[R] Strange results with anova.glm()

[Gustaf Granath]

Hi,
I have been struggling with this problem for some time now. Internet, 
books haven't been able to help me.

## I have factorial design with counts (fruits) as response variable.
 > str(stubb)
'data.frame': 334 obs. of 5 variables:
$ id : int 6 23 24 25 26 27 28 29 31 34 ...
$ infl.treat : Factor w/ 2 levels "0","1": 2 2 2 2 1 1 1 2 1 1 ...
$ def.treat : Factor w/ 4 levels "1","2","3","4": 2 3 1 3 3 3 2 2 3 1 ...
$ initial.size : num 854 158 256 332 396 ...
$ tot.fruit : int 45 8 19 8 10 7 4 7 2 6 ...

## I fit a glm model with initial.size as a covariate, and 
family=quasipoisson. I want to test if infl.treat or def.treat had an 
effect on tot.fruits. (i.e if different cutting treatments of the plants 
had an effect on total ## number of fruits).
## After model testing etc, I ended up with the following model:

 > model<-glm(tot.fruit ~ infl.treat + def.treat + initial.size, 
quasipoisson)
 > summary(model)
Call: glm(formula = tot.fruit ~ infl.treat + def.treat + initial.size,
family = quasipoisson)

Deviance Residuals:
Min 1Q Median 3Q Max
-6.1541 -2.1872 -0.7045 0.9926 7.5629

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.8788185 0.1093306 17.185 < 2e-16 ***
infl.treat1 -0.2456909 0.0924677 -2.657 0.00827 **
def.treat2 -0.1478382 0.1277139 -1.158 0.24788
def.treat3 -0.0780282 0.1207796 -0.646 0.51871
def.treat4 -0.2581576 0.1221538 -2.113 0.03532 *
initial.size 0.0013834 0.0000993 13.931 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasipoisson family taken to be 6.845172)

Null deviance: 3261.5 on 333 degrees of freedom
Residual deviance: 2131.6 on 328 degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

## It seems like both infl.treat and def.treat have an effect. However, 
when I do an ANOVA table. It shows no effect at all of infl.treat!!!! I 
find that very peculiar since I only have two levels of that factor. ## 
Shouldn't it be a significant effect also in the ANOVA table?? In fact. 
It is not even close to significant - 0.886!!
 > anova(model, test="F")
Analysis of Deviance Table
Model: quasipoisson, link: log
Response: tot.fruit
Terms added sequentially (first to last)

Df Deviance Resid. Df Resid. Dev F Pr(>F)
NULL 333 3261.5
infl.treat 1 0.1 332 3261.4 0.0205 0.88632
def.treat 3 58.3 329 3203.1 2.8376 0.03814 *
initial.size 1 1071.4 328 2131.6 156.5253 < 2e-16 ***

## If I do a ML test with a model with infl.treat and one without. The 
infl.treat is also significant and should be in the model!!
 > anova(model,model2, test="F")
Analysis of Deviance Table

Model 1: tot.fruit ~ infl.treat + def.treat + initial.size
Model 2: tot.fruit ~ def.treat + initial.size
Resid. Df Resid. Dev Df Deviance F Pr(>F)
1 328 2131.65
2 329 2180.40 -1 -48.75 7.1221 0.007992 **
## What is going on here?? I thought the ANOVA table would give me a 
quite similar result because I only have two levels (of the infl.treat 
factor) and no interactions in the model.
## I'm afraid I have missed something trivial though so please, be gentle ;)

Cheers,

Gustaf Granath

-- 
Gustaf Granath (PhD student)
Dept of Plant Ecology
Evolutionary Biology Centre (EBC)
Uppsala University