[R] Effect size in GLIM models

[Reader Tom]

Dear All

Thanks very much for the rapid reply Prof Ripley. I had been looking at
this anaysis for my colleague (Prof Behnke) and suggested that he
contact the R mailing list because I couldn't answer his question. I
think some of the detail got lost in translation (he grew up with the
GLIM package!). So here are some more details:

We are indeed following your guidelines in the MASS book, and using
glm.nb to analyse some data on the abundance of several parasite species
in mice. We proceeded with model selection as suggested, and we are
reasonably happy that we end up with decent models for our several
parasite species. 

The question that Prof Behnke asked is: if we fit similar models
(initial full models have the same factors and covariates) with
different response variables (abundances of different species of
parasite), is there a way of comparing the relative effect sizes of the
key explanatory variables across different models? For example, if we
find that the best models for two different species include the term
"sex", is there a way of determining if sex explains more of the
variance in parasite abundance in species A than in species B? 

In a simple ANOVA with Guassian errors, we might compare the percentage
variance explained. We could also look at the overall r^2 for the models
and determine how well (relatively) our different models perform. We
might end up concluding that for species A, we have found the most
important biolgoical factors explaining parasite abundance, but that for
species B we have yet to explain a large proportion of the variance.

Is there something similar we can do with our glm.nb models? Clearly the
coefficients will tell us about relative effect sizes WITHIN a given
model, but what can we do when comparing completely different response
variables?!

Regards

Tom Reader

-----Original Message-----
From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] 
Sent: 17 January 2007 14:02
To: Behnke Jerzy
Cc: r-help at stat.math.ethz.ch; Reader Tom
Subject: Re: [R] Effect size in GLIM models

On Wed, 17 Jan 2007, Behnke Jerzy wrote:

> Dear All,
> I wonder if anyone can advise me as to whether there is a consensus as

> to how the effect size should be calculated from GLIM models in R for 
> any specified significant main effect or interaction.

I think there is consensus that effect sizes are not measured by
significance tests.  If you have a log link (you did not say), the model
coefficients have a direct interpretation via multiplicative increases
in rates.

> In investigating the causes of variation in infection in wild animals,

> we have fitted 4-way GLIM models in R with negative binomial errors.

What exactly do you mean by 'GLIM models in R with negative binomial
errors'?  Negative binomial regression is within the GLM framework only
for fixed shape theta. Package MASS has glm.nb() which extends the
framework and you may be using without telling us.  (AFAIK GLIM is a
software package, not a class of models.)

I suspect you are using the code from MASS without reference to the book
it supports, which has a worked example of model selection.

> These are then simplified using the STEP procedure, and finally each 
> of the remaining terms is deleted in turn, and the model without that 
> term compared to a model with that term to estimate probability

'probability' of what?

> An ANOVA of each model gives the deviance explained by each 
> interaction and main effect, and the percentage deviance attributable 
> to each factor can be calculated from NULL deviance.

If theta is not held fixed, anova() is probably not appropriate: see the
help for anova.negbin.

> However, we estimate probabilities by subsequent deletion of terms, 
> and this gives the LR statistic. Expressing the value of the LR 
> statistic as a percentage of 2xlog-like in a model without any 
> factors, gives lower values than the former procedure.

I don't know anything to suggest percentages of LR statistics are
reasonable summary measures.  There are extensions of R^2 to these
models, but AFAIK they share the well-attested drawbacks of R^2.

> Are either of these appropriate? If so which is best, or alternatively

> how can % deviance be calculated. We require % deviance explained by 
> each factor or interaction,  because we need to compare individual 
> factors (say host age) across a range of infections.
>
> Any advice will be most gratefully appreciated. I can send you a 
> worked example if you require more information.

We do ask for more information in the posting guide and the footer of
every message.  I have had to guess uncomfortably much in formulating my
answers.

> Jerzy. M. Behnke,
> The School of Biology,
> The University of Nottingham,
> University Park,
> NOTTINGHAM, NG7 2RD
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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