Re: anova and addterm with F-tests in a Poisson GLM

[james.king@ey.com]

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The F statistics are different because addterm and anova are estimating the scale parameter differently.
addterm is using the deviance divided by the residual degrees of freedom but anova is using the sum of
the squares of the standardized residuals divided by the residual degrees of freedom. See Venables &
Ripley pages 186 and 187.


>stat.anova(anova(model1, model2), test = "F", scale = deviance(model2)/model2$
        df.resid, model2$df.resid, 10)[, 6:8]
Analysis of Deviance Table

Response: bees

  Deviance  F Value     Pr(F) 
1                            
2 3.393755 2.417303 0.1586095

>stat.anova(anova(model1, model2), test = "F", scale = sum(residuals(model2,
        type = "pearson")^2)/model2$df.resid, model2$df.resid, 10)[, 6:8]
Analysis of Deviance Table

Response: bees

  Deviance  F Value     Pr(F) 
1                            
2 3.393755 2.201395 0.1761781


Note dropterm gives an error for this

>dropterm(model2,test="F")
Problem in ||: No data to interpret as logical value: e1 || e2
Evaluation frames saved in object "last.dump", use debugger() to examine them

Tom Charman <tgc21@cam.ac.uk> Sent by: s-news-owner@lists.biostat.wustl.edu 05/14/2004 06:34 AM

To:        s-news@lists.biostat.wustl.edu         cc:                 Subject:        [S] anova and addterm with F-tests in a Poisson GLM

Hi S-listers,

I am looking into the effects of some environmental conditions 
(temperature, wind speed, etc) on the foraging activity of bumblebees. I'm 
trying to do this using a Poisson GLM with count of foraging bumblebees as 
the response and the different environmental conditions as explanatory 
variables. I have been looking at each environmental condition by adding it 
to a minimal model and testing the change in deviance with an F-test (the 
data is slightly over-dispersed). Recently I stumbled on Venables & 
Ripley's cunning addterm function in their MASS library which would save me 
a lot of time. Unfortunately I get slightly different F and P values when I 
do the test using anova (model1, model2, test = "F") and addterm (model1, 
model2, test = "F"). The deviances are the same using both methods, its 
just the F and P values that differ. I'm not sure what I'm doing wrong, or 
if I've got the wrong idea about these functions, and would be really 
grateful if anyone could give me a clue.

Thanks loads, 
tom

A madeup example of what I'm doing:
> bees<- c(6, 8, 10, 8, 14, 3, 6, 5, 12, 4) temp<- 
> factor(c("hot","hot","hot","hot","hot","cold","cold","cold","cold","cold") 
> ) model1<- glm(bees ~ 1, family = poisson) model2<- glm(bees ~ temp, 
> family = poisson) library (MASS) anova (model1, model2, test = "F")
Analysis of Deviance Table

Response: bees

  Terms Resid. Df Resid. Dev Test Df Deviance  F Value     Pr(F) 
1     1         9   14.62530                                    
2  temp         8   11.23154       1 3.393755 2.201395 0.1761781

> addterm (model1, model2, test = "F")
Single term additions

Model:
bees ~ 1
       Df Deviance      AIC  F value     Pr(F) 
<none>    14.62530 16.62530                   
  temp  1 11.23154 15.23154 2.417303 0.1586095
>

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