Modeling and Multivariate Methods - SAS

Chapter 5 Fitting Multiple Response Models 167
Multivariate Tests
The custom test and contrast features are the same as those for regression with a single response. See the
“Fitting Standard Least Squares Models” chapter on page 53.
“Multivariate Details” on page 680 in the appendix “Statistical Details” on page 651, shows formulas for the
MANOVA table tests.
Table 5.7 describes each Multivariate report (except the Sphericity Test table; see “Univariate Tests and the
Test for Sphericity” on page 168).
Table 5.7 Descriptions of Multivariate Reports
Test
Value
Approx. F (or Exact F)
NumDF
DenDF
Prob>F
Labels each statistical test in the table. If the number of response function
values (columns specified in the M matrix) is 1 or if an effect has only one
degree of freedom per response function, the exact F test is presented.
Otherwise, the standard four multivariate test statistics are given with
approximate F tests: Wilks’ Lambda (Λ), Pillai’s Trace, the Hotelling-Lawley
Trace, and Roy’s Maximum Root.
Value of each multivariate statistical test in the report.
F-values corresponding to the multivariate tests. If the response design yields
a single value or if the test is one degree of freedom, this is an exact F test.
Numerator degrees of freedom.
Denominator degrees of freedom.
Significance probability corresponding to the F-value.
Comparison of Multivariate Tests
Although the four standard multivariate tests often give similar results, there are situations where they differ,
and one might have advantages over another. Unfortunately, there is no clear winner. In general, here is the
order of preference in terms of power:
1. Pillai’s Trace
2. Wilks’ Lambda
3. Hotelling-Lawley Trace
4. Roy’s Maximum Root
When there is a large deviation from the null hypothesis and the eigenvalues differ widely, the order of
preference is the reverse (Seber 1984).