this is a clearer (I hope) version of an earlier post  -

My problem is formulating the  random = argument to give estimates
of all 9 random components for this kind of setup where there are
(I think) 9  variance/covariance components ...

                             Study.1    Study.2   ...  Study.5
 Treatment T1: subject:  1  2  3          4  5  6   ...  13 14 15
 
 Treatment T2: subject: 16 17 18   19 20 21   ...  28 29 30 
 
 A variable is measured at the same 2 fixed sites (a and b) on each 
subject

{ Toy example data at end of email }

so fixed effects are :-
 between-Treatments ( T1 and T2 )
 between-sites   ( a and b )
 Treatment*site interaction

and random effects are :-
 study effects at site a 
 study effects at site b
 correlation between site a and site b study effects 

 study*treatment interaction effects at site a 
 study*treatment interaction effects at site b
 correlation between site a and b study*treatment interaction effects 
 
 residual (between-subject) effects at site a 
 residual (between-subject) effects at site b
 correlation between site a and b residuals (between-subject) effects 

I'm having trouble seeing how to formulate this correctly in  lme()

Hope someone can help ...

        cheers          Bob Kinley

> Toy
   Study Treatment Subject Site    Result
   1        T1       1    a      13.901820
   1        T1       1    b      19.158889
   1        T1       2    a      16.026299
   1        T1       2    b      15.545153
   1        T1       3    a      19.667706
   1        T1       3    b      21.945156
   1        T2      16    a       9.822498
   1        T2      16    b      13.271435
   1        T2      17    a      18.602909
   1        T2      17    b      15.679736
   1        T2      18    a      15.083195
   1        T2      18    b      18.012834
   2        T1       4    a      19.394835
   2        T1       4    b      13.537977
   2        T1       5    a      17.921014
   2        T1       5    b      12.070566
   2        T1       6    a      14.419953
   2        T1       6    b      16.990585
   2        T2      19    a      15.489600
   2        T2      19    b      21.721682
   2        T2      20    a      18.553789
   2        T2      20    b      16.628156
   2        T2      21    a      20.310238
   2        T2      21    b      18.604716
   3        T1       7    a      12.458706
   3        T1       7    b      17.279394
   3        T1       8    a      14.598512
   3        T1       8    b      17.024093
   3        T1       9    a      20.821720
   3        T1       9    b      22.051680
   3        T2      22    a      17.923521
   3        T2      22    b      11.690319
   3        T2      23    a      12.547144
   3        T2      23    b      15.051402
   3        T2      24    a      12.865087
   3        T2      24    b      13.451004
   4        T1      10    a      13.819201
   4        T1      10    b      18.375914
   4        T1      11    a      18.540972
   4        T1      11    b      15.741144
   4        T1      12    a      16.992064
   4        T1      12    b      16.964870
   4        T2      25    a      18.583896
   4        T2      25    b      19.920100
   4        T2      26    a      18.782343
   4        T2      26    b      15.095778
   4        T2      27    a      23.042282
   4        T2      27    b      19.296852
   5        T1      13    a      12.425960
   5        T1      13    b      12.865022
   5        T1      14    a      16.774604
   5        T1      14    b      15.540754
   5        T1      15    a      15.726991
   5        T1      15    b       8.089564
   5        T2      28    a      11.694392
   5        T2      28    b      24.740416
   5        T2      29    a      14.664904
   5        T2      29    b      16.348194
   5        T2      30    a      20.911168
   5        T2      30    b      15.394160
> 
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