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# Proc Mixed Doubly Repeated Measures Var-Cov matrix understanding.

[ Edited ]

Hello everyone.

I am trying to understand the var-covariance structure.

My data is doubly repeated measures over space and time.

For this example, I run the data with 3 repeated levels for space(depth) and 4 for time.

The code is the following.

Proc MIXED DATA=Na;
Class SoilType Depth Source Permeable LawnAccess Time;
Model ConcNa = Depth SoilType Source Permeable LawnAccess Time SoilType*Depth SoilType*Time Depth*Source Permeable*Source Permeable*SoilType;
Repeated Depth Time / Subject= unit type=un@ar(1) r rcorr;

The type used is unstructured for space and autoregressive for time.

See below for the parameters and matrices.

My questions ares:

1)I am trying to calculated by myself using the parameters and the structure examples obtained on the SAS website (https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_mixed_sect0...). However the values do not match with the output of R matrix for subject 1.

2) A direct product between my unstructured matrix (3x3) and my ar(1) matrix (4x4) should not be a 12 x 12 matrix?

The result output is only 4 x 4.

The result  parameters and matrices are:

 Covariance Parameter Estimates Cov Parm Subject Estimate Depth UN(1,1) Unit 2097.9 UN(2,1) Unit 824.5 UN(2,2) Unit 461.99 UN(3,1) Unit 92.203 UN(3,2) Unit 77.9701 UN(3,3) Unit 134.94 Time AR(1) Unit 0.04604

 Estimated R Matrix for Subject 1 Row Col1 Col2 Col3 Col4 1 134.940 6.2123 0.0132 92.2030 2 6.2123 134.940 0.2860 4.2447 3 0.0132 0.2860 134.940 0.0090 4 92.2030 4.2447 0.0090 2097.9 Estimated R Correlation Matrix for Subject 1 Row Col1 Col2 Col3 Col4 1 1 0.0460400 0.0000980 0.1733000 2 0.046040 1 0.0021190 0.0079780 3 0.000098 0.0021190 1 0.0000170 4 0.173300 0.0079780 0.0000170 1

Thank you very much!

Marcelo.

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