The GLMPOWER Procedure

Adjustments for Covariates in Univariate Models

If you specify covariates in a univariate model (whether continuous or categorical), then two adjustments are made in order to compute approximate power in the presence of the covariates. Let n Subscript nu denote the number of covariates (counting dummy variables for categorical covariates individually) as specified in the NCOVARIATES= option in the POWER statement. In other words, n Subscript nu is the total degrees of freedom used by the covariates. The adjustments are as follows:

  1. The error degrees of freedom decrease by n Subscript nu.

  2. The error standard deviation sigma shrinks by a factor of left-parenthesis 1 minus rho squared right-parenthesis Superscript one-half (if the CORRXY= option is used to specify the correlation rho between covariates and response) or left-parenthesis 1 minus r right-parenthesis Superscript one-half (if the PROPVARREDUCTION= option is used to specify the proportional reduction in total upper R squared incurred by the covariates). Let sigma Superscript star represent the updated value of sigma.

As a result of these changes, the power is computed as

normal p normal o normal w normal e normal r equals upper P left-parenthesis upper F left-parenthesis r Subscript upper L Baseline comma normal upper D normal upper F Subscript normal upper E Baseline minus n Subscript nu Baseline comma lamda Superscript star Baseline right-parenthesis greater-than-or-equal-to upper F Subscript 1 minus alpha Baseline left-parenthesis r Subscript upper L Baseline comma upper N minus r Subscript x Baseline minus n Subscript nu Baseline right-parenthesis right-parenthesis

where lamda Superscript star is calculated using sigma Superscript star rather than sigma:

lamda Superscript star Baseline equals upper N left-parenthesis bold upper L bold-italic beta minus bold-italic theta 0 right-parenthesis prime left-parenthesis bold upper L left-parenthesis ModifyingAbove bold upper X With two-dots prime bold upper W ModifyingAbove bold upper X With two-dots right-parenthesis Superscript negative 1 Baseline bold upper L prime right-parenthesis Superscript negative 1 Baseline left-parenthesis bold upper L bold-italic beta minus bold-italic theta 0 right-parenthesis left-parenthesis sigma Superscript star Baseline right-parenthesis Superscript negative 2
Last updated: December 09, 2022