Newsgroups: bit.listserv.stat-l
Date:         Fri, 16 Oct 1992 09:53:00 CDT
From:         T80SMS1@NIU.BITNET
Subject:      PROC MIXED with both split-plot and repeated-measures

I realize that this message is more appropriately directed to
SAS-L, but I do not have that address.  So, I beg your
indulgence and hope that either someone on this list can
answer my question or will forward it to the appropriate
party.

The problem involves the use of the new SAS PROC MIXED to analyse
a complex split-plot plus repeated-measures design experiment.
A graduate student did an experiment looking at the effects
of 2 media on growth of bacteria.  A single block consisted of
growing 1 batch of each media (no replication) and plating out
a sample each day for 4 days.  (As is typical of micro work,
3 plates were done and averaged.)  This entire experiment was
then repeated 6 times.

The problem is this.  The new PROC MIXED works by starting with
the model:  y = X*beta + Z*v + e
where X is the fixed-effects matrix, Z is the random-effects
matrix, v is a vector of random effects, and e is a random
error vector.  The variance of y is thus:
     V = ZGZ' + R, where G and R are the variances of v and e.
Now, you can specify the structure of G and R using the RANDOM
and REPEATED statements, respectively.  The text implies that
both can be specified, but all examples show only one or the
other.  However, in my case both need to be specified as
measurements over days within media are clearly going to be
correlated (probably by a 1st-order autoregressive) while
measurements within blocks will also likely be correlated.

I tried the following set of commands:
PROC MIXED; CLASS MEDIA EXPER;
   MODEL COUNT = MEDIA TIME*MEDIA/NOINT S;
   RANDOM TIME/TYPE=CS SUBJECT=EXPER;
   REPEATED/TYPE=AR(1) SUBJECT=EXPER;

But all that I got back was:
                      THE MIXED PROCEDURE

                    CLASS LEVEL INFORMATION

                 CLASS     LEVELS  VALUES

                 MEDIA          2  L T
                 EXPER          6  1 2 3 4 5 6


                      THE MIXED PROCEDURE

               REML ESTIMATION ITERATION HISTORY

       ITERATION  EVALUATIONS     OBJECTIVE     CRITERION

               0            1  503.35581152
               1           44  491.14234500  469056.70688
               2           43  491.14234500  469056.70688
               3           43  491.14234500  469056.70688

                        DID NOT CONVERGE.


                       THE MIXED PROCEDURE

                    COVARIANCE PARAMETERS AT
                       LAST REML ITERATION

             COV PARM            RATIO      ESTIMATE

             TIME CS       -0.00032970  -41.69820893
             DIAG AR(1)     0.65312422  82602.077219
             RESIDUAL       1.00000000  126472.23036

When I ran this without the RANDOM statement (just the REPEATED
statement), I received what looked like the right answer, but
upon further contemplation, realised that the block-diagonalization
did not properly account for the split-plot nature of the
design.  Any advice would be appreciated, with much thanks
in advance.

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