[R] Unrealistic dispersion parameter for quasibinomial

[Prof Brian Ripley]

For the record

> residuals(model)
           1           2           3           4           5
  5.55860143 -0.00073852  2.49255235 -1.41987341 -0.00042425
           6           7           8
-0.94389158  2.72987046 -1.15760836
> residuals(model, "pearson")
           1           2           3           4           5
  3.5362e+03 -5.2222e-04  2.3366e+00 -1.0080e+00 -2.9999e-04
           6           7           8
-8.8378e-01  2.4038e+00 -1.1646e+00
> fitted(model)
          1          2          3          4          5
1.5994e-08 5.0502e-09 4.9946e-01 1.5873e-02 3.2140e-09
          6          7          8
2.0924e-02 8.0191e-01 6.1900e-01

so according to the model a very rare event occurred.  That is what is
'unrealistic' (and Ben Bolker supposed correctly).

How dispersion should be estimated is a matter of some debate (see 
e.g. McCullagh and Nelder), but the model here is simply inadequate.


On Mon, 2 Mar 2009, Menelaos Stavrinides wrote:

> I am running a binomial glm with response variable the no of mites of two
> species y->cbind(mitea,miteb) against two continuous variables (temperature
> and predatory mites) - see below. My model shows overdispersion as the
> residual deviance is 48.81  on 5  degrees of freedom. If I use quasibinomial
> to account for overdispersion the dispersion parameter estimate is  2501139,
> which seems unrealistic. Any ideas as to why I am getting such a huge
> dispersion parameter?
>
>> y<-cbind(psmno,wsmno)
>> ldhours<-log(idhours+1)
>> lwpm<-log(wpm2wkb+1)
>> y
>     psmno wsmno
> [1,]     1     4
> [2,]     0    54
> [3,]     8     1
> [4,]     0    63
> [5,]     0    28
> [6,]     4   291
> [7,]    46     3
> [8,]   117    85
>> ldhours
> [1] 0.000000 2.308567 5.078473 4.875035 2.339399 3.723039 5.572344 5.250384
>> lwpm
> [1] 0.6931472 2.1972246 0.0000000 0.6931472 2.3025851 0.0000000 0.0000000
> [8] 0.0000000
>> model<-glm(y~ldhours+lwpm,binomial)
>> summary(model)
>
> Call:
> glm(formula = y ~ ldhours + lwpm, family = binomial)
>
> Deviance Residuals:
>         1           2           3           4           5           6
> 5.5586025  -0.0007385   2.4925511  -1.4198734  -0.0004242  -0.9438916
>         7           8
> 2.7298663  -1.1576062
>
> Coefficients:
>            Estimate Std. Error z value Pr(>|z|)
> (Intercept) -14.4029     1.3705 -10.509  < 2e-16 ***
> ldhours       2.8357     0.2656  10.677  < 2e-16 ***
> lwpm         -5.1188     1.4689  -3.485 0.000492 ***
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> (Dispersion parameter for binomial family taken to be 1)
>
>    Null deviance: 441.20  on 7  degrees of freedom
> Residual deviance:  48.81  on 5  degrees of freedom
> AIC: 70.398
>
> Number of Fisher Scoring iterations: 8
>
>> model2<-glm(y~ldhours+lwpm,quasibinomial)
>> summary(model2)
>
> Call:
> glm(formula = y ~ ldhours + lwpm, family = quasibinomial)
>
> Deviance Residuals:
>         1           2           3           4           5           6
> 5.5586025  -0.0007385   2.4925511  -1.4198734  -0.0004242  -0.9438916
>         7           8
> 2.7298663  -1.1576062
>
> Coefficients:
>            Estimate Std. Error t value Pr(>|t|)
> (Intercept)  -14.403   2167.435  -0.007    0.995
> ldhours        2.836    420.015   0.007    0.995
> lwpm          -5.119   2323.044  -0.002    0.998
>
> (Dispersion parameter for quasibinomial family taken to be 2501139)
>
>    Null deviance: 441.20  on 7  degrees of freedom
> Residual deviance:  48.81  on 5  degrees of freedom
> AIC: NA
>
> Number of Fisher Scoring iterations: 8
>
> Thanks,
> Mel
>
> -- 
> Menelaos Stavrinides
> Ph.D. Candidate
> Environmental Science, Policy and Management
> 137 Mulford Hall MC #3114
> University of California
> Berkeley, CA 94720-3114 USA
> Tel: 510 717 5249
>
> 	[[alternative HTML version deleted]]
>
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595