For a testable hypothesis , you can request different Wald tests by using the DF=
option in the MODEL
statement.
Let
where is a contrast vector or matrix that you specify,
is the vector of regression parameters,
is the estimated regression coefficients,
is the estimated covariance matrix of
, and
is a matrix such that the following are true:
has the same number of columns as
.
has full row rank.
The rank of equals the rank of the
matrix.
All rows of are estimable functions.
The Wald F statistic that is computed by using the matrix is equivalent to the Wald F statistic computed by using the
matrix.
If is a full-rank matrix and all rows of
are estimable functions, then
is the same as
. It is possible that such an
matrix cannot be constructed for a given set of linear contrasts, in which case the contrasts are not testable. Let r be the rank of
. The following table describes the Wald tests available in PROC SURVEYPHREG.
Numerator |
Denominator |
|||
---|---|---|---|---|
Value of DF= |
Test Request |
Test Statistic |
Degrees of Freedom |
Degrees of Freedom |
NONE |
Chi-square |
Q |
r |
|
v |
Customized F |
vQ/rd |
r |
v |
DESIGN |
Unadjusted F |
Q/r |
r |
d |
DESIGN (v) |
Unadjusted F |
Q/r |
r |
v |
PARMADJ |
Adjusted F |
(d–r+1)Q/rd |
r |
d–r+1 |
PARMADJ (v) |
Adjusted F |
(v–r+1)Q/rv |
r |
v–r+1 |
DESIGNADJ |
Adjusted F |
Q/r |
r |
d |