Modeling and Multivariate Methods - SAS

658 Statistical Details Appendix A
The Factor Models
Interactions and Crossed Effects
Interaction effects with both GLM and JMP are constructed by taking a direct product over the rows of the
design columns of the factors being crossed. For example, the GLM code
PROC GLM;
CLASS A B;
MODEL A B A*B;
yields this design matrix:
Table A.3 Design Matrix
A B AB
A B 1 2 3 1 2 3 1
1
1
2
1
3
2
1
2
2
2
3
3
1
3
2
3
3
A1 B1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0
A1 B2 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0
A1 B3 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0
A2 B1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0
A2 B2 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
A2 B3 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0
A3 B1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0
A3 B2 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0
A3 B3 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1
Using the JMP Fit Model command and requesting a factorial model for columns A and B produces the
following design matrix. Note that A13 in this matrix is A1–A3 in the previous matrix. However, A13B13 is
A13*B13 in the current matrix.