On Jan 13, 2009, at 5:15 PM, Stefano Leonardi wrote:
Peter Dalgaard wrote:
Actually, notice that you are averaging identical values, so the
"mean"
in the tapply is slightly misleading.
Notice also that the intercept may be defined even when _no_
observations have zero entries in the design matrix. This is the
usual
case in linear regression, for instance, but it can happen in
factorial
designs (unbalanced, or using other than treatment contrasts) as
well.
Thanks for the answers.
Still I am not totally convinced about the interpretation of
intercept as a mean of fitted values for group belonging to first
level of each factor (those having 0 in all columuns in
matrix.models, except the first column) because the reasoning seems
to me a little cirucular.
Being the intercept value the expected value for that group and, as
Peter point out, being the same value for all observations in the
group it seem clear that it intercept it is the mean of these value.
It is not completeley clear to me why (in some cases, not always)
the intercept is not equal to the mean of the first group of raw data.
It would be so *if* you had estimated a saturated model, but you did
not. Your fit
of Y|A values is adjusted for the B values.
Try instead with lm(Y ~ A * B). You should get intercept (1), main
effects(1+2) and
interaction terms(2) which should total the number of groups.
Appropriately combined,
these estimates will now exactly fit the "raw values".
--
David Winsemius
Sorry if I am annoying with this issue... but I found in several
books about R and also in this same mailing list that intercept
*should* be equal to the mean of the first group.
Thanks
Stefano
--
======================================================================
Stefano Leonardi
Dipartimento di Scienze Ambientali
Universita` di Parma E-mail: stefano.leona...@unipr.it
Viale Usberti 11/A Phone : +39-0521-905659
43100 PARMA (Italy) Fax : +39-0521-905402
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