[R-sig-eco] deviance as a goodness of fit in GLM

[Bob O'Hara]

On 21/07/14 19:52, Samantha PameLa wrote:
> Good day everybody,
>   
> I'm a marine biologist student, working on my bachelor thesis and I'm stucked with a statistical doubt in the process, I hope someone here could help me. My thesis aims to understand which biological and environmental factors influences the male aggressive rate of male California sea lions. For that purpose I'm using GLM’s where the response variable is the male aggressive rate. Right now I am testing the goodness of fit of the global models and for that I'm using the deviances as a goodness of fit test. I calculated pseudoR2 (Zuur, 2009) in order to know the percentage of explanation of each candidate model. However I’m not sure how to choose the “good models”; since I am not sure over which percent of explanation indicates a “model with good fit”. For my data I am working with three different scenarios, and it seems that 20%, is a good value to could indicate the best models, but I’m not sure how to choose the value.
>   
> I thank you in advance for your time and the help you can give me.
>   
> Best regards,
>   
Just to follow up, AIC isn't a measure of model fit either: it's a 
measure of model adequacy, and can be used to compare different models.

For model fit, you can (usually) compare the residual deviance to the 
degrees of freedom (they should be approximately equal, and you can use 
a chi-squared test, if you feel the need to generate a p-value). This 
doesn't work if your response is binomial with a small N (and psuedo R2 
doesn't work terribly well for this case either).

A better approach to checking if the model fits is to check to see if 
the residuals have any gross patterns in them, by plotting them against 
the fitted values and also against covariates.

If you'll excuse my self-promotion, PNAS recently gave me an excuse to 
show some residual plots to the general public: 
<http://www.theguardian.com/science/grrlscientist/2014/jun/04/hurricane-gender-name-bias-sexism-statistics> 
(my explanation for why this is not just gratuitous self-promotion is 
that I linked to the R code to generate the plots too, so you have 
something to work from).

Bob

-- 

Bob O'Hara

Biodiversity and Climate Research Centre
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