Thanks for: Re: Under dispersion; Was: [R] binomial glm warnings revisited

[Tord Snall]

Dear Peter and Spencer,

I guess that you are busy with other things now. 

I just want to tell that I appreciated your help.

Thanks very much!


Sincerely,
Tord



At 15:04 2003-10-09 +0200, Peter Dalgaard BSA wrote:
>Tord Snall <tord.snall at ebc.uu.se> writes:
>
>>     Null deviance: 13.1931  on 269  degrees of freedom
>> Residual deviance:  9.9168  on 268  degrees of freedom
>> AIC: 13.917
>.
>
>> BUT, note the under dispersion. I GUESS it is because I have surveyed a
>> moss on marked trees at three occations (with two years in between). The
>> response 1 means that the moss has disappeared, and dbh is tree diameter.
>> (This corresponds to revisitng patients who has a disease, and whose weight
>> is unchanged between the visits. H0: weight does not affect tha chance of
>> recovery from the disease)
>
>Don't trust deviances as measures of dispersion with binary data! 
>
>> Here is a version with quasibinomial:
>> 
>.
>> 
>> Note, no warning.
>> 
>> I guess that this quasibinomial model is more reliable than the binomial.
>> Now I can trust the SE of the Estim. too, can't I? 
>
>No. Neither nor.
> 
>With binary data, the deviance is purely a function of the fitted
>parameters. It is the difference in -2 log L between a "perfect fit"
>and the observed fit. A perfect fit has a zero prob. where the obs is
>"0" and probability 1 where it is "1", and L == 1 identically in that
>case. Now consider the likelihood for the "complete toss-up" i.e.
>intercept and slope both equal to 0 so all probabilities are 0.5. The
>likelihood in that case is 0.5^269, i.e. a constant. Take logarithms
>and notice that the model deviance plus the change in deviance from
>the model to the "toss-up" model is constant (2*269*log(2) to be
>precise). So what appears to be a measure of residual error is
>really just a measure of how far the fitted probabilities are from
>0.5!
>
>
>-- 
>   O__  ---- Peter Dalgaard             Blegdamsvej 3  
>  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
> (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
>~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
>

-----------------------------------------------------------------------
Tord Snäll
Avd. f växtekologi, Evolutionsbiologiskt centrum, Uppsala universitet
Dept. of Plant Ecology, Evolutionary Biology Centre, Uppsala University
Villavägen 14			
SE-752 36 Uppsala, Sweden
Tel: 018-471 28 82 (int +46 18 471 28 82) (work)
Tel: 018-25 71 33 (int +46 18 25 71 33) (home)
Fax: 018-55 34 19 (int +46 18 55 34 19) (work)
E-mail: Tord.Snall at ebc.uu.se
Check this: http://www.vaxtbio.uu.se/resfold/snall.htm!