[R-sig-ME] Fidelity data - false convergence problem - use of glm instead of glmer

[Douglas Bates]

On Wed, Mar 9, 2011 at 11:41 AM, Julia Sommerfeld
<Julia.Sommerfeld at utas.edu.au> wrote:
> OK, glm instead of lmer.

> Now, if I do understand this correctly, a GLM with a binary response is
> still based on a logistic regression (family binomial). Thus, the
> interpretation of the summary ouput (intercept, z-value, plogis, etc) is the
> same as in lmer? Except that I also obtain values of the null deviance and
> residual deviance?

Yes.  And you don't have an estimate for the standard deviation of the
random effects because there are no random effects.

> anova(fm5,fm4,test="Chsiq") computes the analysis of deviance table (null
> deviance vs. residual deviance?). And we're not talking any longer about a
> LRT?

That is a likelihood ratio test comparing the residual deviance from
the two models.   The "null deviance" is the deviance that would be
calculated for a trivial model (all probabilities are equal) and is
not of interest here.

> Apologies for the lame question - you mentioned the deviance in your
> previous email, but I'm still having some trouble in understanding the anova
> function in this case: Why does the model incl. SameMate~BreedSuc1+Sex
> differs significantly from SameMate~Sex?

> Analysis of Deviance Table
>
> Model 1: SameMate ~ Sex
> Model 2: SameMate ~ BreedSuc1 + Sex
>   Resid. Df   Resid. Dev  Df  Deviance P(>|Chi|)
> 1            61     58.200
> 2            60     53.602       1    4.5982   0.03200 *
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Does this mean that the model incl. BreedSuc1+Sex fits better than the model
> without BreedSuc1? Why if BreedSuc1 apparently doesn't influence SameMate?

This is indicating that BreedSuc1 has a significant effect on the
probability of SameMate.  The p-value here is slightly different from
the p-value for the z statistic.  This one is more reliable.

>
>> summary(fm)
>
> Call:
> glm(formula = SameMate ~ BreedSuc1 + Sex, family = binomial,
>    data = DSS1)
>
> Deviance Residuals:
>    Min       1Q   Median       3Q      Max
> -2.2500   0.3445   0.4072   0.7283   0.8453
>
> Coefficients:
>                   Estimate   Std. Error  z value  Pr(>|z|)
> (Intercept)   0.8453      0.5159     1.638     0.1013
> BreedSuc1  1.6030      0.8325     1.925     0.0542 .
> SexM           0.3463     0.6912      0.501    0.6164
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> (Dispersion parameter for binomial family taken to be 1)
>
>    Null deviance:     58.352  on 62  degrees of freedom
> Residual deviance: 53.602  on 60  degrees of freedom
> AIC: 59.602
>
> Number of Fisher Scoring iterations: 5
>
> Thanks
>
> Julia
>
>
>
>
> 2011/3/8 Douglas Bates <bates at stat.wisc.edu>
>
>> On Tue, Mar 8, 2011 at 10:57 AM, Julia Sommerfeld
>> <Julia.Sommerfeld at utas.edu.au> wrote:
>> > Dear Douglas,
>>
>> > Thanks for your help - very much appreciated. Setting the verbose=TRUE
>> > unfortunately doesn't fix the problem either. Please find attached a csv
>> > file containing the data and the script. It would be great if you could
>> have
>> > a look at this.
>>
>> > I've also tried to run MCMCglmm:
>>
>> > mate<-MCMCglmm(SameMate~BreedSuc1+Sex,random=~Bird, data=DSS1,
>> nitt=100000,
>> > family="categorical")
>>
>> > However, every time I run MCMCglmm I get different results for exactly
>> the
>> > same data, i.e. sometimes the p value is significant, sometimes it is
>> not...
>>
>> The problem is that the estimate of the standard deviation of the
>> random effects is so poorly determined because most birds only have
>> one observation.  After the na.omit operation you have 63 observations
>> on 55 birds.  47 of the birds have only one observed, binary response.
>>  That is simply not enough information to determine parameter
>> estimates with any precision.
>>
>> If you look at the different fits for the model with BreedSuc1 in it
>> you will see that the estimate of the standard deviation of the random
>> effects bounces all over the place at essentially the same value of
>> the deviance (about 53.6).  It can be anywhere from 0.21 to 0.70 and
>> produce values of the deviance that are very close to one another.
>> This means that it is not determined with any precision at all.
>> Similarly for the second model a deviance of 59.5 can be achieved with
>> values of the standard deviation ranging from 0.49 to 1.14.
>>
>> Your model is overparameterized.  i would suggest using a glm instead
>> of a glmm and omit the random-effects term.  Notice that the deviance
>> from the glm fits is essentially the same as the deviance from the
>> glmer fits.  This indicates that the standard deviation of the random
>> effects is not significantly different from zero.
>>
>
>
>
>
> --
> Julia Sommerfeld - PhD Candidate
> Institute for Marine and Antarctic Studies
> University of Tasmania
> Private Bag 129, Hobart
> TAS 7001
>
> Phone: +61 458 247 348
> Email: julia.somma at gmx.de
> Julia.Sommerfeld at utas.edu.au
>
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