
On 15 Oct 2010, at 13:55, Berwin A Turlach wrote:

> G'day Michael,
> 

Hi Berwin

Thanks for the reply

> On Fri, 15 Oct 2010 12:09:07 +0100
> Michael Hopkins <hopkins@upstreamsystems.com> wrote:
> 
>> OK, my last question didn't get any replies so I am going to try and
>> ask a different way.
>> 
>> When I generate contrasts with contr.sum() for a 3 level categorical
>> variable I get the 2 orthogonal contrasts:
>> 
>>> contr.sum( c(1,2,3) )
>>  [,1] [,2]
>> 1    1    0
>> 2    0    1
>> 3   -1   -1
> 
> These two contrasts are *not* orthogonal.
> 
I'm surprised.  Can you please tell me how you calculated that.

>> This provides the contrasts <1-3> and <2-3> as expected.  But I also
>> want it to create <1-2> (i.e. <1-3> - <2-3>).  So in general I want
>> all possible orthogonal contrasts - think of it as the contrasts for
>> all pairwise comparisons between the levels.
> 
> You have to decide what you want.  The contrasts for all pairwise
> comparaisons between the levels or all possible orthogonal contrasts?
> 

Well the pairwise contrasts are the most important as I am looking for evidence of whether they are zero (i.e. no difference between levels) or not.  But see my above comment about orthogonality.

> The latter is actually not well defined.  For a factor with p levels,
> there would be p orthogonal contrasts, which are only identifiable up to
> rotation, hence infinitely many such sets. But there are p(p-1)
> pairwise comparisons. So unless p=2, yo have to decide what you want....
> 
Well of course the pairwise comparisons are bi-directional so in fact only p(p-1)/2 are of interest to me.

>> Are there are any options for contrast() or other functions/libraries
>> that will allow me to do this automatically?
> 
> Look at package multcomp, in particular functions glht and mcp, these
> might help.
> 
Thanks I will have a look.  

But I want to be able to do this transparently "within" lm() using regsubsets() etc as I am collecting large quantities of summary stats from all possible models to use with a model choice criterion based upon true Bayesian model probabilities.

> Cheers,
> 
> 	Berwin
> 
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Michael Hopkins
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