The HPQLIM Procedure

TEST Statement

<’label’:>

  • TEST <’string’:> equation <,equation…> / options ;

The TEST statement performs Wald, Lagrange multiplier, and likelihood ratio tests of linear hypotheses about the regression parameters in the preceding MODEL statement. Each equation specifies a linear hypothesis to be tested. All hypotheses in one TEST statement are tested jointly. Variable names in the equations must correspond to regressors in the preceding MODEL statement, and each name represents the coefficient of the corresponding regressor. Use the keyword INTERCEPT for a test that includes a constant.

You can specify the following options after the slash (/):

ALL

requests Wald, Lagrange multiplier, and likelihood ratio tests.

LM

requests the Lagrange multiplier test.

LR

requests the likelihood ratio test.

WALD

requests the Wald test.

The following statements illustrate the use of the TEST statement (note the use of the INTERCEPT keyword in the second TEST statement): 

   proc hpqlim;
      model y = x1 x2 x3;
      test x1 = 0, x2 * .5 + 2 * x3 = 0;
      test _int: test intercept = 0, x3 = 0;
   run;

The first TEST statement investigates the joint hypothesis that

\[ \beta _{1} = 0 \]

and

\[ 0.5 \beta _{2} + 2 \beta _{3} = 0 \]

Only linear equality restrictions and tests are permitted in PROC HPQLIM. Test expressions can be composed only of algebraic operations that involve the addition symbol (+), subtraction symbol (–), and multiplication symbol (*).

The TEST statement accepts labels that are reproduced in the printed output. You can label a TEST statement in two ways: you can specify a label followed by a colon before the TEST keyword, or you can specify a quoted string after the TEST keyword. If you specify both a label before the TEST keyword and a quoted string after the keyword, PROC HPQLIM uses the label that precedes the colon. If no label or quoted string is specified, PROC HPQLIM labels the test automatically.