PROC MIXED: The difference between two covariance structures

[Emma_at_SAS]

May you please help me understand how UN(1) and UN differ? I looked at the book "SAS for Mixed Models, 2nd Edition, by R. Littell et al. (SAS Press)" but still I do not see the difference.

Thanks

[Rick_SAS · Accepted solution]

Look at the table of covariance structures in the PROC MIXED documentation.

It tells you that UN is an unstructured (t x t) matrix, which (b/c of symmetry) has t(t+1)/ parameters.

In contrast, UN(q) is a banded structure that is zero except for cells (i,j) such that |i-j|<q. When q=1, that means UN(1) is diagonal. It has t parameters.

[Emma_at_SAS]

Thank you, Rick_SAS!

Is t the number of times we measured the outcome variable? And for TYPE=UN we have t(t-1) parameters because of symmetry?

Thanks!

[Rick_SAS]

Yes. For a balanced design, t is the number of times you measure the outcome for each subject.  

[FreelanceReinh]

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@Emma_at_SAS wrote:

(...) And for TYPE=UN we have t(t-1) parameters because of symmetry?

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The number of parameters in this case is t(t+1)/2, i.e., t variances on the diagonal of the covariance matrix plus t(t-1)/2 covariances below (and, due to symmetry, the same above) the diagonal. (The "2" in the denominator is somehow not displayed in @Rick_SAS's reply.)

[Emma_at_SAS]

Thank you, Rick_SAS and FreelanceReinhard.