[R] Difference between drop1() vs. anova() for Gaussian glm models

[Karl Ove Hufthammer]

Dear list members,

I’m having some problems understanding why drop1() and anova() gives 
different results for *Gaussian* glm models. Here’s a simple example:

  d = data.frame(x=1:6,
                 group=factor(c(rep("A",2), rep("B", 4))))
  l = glm(x~group, data=d)

Running the following code gives *three* different p-values. (I would expect 
it to give two different p-values.)

  anova(l, test="F")     # p = 0.04179
  anova(l, test="Chisq") # p = 0.00313
  drop1(l, test="Chisq") # p = 0.00841

I’m used to anova() and drop1() giving identical results for the same ‘test’ 
argument. However, it looks like the first two tests above use the F-
statistic as a test statistic, while the last one uses a ‘scaled deviance’ 
statistic:

  1-pf(8.7273, 1, 4)  # F-statistic
  1-pchisq(8.7273, 1) # F-statistic
  1-pchisq(6.9447, 1) # Scaled deviance

I couldn’t find any documentation on this difference. The help page for 
drop1() does say:

  The F tests for the "glm" methods are based on analysis of
  deviance tests, so if the dispersion is estimated it is based
  on the residual deviance, unlike the F tests of anova.glm.

But here it’s talking about *F* tests. And drop1() with test="F" actually 
gives the *same* p-value as anova() with test="F":

  drop1(l, test="F") # p = 0.04179

Any ideas why anova() and drop(1) uses different test statistics for the 
same ‘test’ arguments? And why the help page implies (?) that the results 
should differ for F-tests (while not mentioning chi-squared test), but here 
they do not (and the chi-squared tests do)?

$ sessionInfo()
R version 3.2.1 (2015-06-18)
Platform: x86_64-suse-linux-gnu (64-bit)
Running under: openSUSE 20150714 (Tumbleweed) (x86_64)

locale:
 [1] LC_CTYPE=nn_NO.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=nn_NO.UTF-8        LC_COLLATE=nn_NO.UTF-8    
 [5] LC_MONETARY=nn_NO.UTF-8    LC_MESSAGES=nn_NO.UTF-8   
 [7] LC_PAPER=nn_NO.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=nn_NO.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets 
[6] methods   base     

loaded via a namespace (and not attached):
[1] tools_3.2.1

-- 
Karl Ove Hufthammer
E-mail: karl at huftis.org
Jabber: huftis at jabber.no