You've already asked this question and gotten answers (from "marKo" and
Chris Howden), but I'll add these points:

* for a non-binary GLMM (which seems to be your case), the sum of the
squared Pearson residuals should be *approximately* chi-square distributed
(subject also to various guesses about the appropriate calculation for the
residual degrees of freedom) (not sure where you got your number 952.5 from
-- the sum of squares of the deviance residuals should also work adequately)

*  You got zero because your fit is very bad, i.e. the probability of the
observed (or more extreme) statistic is *very* small.  A more accurate
version of 1-pchisq(952.5144 , df=251) is
pchisq(952.5144,df=251,lower.tail=FALSE)  which tells you the p-value is
10^{-82} (you may also want `log.p=TRUE` for even more extreme p-values).

* Chris Howden is probably right that your GLM and GLMM fits are probably
similar because your random effects variance has collapsed to zero.

* possibly most important: I think it would be a VERY bad idea to draw any
conclusions whatsoever from this model before you inspect the data and the
graphical model diagnostics to try to see what's giving you so much
overdispersion/such a bad fit (see http://rpubs.com/bbolker/glmmchapter for
examples)



On Thu, Jul 31, 2014 at 5:53 PM, Yuki Fujita <fujyu654@student.otago.ac.nz>
wrote:

> Hi
>
>
> I need a help with testing goodness of fit for Generalized linear mixed
> model.
>
> It seems there is no solid way of doing it, but I'd like to make sure the
> model is a good fit.
>
>
> My model is
>
>
> model1 <- glmer(cbind(CorrectHits,12-CorrectHits)~ ADHDYN*Condition + (1
> |ï..ID),
>                 data = bert, family="binomial")
>
>
> where ADHDYN has a 2 levels and 3 levels in Condition, and interaction.
> (so 6 fixed effect parameters). We have allowed random inetrcept for
> individuals. The number of observation is 258.
>
>
> I tried to carry our the goodness of fit test by using chi-square test,
> but I get 0 as a answer so I am not sure if I did right.
>
> # The degrees of freedom is obtained by number of obs - number of fixed
> params
> df <- length(bert$ï..ID)-6;df
> 1-pchisq(952.5144 , df=251) # The output was 0
>
>
> Any better way of testing the goodness of fit?
>
>
> We carried out the same model but with glm, but we want to compare which
> model gives us smaller Satandard error. The estimate of coefficients were
> very similay between GLm and GLMM models.
>
>
> Thanks in advance
>
> Yuki
>
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>
>
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