R help - Nov 2010 - d.f. in F test of nested glm models

Dear all,

I am fitting a glm to count data using poison errors with the log link.  My
goal is to test for the significance of model terms by calling the anova
function on two nested models following the recommendation in Michael
Crawley's guide to Statistical Computing.

Without going into too much detail, essentially, I have a small
overdispersion problem (errors do not fit the poisson assumption) so I am
following Crawley's recommendation and setting family=quasipoisson and using
an F test (rather than a chi-square test) to test for significance.

This is working fine, but I cannot figure out how the F value in the
analysis of deviance table was obtained and what degrees of freedom were
used to obtain the P value (essentially I don't know how to report the
result).  The following example (while errors are not overdispersed)
otherwise generates a comparable analysis of deviance table to my analysis.
Any help would be much appreciated.

Jonathan

counts <- c(rpois(100,5),rpois(100,20))
sites <- rep(100,200)
fac1 <- factor(c(rep("A",100),rep("B",100)))
fac2 <-
factor(c(rep("C",50),rep("D",100),rep("C",50)))
model1 <- glm(counts ~ fac1 * fac2,family=quasipoisson, offset=log(sites))
model2 <- glm(counts ~ fac1 + fac2,family=quasipoisson, offset=log(sites))
anova(model1,model2,test="F")
Analysis of Deviance Table

Model 1: counts ~ fac1 * fac2
Model 2: counts ~ fac1 + fac2
  Resid. Df Resid. Dev  Df Deviance      F Pr(>F)
1       196    218.432
2       197    219.210  -1   -0.778 0.7134 0.3993

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On Nov 26, 2010, at 9:30 PM, Jonathan Flowers wrote:
> Dear all,
>
> I am fitting a glm to count data using poison errors with the log  
> link.  My
> goal is to test for the significance of model terms by calling the  
> anova
> function on two nested models following the recommendation in Michael
> Crawley's guide to Statistical Computing.
>
> Without going into too much detail, essentially, I have a small
> overdispersion problem (errors do not fit the poisson assumption) so  
> I am
> following Crawley's recommendation and setting family=quasipoisson  
> and using
> an F test (rather than a chi-square test) to test for significance.
>
> This is working fine, but I cannot figure out how the F value in the
> analysis of deviance table was obtained and what degrees of freedom  
> were
> used to obtain the P value (essentially
Numerator df are the absolute values of differences and the  
denominator df's are the starting point.
 > 1-pf(0.7134, 1, 197)
[1] 0.3993472

Or equivalently:
 > pf(0.7134, 1, 196, lower.tail=FALSE)
[1] 0.3993472
> I don't know how to report the
> result).
Ergo: Time for a statistician.
> The following example (while errors are not overdispersed)
> otherwise generates a comparable analysis of deviance table to my  
> analysis.
> Any help would be much appreciated.
>
> Jonathan
>
> counts <- c(rpois(100,5),rpois(100,20))
> sites <- rep(100,200)
> fac1 <- factor(c(rep("A",100),rep("B",100)))
> fac2 <-
factor(c(rep("C",50),rep("D",100),rep("C",50)))
> model1 <- glm(counts ~ fac1 * fac2,family=quasipoisson,  
> offset=log(sites))
> model2 <- glm(counts ~ fac1 + fac2,family=quasipoisson,  
> offset=log(sites))
> anova(model1,model2,test="F")
> Analysis of Deviance Table
>
> Model 1: counts ~ fac1 * fac2
> Model 2: counts ~ fac1 + fac2
>  Resid. Df Resid. Dev  Df Deviance      F Pr(>F)
> 1       196    218.432
> 2       197    219.210  -1   -0.778 0.7134 0.3993
>
> 	[[alternative HTML version deleted]]
>
-- 

David Winsemius, MD
West Hartford, CT