Date:  Fri, 14 May 2004 14:41:58 0400 
ReplyTo:  Agustin Calatroni <acalatr@UMICH.EDU> 
Sender:  "SAS(r) Discussion" <SASL@LISTSERV.UGA.EDU> 
From:  Agustin Calatroni <acalatr@UMICH.EDU> 
Subject:  Re: PROC MIXED for NL repeated meas models 

InReplyTo:  <200405141723.i4EHNe200947@listserv.cc.uga.edu> 
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If I understand your problem correctly you need to know how to estimate
a mixed model when C(i) is assumed to be known.
The parms statement in proc mixed in conjunction with the eqcons option
can be used to specify which parameter should be hold equal.
* fit the mixed model for the 2nd stage with variance of error
constrained to be equal to 1;
* mixed model assuming D 2x2;
proc mixed method=ml;
class id;
model dv = iv ;
random b(i) / type=un subject= id;
parms (var) (cov) (var) (1) / eqcons=4;
run;
Original Message
From: SAS(r) Discussion [mailto:SASL@LISTSERV.UGA.EDU] On Behalf Of
Stan Wheeler
Sent: Friday, May 14, 2004 1:24 PM
To: SASL@LISTSERV.UGA.EDU
Subject: PROC MIXED for NL repeated meas models
Hope this is not a repeat but I think my previous attempt got lost in
the ether.
I want to use PROC MIXED as part of an implementation of the 2stage
approach for estimating parameters described in the book by Davidian and
Giltman.
Problem:
We have a set of M treaatments and K subjects. Subject i is assigned to
one of the treatments and variable y is observed at various times. A
nonlinear equation, say y=A(1exp(B*t)), predicts the value of y at time
t where A and B are unknown and depend on the Treatment. We want to
estimate and make inferences about values of A and B for the Treatments.
2Stage Approach
1. Use PROC NLIN to estimate A and B for each Treatment.
Let Beta*(i) = {A*(i), B*(i)} Be the estimate of Beta(i) = {A(i),B(i)}
for subject i. PROC NLIN also genrates a largesample VC matrix C(i) for
Beta*(i).
2. Let Beta be the (unknown) vector containing the true, population,
values of A and B for the treatments.
3. Assume
Beta*(i) = A(i)*Beta + b(i) + e(i)
where A(i) is a known design matrix,
b(i) is a random error with mean zero and VC matrix D and
e(i) is a random error with mean zero and VC matrix C(i) which is
assumed to be known (from PROC NLIN).
4. This looks like a pretty standard linear mixed model except that C(i)
is KNOWN. I think that C(i) corresponds to R, in PROC MATRIX notation
and D corresponds to G.
I have an IML solution for this problem using the EM approach outlined
in the book but would like a PROC MIXED solution because it would be
more flexible. My main problem is that I haven't figured out how to
specidy the KNOWN value of C(i) in the PROC MIXED syntax.
Thanks for any ideas.
Stan Wheeler
