Modeling and Multivariate Methods - SAS

124 Fitting Standard Least Squares Models Chapter 3
Method of Moments Results
• The coefficients of expected mean squares for all the random effects, including the residual error, are
gathered into a matrix, and this is used to solve for variance components for each random effect.
• For each effect to be tested, a denominator for that effect is synthesized using the terms of the linear
combination of mean squares in the numerator that do not contain the effect to be tested or other fixed
effects. Thus, the expectation is equal for those terms common to the numerator and denominator. The
remaining terms in the numerator then constitute the effect test.
• Degrees of freedom for the synthesized denominator are constructed using Satterthwaite’s method.
• The effect tests use the synthetic denominator.
JMP handles random effects like the SAS GLM procedure with a Random statement and the Test option.
Figure 3.50, shows example results.
Caution: Standard errors for least squares means and denominators for contrast F-tests also use the
synthesized denominators. Contrasts using synthetic denominators might not be appropriate, especially in
crossed effects compared at common levels. The leverage plots and custom tests are done with respect to the
residual, so they might not be appropriate.
Caution: Crossed and nested relationships must be declared explicitly. For example, if knowing a subject
ID also identifies the group that contains the subject (that is, if each subject is in only one group), then
subject must be declared as nested within group. In that situation, the nesting must be explicitly declared to
define the design structure.
Note: JMP cannot fit a layered design if the effect for a layer’s error term cannot be specified under current
effect syntax. An example of this is a design with a Latin Square on whole plots for which the error term
would be Row*Column–Treatment. Fitting such special cases with JMP requires constructing your own
F-tests using sequential sums of squares from several model runs.
For the Animals example above, the EMS reports are as follows.