[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)
http://tolstoy.newcastle.edu.au/R/help/02a/3721.html
http://www.commanster.eu/rcode.html
Cheers,
Simon.
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
Australia
T: +61 7 3365 2506
email: S.Blomberg1_at_uq.edu.au
http://www.uq.edu.au/~uqsblomb/
Policies:
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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