The SYSLIN Procedure

RESTRICT Statement

RESTRICT equation , …, equation ;

The RESTRICT statement places restrictions on the parameter estimates for the preceding MODEL statement. Any number of RESTRICT statements can follow a MODEL statement. Each restriction is written as a linear equation. If more than one restriction is specified in a single RESTRICT statement, the restrictions are separated by commas.

Parameters are referred to by the name of the corresponding regressor variable. Each name used in the equation must be a regressor in the preceding MODEL statement. The keyword INTERCEPT is used to refer to the intercept parameter in the model.

RESTRICT statements can be given labels. The labels are used in the printed output to distinguish results for different restrictions. Labels are specified as follows:

label : RESTRICT …;

The following is an example of the use of the RESTRICT statement, in which the coefficients of the regressors X1 and X2 are required to sum to 1.

   proc syslin data=a;
      model y = x1 x2;
      restrict x1 + x2 = 1;
   run;

Variable names can be multiplied by constants. When no equal sign appears, the linear combination is set equal to 0. Note that the parameters associated with the variables are restricted, not the variables themselves. Here are some examples of valid RESTRICT statements:

   restrict x1 + x2 = 1;
   restrict x1 + x2 - 1;
   restrict 2 * x1 = x2 + x3 , intercept + x4 = 0;
   restrict x1 = x2 = x3 = 1;
   restrict 2 * x1 - x2;

Restricted parameter estimates are computed by introducing a Lagrangian parameter ${\lambda }$ for each restriction (Pringle and Rayner 1971). The estimates of these Lagrangian parameters are printed in the “Parameter Estimates” table. If a restriction cannot be applied, its parameter value and degrees of freedom are listed as 0.

The Lagrangian parameter ${\lambda }$ measures the sensitivity of the sum of squared errors (SSE) to the restriction. If the restriction is changed by a small amount ${\epsilon }$ , the SSE is changed by 2 ${\lambda }$ ${\epsilon }$ .

The t ratio tests the significance of the restrictions. If ${\lambda }$ is zero, the restricted estimates are the same as the unrestricted.

Any number of restrictions can be specified on a RESTRICT statement, and any number of RESTRICT statements can be used. The estimates are computed subject to all restrictions specified. However, restrictions should be consistent and not redundant.

Note: The RESTRICT statement is not supported for the FIML estimation method.