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- Repeated measure ANOVA using PROC MIXED

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09-17-2008 10:08 PM

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

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

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09-26-2008 01:27 PM

In the REPEATED statement, there is an option called TYPE= that allows you to specify the covariance matrix. Try compound symmetry (CS) or autoregressive 1 (AR(1)). Autoregressive may suit you better since the correlation between two timepoints could be considered higher if the timepoints are closer together.