Modeling and Multivariate Methods - SAS

670 Statistical Details Appendix A
The Factor Models
Ordinal Least Squares Means
As stated previously, least squares means are the predicted values corresponding to some combination of
levels, after setting all the other factors to some neutral value. JMP defines the neutral value for an effect
with uninvolved ordinal factors as the effect at the first level, meaning the control or baseline level.
This definition of least squares means for ordinal factors maintains the idea that the hypothesis tests for
contained effects are equivalent to tests that the least squares means are equal.
Singularities and Missing Cells in Ordinal Effects
With the ordinal coding, you are saying that the first level of the ordinal effect is the baseline. It is thus
possible to get good tests on the main effects even when there are missing cells in the interactions—even if
you have no data for the interaction.
Example with Missing Cell
The example is the same as above, with two observations per cell except that the A3B2 cell has no data. You
can now compare the results when the factors are coded nominally with results when they are coded
ordinally. The model as a whole fits the same as seen in tables shown in Figure A.1.
Table A.15 Observations
Y A B
12 1 1
14 1 1
15 1 2
16 1 2
17 2 1
17 2 1
18 2 2
19 2 2
20 3 1
24 3 1