# Re: [R] dreaded p-val for d^2 of a glm / gam

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Thu, 27 Mar 2008 16:38:12 -0700

I assume you mean 'deviance', not 'squared deviance'; if the latter, then I have no idea.

If the former, then a short and fairly quick answer to your question is that 2*log(likelihood ratio) for nested hypotheses is approximately chi-square with numbers of degrees of freedom = the number of parameters in the larger model fixed to get the smaller model, under standard regularity conditions, the most important of which is that the maximum likelihood is not at a boundary.

For specificity, consider the following modification of the first example in the 'glm' help page:

```     counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
glm.D93 <- glm(counts ~ outcome + treatment, family=poisson())
glm.D93t <- glm(counts ~ treatment, family=poisson())
anova(glm.D93t, glm.D93, test="Chisq")

The p-value is not printed by default, because some people would
```
rather NOT give an answer than give an answer that might not be very accurate in the cases where this chi-square approximation is not very good. To check that, you could do a Monte Carlo, refit the model with, say, 1000 random permutations of your response variable, collect anova(glm.D93t, glm.D93)[2, "Deviance"] in a vector, and then find out how extreme the deviance you actually got is relative to this permutation distribution.
```      Hope this helps.
Spencer Graves
```

Monica Pisica wrote:
> OK,
>
> I really dread to ask that .... much more that I know some discussion about p-values and if they are relevant for regressions were already on the list. I know to get p-val of regression coefficients - this is not a problem. But unfortunately one editor of a journal where i would like to publish some results insists in giving p-values for the squared deviance i get out from different glm and gam models. I came up with this solution, but sincerely i would like to get yours'all opinion on the matter.
>
> p1.glm <- glm(count ~be+ch+crr+home, family = 'poisson')
>
> # count - is count of species (vegetation)
> # be, ch, crr, home - different lidar metrics
>
> # calculating d^2
> d2.p1 <- round((p1.glm[]-p1.glm[])/p1.glm[],4)
> d2.p1
> 0.6705
>
> # calculating f statistics with N = 148 and n=4; f = (N-n-1)/(N-1)(1-d^2)
> f <- (148-4-1)/(147*(1-0.6705))
> f
>  2.952319
>
> #calculating p-value
> pval.glm <- 1-pf(f, 147,143)
> pval.glm
>  1.135693e-10
>
> So, what do you think? Is this acceptable if i really have to give a p-value for the deviance squared? If it is i think i will transform everything in a fuction ....
>
> Thanks,
>
> Monica
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