glm with binomial errors - problem with overdispersion

model <- glm(y ~ fragment+type, binomial)

Dear all,

I am new to R and my question may be trivial to you...
I am doing a GLM with binomial errors to compare proportions of species in
different categories of seed sizes (4 categories) between 2 sites.

In the model summary the residual deviance is much higher than the degree
of freedom (Residual deviance: 153.74  on 4  degrees of freedom) and even
after correcting for overdispersion by using a quasibinomial error structure
instead of binomial the residual deviance does not change. Is this a data
problem and I cannot use this statistic or is it because I do something
wrong with R (see models attached)?

Thanks a lot for your help!
Anna


first model with binomial error structure:

success<-c(14,43,44,1,13,28,56,8)
failure<-c(88,59,58,101,92,77,49,97)
"fragment"<-c(1,1,1,1,2,2,2,2)
"type"<-c(1,2,3,4,1,2,3,4)
y<-cbind(success,failure)
model<-glm(y~fragment*type,binomial)
summary(model)

Call:
glm(formula = y ~ fragment * type, family = binomial)

Deviance Residuals:
     1        2        3        4        5        6        7        8
-4.0175   3.3716   4.5052  -6.0071  -2.8063   0.5449   6.0414  -5.0184

Coefficients:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)    0.04433    0.61072   0.073   0.9421
fragment      -0.65477    0.39001  -1.679   0.0932 .
type          -0.46664    0.23027  -2.027   0.0427 *
fragment:type  0.26636    0.14455   1.843   0.0654 .
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

(Dispersion parameter for binomial family taken to be 1)

   Null deviance: 157.96  on 7  degrees of freedom
Residual deviance: 153.74  on 4  degrees of freedom
AIC: 196.31

Number of Fisher Scoring iterations: 5

second model with quasibinomial error structure:

summary(model2)

Call:
glm(formula = y ~ fragment * type, family = quasibinomial)

Deviance Residuals:
     1        2        3        4        5        6        7        8
-4.0175   3.3716   4.5052  -6.0071  -2.8063   0.5449   6.0414  -5.0184

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)    0.04433    3.63550   0.012    0.991
fragment      -0.65477    2.32169  -0.282    0.792
type          -0.46664    1.37073  -0.340    0.751
fragment:type  0.26636    0.86048   0.310    0.772

(Dispersion parameter for quasibinomial family taken to be 35.43628)

   Null deviance: 157.96  on 7  degrees of freedom
Residual deviance: 153.74  on 4  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

	[[alternative HTML version deleted]]

I presume you intended 'type' and 'fragment' to be factors (see below).  Such a model would fit exactly.  The additive model

model <- glm(y ~ fragment+type, binomial)

is only modestly over-dispersed, and shows that 'fragment' has zero effect.  Not 'a negligible effect', but no effect.  So something really odd is going on: is this an exercise with artificial data?
Otherwise you need to explain the exact balance between the two 'fragments' (each fragment has exactly 1/4 success) and your assumption of independent binomial sampling cannot be true.

Also note that success+failure is exactly 102 in fragment 1 and 105 in fragment 2, as is the sum of the successes for each fragment (of course it has to to make exactly 1/4). It is rather easy to suspect that it is actually a 0/1 coding of the type (as in "tick exactly one box"), and not independent binomial data.
 
sorry for the dumb question: so do you think, that my data is independent and the model appropriate?  
Thanks, Anna

--
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com