Trouble Replicating Unstructured Mixed Procedure in R

It is not really a matter of computational accuracy.  One can get highly
accurate values for an inappropriate statistic.  

Or if there is insistence on using the word, accuracy, what is the 
meaning?

i) the wrong formula is used?  Then in what sense is it 'wrong'?

ii) there is a numerical inaccuracy in the calculation?  This is almost
never an issue in a relatively simple calculation such as this, given
the care taken by the code writers in such matters.

iii) where an approximation is used, as in using an F-distribution
approximation, is the best choice of degrees of freedom  made to
for use of this approximation?  I judge that the degrees of freedom 
for lme's F-statistic for the interaction are not well chosen.  Users
really have to sort this out for themselves, rather than relying on
what may be a fairly wild approximation that appears in lm's
output.  Using 75df rather than 25df does not however make the 
difference that a choice between (e.g.) 5df and 25df would.

A further and more basic issue is whether the statistic that is 
provided is appropriate to the intended generalisation.  I'd take
this to be generalisation to another sample of youths from the
same population.  In order to understand why R and SAS are 
giving different F-statistics for the interaction, one needs to
understand just what variance-covariance structure is assumed
in each case.  One might extract the two estimates of the 
var-cov structure and compare them. Look for terms in one that
do not appear, or maybe that are zero, in the other.

Finally, it is not just that Venables does not like type III SS.
He is saying that they almost never correspond to a null
hypothesis that makes any sense.  Those who disagree try to 
write down the model to which the null hypothesis corresponds
in testing for the main effect of factor1 with a factor1:factor2
interaction.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

Trouble Replicating Unstructured Mixed Procedure in R

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