[R] Effect size in GLIM models

[Prof Brian Ripley]

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
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-- 
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