Dear R-helpers,
In the case of two categorical factors, say a and b, once I have
fixed the constrasts, the model matrix is set according to these
contrasts with "lm", and the t-tests for the significance of the
parameters provided by "summary" indeed concern the comparison of the
model with each submodel obtained by removing the corresponding
column of the model matrix. So :
options(contrasts=c("contr.sum", "contr.poly"))
mod = lm(Y ~ a*b, x=TRUE)
print(mod$x)
print(summary(mod))
provide the expected results.
When using "anova" for the corresponding two-way anova, I was
expecting to obtain the p-values of the Fisher tests corresponding to
:
a : the removal of the columns coding for factor a
b : the removal of the columns coding for factor b
a:b : the removal of the columns coding for the interaction of factors a and b
BUT :
print(anova(mod))
does not provide the expected results. Moreover, the results of
"anova" do not depend on the contrasts, since setting
options(contrasts=c("contr.treeatment", "contr.poly"))
leads to the same result.
I manage to obtain the desired results by creating the submodels
without the corresponding columns, and by comparing them with "anova"
, for example :
xsub = mod$x[,-c(2)]
submod = lm(Y ~ xsub-1)
print(anova(submod,mod))
So my questions are :
1) is there a direct way to perform the anova I want ?
2) what does "anova" really test, and why is it independant from the
chosen model matrix ?
Thanks in advance,
Isabelle
P.S. I do not directly see the answers to my questions in MASS by
Venables and Ripley.
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