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

Simon Blomberg s.blomberg1 at uq.edu.au
Mon Nov 1 01:41:15 CET 2010

Jim Lindsey has a function for HGLMs called hnlmix in his "repeated" 
package (non-CRAN)





On 01/11/10 09:34, Murray Jorgensen wrote:
> Roger Payne's obituary for John Nelder may be found at
> http://www.vsni.co.uk/home-pages/john-nelder/
> 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.
> <quote>
> 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.
> </quote>
> 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
> @ARTICLE{lr83,
>   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 that.
> Also, is anyone aware if someone is planning to implement HGLMs, by 
> any estimation method, in R?
> Best wishes,  Murray

Simon Blomberg, BSc (Hons), PhD, MAppStat, AStat
Lecturer and Consultant Statistician
School of Biological Sciences
The University of Queensland
St. Lucia Queensland 4072
T: +61 7 3365 2506
email: S.Blomberg1_at_uq.edu.au

1.  I will NOT analyse your data for you.
2.  Your deadline is your problem

Statistics is the grammar of science - Karl Pearson.

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