[R] summary(lm ... conrasts=...)

[(Ted Harding)]

Hi Folks,

I've encountered something I hadn't been consciously
aware of previously, and I'm wondering what the
explanation might be.

In (on another list) using R to demonstrate the difference
between different contrasts in 'lm' I set up an example
where Y is sampled from three different normal distributions
according to the levels ("A","B","C") of a factor X:

Y<-c(rnorm(mean=0,n=12),rnorm(mean=2,n=12),rnorm(mean=4,n=12))
X<-factor(c(rep("A",12),rep("B",12),rep("C",12)))

Then I do a summary(lm(Y~X)...) using first "Treatment" contrasts
and then "Helmert" contrasts. Here are the coefficient parts
of the results in each case:


summary(lm(Y~X,contrasts=list(X="contr.treatment")))
Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.2303     0.3220   0.715  0.47944
XB            1.3057     0.4554   2.867  0.00716 **
XC            3.4204     0.4554   7.511 1.23e-08 ***


summary(lm(Y~X,contrasts=list(X="contr.helmert")))
Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   1.8057     0.1859   9.713 3.34e-11 ***
X1            0.6529     0.2277   2.867  0.00716 **
X2            0.9225     0.1315   7.017 5.00e-08 ***


What I'm wondering is why the "effect names" are "X.B"
and "X.C" for Treatment, and "X1", "X2" for Helmert.

Why not "X.B" and "X.C" in both cases? Just as "XB"
contrasts B with the overall mean and "XC" contrasts C
with the overall mean, "XA" being implicit, in the
Treatment contrasts, so "X1" contrasts B with A and
"X2" contrasts C with (A+B) in Helmert, so there
is to my mind just as definite an association of "B"
with the first contrast, and "C" with the second, in
the Helmert case as in the Treatment case!

I know it's just a matter of "notation", but in the
Helmert case the association with the names of the
factor levels has been lost, and it could be useful
to have it explicit. (Or is it intended simply as a
reminder that one is using a particular system of
contrasts?)

Thanks, and best wishes to all,
Ted.

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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 22-Aug-06                                       Time: 14:45:17
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