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The SYSLIN Procedure |
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 for each restriction (Pringle and Raynor 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, , measures the sensitivity of the SSE to the restriction. If the restriction is changed by a small amount , the SSE is changed by 2.
The t-ratio tests the significance of the restrictions. If 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.
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