topic Repeated measure ANOVA in SAS Procedures

Repeated measure ANOVA

deleted_user — Thu, 18 Sep 2008 02:14:12 GMT

My dataset has 16 subjects, each subject was exposed to 3 treatments, each treatment was repeated 4 times. So there is a correlation b/w the 4 times within a treatment, and another correlation factor b/w the 3 treatments within a subjects. The data looks like
ID Treatment Time
1 1 1
1 1 2
... ... ...
1 1 4
1 2 1
... ... ...
1 2 4
... ... ...
1 3 4
So the correlation matrix for subject 1 should be a 12*12 matrix, formed by 3*3=9 block matrices, and each matrix is a 4*4. The 3 diagonal 4*4 matrices should be the same. The off-diagonal 4*4 matrices don't need to be the same.
There are 2 difference correlation factors within a subject. My question is how to specify such a correlation matrix. Hopefully the correlation matrix should look like something like this
1 .5 .5 .5 .3 .3 .3 .3 .1 .1 .1 .1
.5 1 .5 .5 .3 .3 .3 .3 .1 .1 .1 .1
.5 .5 1 .5 .3 .3 .3 .3 .1 .1 .1 .1
.5 .5 .5 1 .3 .3 .3 .3 .1 .1 .1 .1
.3 .3 .3 .3 1 .5 .5 .5 .2 .2 .2 .2
.3 .3 .3 .3 .5 1 .5 .5 .2 .2 .2 .2
.3 .3 .3 .3 .5 .5 1 .5 .2 .2 .2 .2
.3 .3 .3 .3 .5 .5 .5 1 .2 .2 .2 .2
.1 .1 .1 .1 .2 .2 .2 .2 1 .5 .5 .5
.1 .1 .1 .1 .2 .2 .2 .2 .5 1 .5 .5
.1 .1 .1 .1 .2 .2 .2 .2 .5 .5 1 .5
.1 .1 .1 .1 .2 .2 .2 .2 .5 .5 .5 1

I used PROC MIXED
If I specify RANDOM INT/ subject=ID, then all the off-diagonal will be the same. If I specify RANDOM INT/ subject=ID*TREATMENT, then I can only get a 4*4 correlation matrix, with no off-diagonal blocks.

Re: Repeated measure ANOVA

deleted_user — Fri, 19 Sep 2008 14:28:58 GMT

This post is kind of sinking, but I really need some hints there.
Anyone please, if you feel you can help but I didn't state my question clearly, let me know.
Thanks.

Re: Repeated measure ANOVA

SteveDenham — Fri, 26 Sep 2008 14:44:54 GMT

If you want the off-diagonals, look at the TYPE= option. TYPE=UN should certainly give what you need. The problem here is that you have 66 cov parms to estimate, with only 192 obs. Things may not converge real well. DO NOT specify a GROUP=treatment option to model different covariances within treatment. That leads to 192 cov parms.

Good luck.

Re: Repeated measure ANOVA

deleted_user — Wed, 01 Oct 2008 04:28:34 GMT

Thank you for your reply.
I know I can try type=un, but that's not what I really want. As you can see from my example, I'd like something with kind of compond symmetry with elements as blocks. So there are much less parameters needed for estimation. In my example, for that 12*12 correlation matrix, only 4 parameters will be enough to describe the relationship.