# The SURVEYPHREG Procedure

#### Contrasts

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

Q/r

r

d

DESIGN (v)

Q/r

r

v

(dr+1)Q/rd

r

dr+1

(vr+1)Q/rv

r

vr+1