``The only stupid question is the one that is not asked.''
--- Anon. (???)
The reason that there is no value for level "A" of treatment is
that level "A" is the reference level, under the default
``treatment''
contrasts.
See ?contr.treatment.
Some insight may be obtained by doing:
lm(decrease ~ 0 + ., data=OrchardSprays)
which gives:
Coefficients:
rowpos colpos treatmentA treatmentB treatmentC treatmentD
-2.784 -1.234 22.705 25.705 43.330 53.080
treatmentE treatmentF treatmentG treatmentH
81.205 87.080 86.580 108.330
Note that the coefficient for "treatmentA" which now magically appears
is the same as the intercept coefficient in your "original" version.
(Note
also that the intercept coefficient magically disappears.)
The value for treatmentB in the "original" version is the *difference*
between the treatmentA coefficient and the treatmentB coefficient
in the "new" version. And so on.
Mathematically, the intercepts for each (the i-th) treatment are mu +
alpha_i,
but this gives ``too many parameters'' --- mu, alpha_1, ..., alpha_k,
i.e. k+1
parameters where only k can be used. So ``constraints'' are put on the
parameters. The treatment contrasts constrain alpha_1 to 0. Sticking in
the ``0 + '' constrains mu to be 0 instead.
HTH
cheers,
Rolf Turner
On 14/09/11 10:06, Carl Witthoft wrote:> I feel bad even asking, but:
>
> Rgames> data(OrchardSprays)
> Rgames> model<-lm(decrease~.,data=OrchardSprays)
> Rgames> model
>
> Call:
> lm(formula = decrease ~ ., data = OrchardSprays)
>
> Coefficients:
> (Intercept) rowpos colpos treatmentB treatmentC
> 22.705 -2.784 -1.234 3.000 20.625
> treatmentD treatmentE treatmentF treatmentG treatmentH
> 30.375 58.500 64.375 63.875 85.625
>
>
> Rgames> levels(OrchardSprays$treatment) #just double-checking...
> [1] "A" "B" "C" "D" "E"
"F" "G" "H"
>
> So: why isn't there a value for the level "A" of treatment?
Is it
> because the (alphabetically) first level is treated as the control?
> And if so, what should I do (calculate) with the coefficients to
> compare them with the statistics of the data subset with level
"A" ?
>
>
> Please feel free to tell me to shut up and read some part of R-inferno
> or other helpful document.
>
>
> Thanks.
> Carl
>
>