[R-sig-ME] John Nelder and Nelder-Lee HGLMs

Murray Jorgensen maj at waikato.ac.nz
Mon Nov 1 00:34:22 CET 2010

Roger Payne's obituary for John Nelder may be found at


There can be no doubt that John Nelder has changed the face of modern 
statistics with his work on linear models and generalized linear models 
which form the core of the Genstat package and were central in the 
development of S and R.

I want to draw the attention of this Sig to the following passage in the 
obituary in which GLMMs are criticised.

John’s other major activity at Imperial College was his collaboration 
with Youngjo Lee to develop the theory of hierarchical generalized 
linear models (HGLMs); see the papers by Lee & Nelder (1996, 2001, 2006) 
and the book by Lee, Nelder & Pawitan (2006). The 1996 and 2006 papers 
were presented as “read papers” at meetings of the Royal Statistical 
Society; it is impressive to note that John was 81 years old when he and 
Youngjo presented the 2006 paper. HGLMs aimed to provide satisfactory 
methods of analysis for non-Normal data when there is more than one 
source of random variation. John viewed generalized linear models as a 
way of liberating statisticians from the “tyranny” of the Normal 
distribution, and was a little bemused to see this same tyranny 
reestablished in methods that were devised initially to extend 
generalized linear models. These generalized linear mixed models (GLMMs) 
catered for additional random variation by adding additional 
Normally-distributed random effects into the linear model of the 
generalized linear model. John and Youngjo’s new HGLMs extended the 
methodology to include the beta-binomial, gamma and inverse-gamma 
distributions, and showed that the conjugate HGLMs (namely binomial GLM 
with additional beta-binomial random effects, or Poisson with gamma, or 
gamma with inverse gamma) had attractive advantages in their 
mathematical theory, computing algorithms and philosophical 
interpretation. HGLMs can be fitted very efficiently by two interlinked 
generalized linear models. So we have access to a familiar repertoire of 
model checking techniques, and can base our choice of error 
distributions on the data rather than on prejudice or software 
limitations. Furthermore the analysis can still be carried out 
interactively – always a very important consideration for John.

I have some difficulties with the views of this paragraph and wish to 
make some comments. Firstly HGLMs do allow added flexibility to the 
modelling of non-normal data by allowing for non-normal distributions of 
random effects. However unless there is knowledge about the about the 
nature of the random effect distributions from the context of the 
application this flexibility just adds problems by allowing a much 
larger model space within which to choose and estimate a model.

Secondly Nelder and Lee do not use standard likelihood or Bayesian 
methods to fit their HGLMs but instead develop another construction 
called h-likelihood. It is a while since I tried to look at these but I 
remember being reminded of the 'classification likelihood' approach to 
finite mixture modelling where assignments of data to components were 
treated as parameters to be estimated along with the component 
parameters and mixing proportions. A number of papers have commented 
that this is not a good idea, for example
   author  = {Little, R. J. A. and Rubin, D. B.},
   title   = {On jointly estimating parameters and
missing data by maximizing the complete data likelihood},
   journal = {Amer. Statist.},
   volume  = {37},
   number  = {},
   pages   = {218-220},
   year    = {1983}

I wonder if members of this list can point me to discussions, critical 
or supportive, of Lee and Nelder's models and methods. Of course I am 
aware of the discussion of their JRSS paper so you needn't remind me of 

Also, is anyone aware if someone is planning to implement HGLMs, by any 
estimation method, in R?

Best wishes,  Murray

Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441   Mobile 021 0200 8350

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