The LOGISTIC Procedure

Testing Linear Hypotheses about the Regression Coefficients

Linear hypotheses for bold-italic beta are expressed in matrix form as

upper H 0 colon bold upper L bold-italic beta equals bold c

where bold upper L is a matrix of coefficients for the linear hypotheses, and bold c is a vector of constants. The vector of regression coefficients bold-italic beta includes slope parameters as well as intercept parameters. The Wald chi-square statistic for testing upper H 0 is computed as

chi Subscript normal upper W Superscript 2 Baseline equals left-parenthesis bold upper L ModifyingAbove bold-italic beta With caret minus bold c right-parenthesis prime left-bracket bold upper L ModifyingAbove bold upper V With caret left-parenthesis ModifyingAbove bold-italic beta With caret right-parenthesis bold upper L prime right-bracket Superscript negative 1 Baseline left-parenthesis bold upper L ModifyingAbove bold-italic beta With caret minus bold c right-parenthesis

where ModifyingAbove bold upper V With caret left-parenthesis ModifyingAbove bold-italic beta With caret right-parenthesis is the estimated covariance matrix. Under upper H 0, chi Subscript normal upper W Superscript 2 has an asymptotic chi-square distribution with r degrees of freedom, where r is the rank of bold upper L.

Last updated: December 09, 2022