al.  An extended quasi-likelihood function , 1987 .

[8]  J. Nelder,et al.  Hierarchical Generalized Linear Models , 1996 .

[9]  D. Cox,et al.  Parameter Orthogonality and Approximate Conditional Inference , 1987 .

[10]  N. Breslow,et al.  Bias correction in generalised linear mixed models with a single component of dispersion , 1995 .

[11]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[12]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[13]  J. Nelder,et al.  Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions , 2001 .

[14]  S. Merhar,et al.  Letter to the editor , 2005, IEEE Communications Magazine.

[15]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[16]  Youngjo Lee,et al.  Modelling and analysing correlated non-normal data , 2001 .

[17]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[18]  John A. Nelder,et al.  The robustness of the quasilikelihood estimator , 1999 .

[19]  R. Schall.  Estimation in generalized linear models with random effects , 1991 .