[R] Trouble about the interpretation of intercept in lm models

[David Winsemius]

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.leonardi at unipr.it
> Viale Usberti 11/A                            Phone : +39-0521-905659
> 43100 PARMA  (Italy)                          Fax   : +39-0521-905402
>
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