PROC LOGISTIC: Testing Linear Hypotheses about the Regression Coefficients :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The LOGISTIC Procedure

Testing Linear Hypotheses about the Regression Coefficients

Linear hypotheses for $\text{[math]}$ are expressed in matrix form as

$\text{[math]}$

where $\text{[math]}$ is a matrix of coefficients for the linear hypotheses, and $\text{[math]}$ is a vector of constants. The vector of regression coefficients $\text{[math]}$ includes slope parameters as well as intercept parameters. The Wald chi-square statistic for testing $\text{[math]}$ is computed as

$\text{[math]}$

where $\text{[math]}$ is the estimated covariance matrix. Under $\text{[math]}$ , $\text{[math]}$ has an asymptotic chi-square distribution with $\text{[math]}$ degrees of freedom, where $\text{[math]}$ is the rank of $\text{[math]}$ .

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