Bioequivalence and Bioavailability Forum

Dear d_labes,

❝ Thanks for the flowers.

You're welcome — I thought your write-up laying out the matrices deserved something.

❝ Really?

❝

❝ I got the G matrix for the second code set (armcd renamed to sequence) for the above mentioned Example 9.3.3 in Chow/Liu - a 2-sequence-3-period replicate study as:

❝

❝                                 Estimated G Matrix

❝

❝ Row  Effect             sequence  subject    Col1      Col2     Col3

❝ ...

❝

❝    1  subject(sequence)  RTT        1       75.6238

❝    2  subject(sequence)  RTT        3                 75.6238

❝    3  subject(sequence)  RTT        4                           75.6238

❝ ...

❝                                         ...  Col10     Col11     Col12

❝ ...

❝   10  subject(sequence)  TRR        2       75.6238

❝   11  subject(sequence)  TRR        5                 75.6238

❝   12  subject(sequence)  TRR        6                           75.6238

❝ ...

❝

❝ For me this looks block diagonal at its best .

This is not a block-diagonal G-matrix. This is the default covariance structure for PROC MIXED in SAS (VC – variance components) when no TYPE= option is specified. It is true it does have values along the diagonal, but this demonstrates the VC structure.

The 'Dimensions' output from SAS will indicate how your Z-matrix is constructed, and thus your G-matrix. A blocked-diagonal G-matrix will be indicated by the number of columns in the Z-matrix defined per subject, with the number of max observations per subject matching correctly (max 3 observations for this design), for a total of max observations x the number of subjects.

A standard VC structure will list the number of columns in the Z-matrix equal to the subjects, with the number of subjects equal 1, and the max observations per subject equal to the total number of observations.

For the output above (Chow/Liu data) the SAS output dimensions will specify there are 18 (subject) columns (with 18x3 rows for this design) in the Z-matrix, with an 18x18 G-matrix (the full matrix of your excerpt above).