FRONTIER Procedure

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The TEST statement performs Wald, Lagrange multiplier, and likelihood ratio tests of linear hypotheses about the regression parameters that are specified in the preceding MODEL statement.

Each test is written either as a single linear equation or as a comma-separated list of two or more linear equations. A test equation specifies a linear hypothesis to be tested and consists of an expression, followed by the equality operator (=), followed by a second expression:

 expression = expression

The rules for valid test expressions are the same as those for restriction expressions. For more information, see the section RESTRICT Statement Expressions.

All hypotheses in one TEST statement are tested jointly.

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

By default, the Wald test is performed. Each type of test is described in the section Tests on Parameters.

You can add a label (which is printed in the output) to a TEST statement in two ways: by adding an unquoted label followed by a colon before the TEST keyword, or by adding a quoted string after the TEST keyword. The unquoted label cannot contain any spaces. If you include both an unquoted label and a quoted string, PROC FRONTIER uses only the unquoted label. If you specify neither an unquoted label nor a quoted string, PROC FRONTIER automatically labels the tests.

The following example illustrates the use of the TEST statement:

proc frontier;
   model y = x1 x2 x3;
   test x1 = 0, 1.5 * x2 + 2 * x3 = 0;
   test_int: test intercept = 0, x3 = 0.75;
run;

In the example, two separate tests are performed. The first test investigates the joint hypothesis that

and

The second test is labeled "test_int" and investigates the joint hypothesis that

and