The LOGISTIC Procedure

TEST Statement

<label:> TEST equation1 <, equation2, …> </ option>;

The TEST statement tests linear hypotheses about the regression coefficients. The Wald test is used to perform a joint test of the null hypotheses $H_0\colon \bL \bbeta =\mb{c}$ specified in a single TEST statement, where $\bbeta$ is the vector of intercept and slope parameters. When $\mb{c} = \bm {0}$ you should specify a CONTRAST statement instead.

Each equation specifies a linear hypothesis (a row of the $\bL$ matrix and the corresponding element of the $\mb{c}$ vector). Multiple equations are separated by commas. The label, which must be a valid SAS name, is used to identify the resulting output and should always be included. You can submit multiple TEST statements.

The form of an equation is as follows:

term< $\bm {\pm }$ term $\bm {\ldots }$ > < $\bm {=\pm }$ term < $\bm {\pm }$ term $\bm {\ldots }$ >>

where term is a parameter of the model, or a constant, or a constant times a parameter. Intercept and CLASS variable parameter names should be specified as described in the section Parameter Names in the OUTEST= Data Set. For multinomial response models, this form enables you to construct tests of parameters from specific logits. When no equal sign appears, the expression is set to 0. The following statements illustrate possible uses of the TEST statement:

proc logistic;
   model y= a1 a2 a3 a4;
   test1: test intercept + .5 * a2 = 0;
   test2: test intercept + .5 * a2;
   test3: test a1=a2=a3;
   test4: test a1=a2, a2=a3;
run;

Note that the first and second TEST statements are equivalent, as are the third and fourth TEST statements.

You can specify the following option in the TEST statement after a slash(/):

PRINT

displays intermediate calculations in the testing of the null hypothesis $H_0\colon \bL \bbeta =\mb{c}$ . These calculations include ${\bL \widehat{\bV }({\widehat{\bbeta }})\bL ’}$ bordered by $(\bL {\widehat{\bbeta }} - \mb{c})$ and $[{\bL \widehat{\bV }({\widehat{\bbeta }})\bL ’}]^{-1}$ bordered by $[{\bL \widehat{\bV }({\widehat{\bbeta }})\bL ’}]^{-1}(\bL {\widehat{\bbeta }} - \mb{c})$ , where ${\widehat{\bbeta }}$ is the maximum likelihood estimator of $\bbeta$ and $\widehat{\bV }({\widehat{\bbeta }})$ is the estimated covariance matrix of ${\widehat{\bbeta }}$ .

For more information, see the section Testing Linear Hypotheses about the Regression Coefficients.