Modeling and Multivariate Methods - SAS

Appendix A Statistical Details 665
The Factor Models
JMP and GLM Hypotheses
GLM works differently than JMP and produces different hypothesis tests in situations where there are
missing cells. In particular, GLM does not recognize any difference between a nesting and a crossing in an
effect, but JMP does. Suppose that you have a three-layer nesting of A, B(A), and C(A B) with different
numbers of levels as you go down the nested design.
Table A.10 on page 665, shows the test of the main effect A in terms of the GLM parameters. The first set
of columns is the test done by JMP. The second set of columns is the test done by GLM Type IV. The third
set of columns is the test equivalent to that by JMP; it is the first two columns that have been multiplied by
a matrix
21
12
to be comparable to the GLM test. The last set of columns is the GLM Type III test. The difference is in
how the test distributes across the containing effects. In JMP, it seems more top-down hierarchical. In GLM
Type IV, the test seems more bottom-up. In practice, the test statistics are often similar.
Table A.10 Comparison of GLM and JMP Hypotheses
Parameter JMP Test for A GLM-IV Test for A JMP Rotated Test GLM-III Test for A
u 0 0 0 0 0 0 0 0
a1 0.6667 -0.3333 1 0 1 0 1 0
a2 –0.3333 0.6667 0 1 0 1 0 1
a3 –0.3333 -0.3333 -1 -1 -1 -1 -1 -1
a1b1 0.1667 -0.0833 0.2222 0 0.25 0 0.2424 0
a1b2 0.1667 -0.0833 0.3333 0 0.25 0 0.2727 0
a1b3 0.1667 -0.0833 0.2222 0 0.25 0 0.2424 0
a1b4 0.1667 -0.0833 0.2222 0 0.25 0 0.2424 0
a2b1 -0.1667 0.3333 0 0.5 0 0.5 0 .5
a2b2 -0.1667 0.3333 0 0.5 0 0.5 0 .5
a3b1 -0.1111 -0.1111 -0.3333 -0.3333 -0.3333 -0.3333 -0.3333 -0.3333
a3b2 -0.1111 -0.1111 -0.3333 -0.3333 -0.3333 -0.3333 -0.3333 -0.3333