Warren makes an excellent point here, and that was the driver on my second post on this. Still I can't help but think Neter et al. are splitting hairs. Both types are subsamples on an experimental unit. In one case the measures are repeated in time, in the other repeated in space (in some sense). We can still apply structure to the subsampling. I think this might a case where the PROC GLIMMIX approach really has it right. It forces us to think about this as a random effect, and structured on the residuals.

So...

what about fitting the mean of the replicates, with a weight of 1/var(replicates)?

Steve Denham Associate Director, Biostatistics MPI Research

----- Original Message ---- From: Warren Schlechte <Warren.Schlechte@TPWD.STATE.TX.US> To: SAS-L@LISTSERV.UGA.EDU Sent: Thursday, March 27, 2008 9:48:13 AM Subject: Re: Repeated measure in Mixed procedure

I'm not at all sure if this can help the discussion, but here goes:

In Applied Linear Statistical Models (Neter et al.), they make a strict distinction between repeated measures, and repeated observations. Repeated observations (aka subsampling), occurs when a single experimental unit is observed repeatedly, such as the 3 replicates in Walid's example.

Given that the replicates are repeated observations, done to get a true idea of the central tendency of the measure, I don't see why a mean cannot be used, if needed to simplify the model. All that is lost is measurement error associated with the response. And this could be analyzed separately if that is desired.

Warren Schlechte

-----Original Message----- From: Steve Denham [mailto:stevedrd@YAHOO.COM] Sent: Thursday, March 27, 2008 6:51 AM Subject: Re: Repeated measure in Mixed procedure

Hi Walid,

Looks like a doubly repeated measures design, with both day and replicate as repeated measures. The following (UNTESTED) code should get you started down the right track.

proc mixed data=data; class pen TRT Day animal replicate; model response= TRT Day TRT*Day ; random pen; repeated replicate Day / subject = animal(TRT) type = un@ar(1) r rcorr; lsmeans TRT Day TRT*Day/diff; run;

Note the Kronecker product specification in the type. This assumes that your Day variable are equally spaced (according to your post, once a week).

I hope this helps. I would guess that if you don't do something with replicate, you are going to run into infinite likelihood problems with the repeated statement (multiple obs with identical qualifiers). The big problem with this approach is computing resources--that is going to be one big matrix to have in memory. If it doesn't work, you're probably going to have to fiddle around some with replicate as a random effect somehow. Maybe some of the other PROC MIXED gurus will jump in with a more elegant solution.

Steve Denham Associate Director, Biostatistics MPI Research

----- Original Message ---- From: Walid Alali <walidalali@GMAIL.COM> To: SAS-L@LISTSERV.UGA.EDU Sent: Wednesday, March 26, 2008 3:16:13 PM Subject: Repeated measure in Mixed procedure

Hello all,

I am having trouble finding the best way of including all sources of variability in my mixed model.

My study design (which is a clinical trial) goes like this: I have 3 pens, in each pen; 10 animals (5 exposed and 5 controls). The response (i.e. the outcome) is measured over time (every week for 2 months). To make this complicated, the response was measured in triplicate (i.e. 3 times) at each time point.

Here is a glimpse of the data (just for the 1st pen): Animal TRT DAY Pen Replicate response 151 E 0 5 1 6.75E+03 151 E 0 5 1 6.22E+03 151 E 0 5 1 4.98E+03 152 E 0 5 10 6.25E+03 152 E 0 5 10 8.92E+03 152 E 0 5 10 6.09E+03 153 E 0 5 2 7.38E+03 153 E 0 5 2 4.68E+03 153 E 0 5 2 6.94E+03 154 E 0 5 3 2.49E+03 154 E 0 5 3 2.31E+03 154 E 0 5 3 2.03E+03 155 E 0 5 4 1.32E+04 155 E 0 5 4 9.92E+03 155 E 0 5 4 9.49E+03 156 C 0 5 5 4.22E+03 156 C 0 5 5 4.21E+03 156 C 0 5 5 3.46E+03 157 C 0 5 6 3.70E+03 157 C 0 5 6 3.62E+03 157 C 0 5 6 2.85E+03 158 C 0 5 7 1.54E+03 158 C 0 5 7 1.38E+03 158 C 0 5 7 1.63E+03 159 C 0 5 8 5.16E+03 159 C 0 5 8 5.00E+03 159 C 0 5 8 4.66E+03 160 C 0 5 9 5.37E+03 160 C 0 5 9 5.30E+03 160 C 0 5 9 5.41E+03

I have the model set up like this, but not sure how to include 'replicate' in it??

proc mixed data=data; class pen TRT Day animal; model response= TRT Day TRT*Day ; random pen; repeated Day / subject = animal(TRT) type = un r rcorr; lsmeans TRTcode Day TRTcode*Day/diff; run;

Any comments, suggestions are very wellcome. Thanks in advance, Walid.

Walid Alali DVM, MS, PhD Epidemiology Post-doctoral Research Associate Department of Veterinary Integrative Biosciences College of Veterinary Medicine and Biomedical Sciences Texas A&M University 4458 TAMU College Station, TX, USA 77843-4458

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