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The REG Procedure |

**RESTRICT***equation < , ... , equation >***;**

restrict equation1=equation2=equation3;

is equivalent to imposing the two restrictions

restrict equation1=equation2; restrict equation2=equation3;

Each restriction is written as a linear equation and can be written as

orequation

equation = equation

The form of each

where the *c*_{j}'s are constants and the
*variable*_{j}'s are any regressor variables.

When no equal sign appears, the linear combination is set equal to zero. Each variable name mentioned must be a variable in the MODEL statement to which the RESTRICT statement refers. The keyword INTERCEPT can also be used as a variable name, and it refers to the intercept parameter in the regression model.

Note that the parameters associated with the variables are restricted, not the variables themselves. Restrictions should be consistent and not redundant.

Examples of valid RESTRICT statements include the following:

restrict x1; restrict a+b=l; restrict a=b=c; restrict a=b, b=c; restrict 2*f=g+h, intercept+f=0; restrict f=g=h=intercept;

The third and fourth statements in this list produce identical restrictions. You cannot specify

restrict f-g=0, f-intercept=0, g-intercept=1;

because the three restrictions are not consistent. If these restrictions are included in a RESTRICT statement, one of the restrict parameters is set to zero and has zero degrees of freedom, indicating that PROC REG is unable to apply a restriction.

The restrictions usually operate even if the model is not of full rank. Check to ensure that DF=-1 for each restriction. In addition, the Model DF should decrease by 1 for each restriction.

The parameter estimates are those that minimize the quadratic criterion (SSE) subject to the restrictions. If a restriction cannot be applied, its parameter value and degrees of freedom are listed as zero.

The method used for restricting the parameter
estimates is to introduce a Lagrangian parameter
for each restriction (Pringle and Raynor 1971).
The estimates of these
parameters are displayed with test statistics. Note that the *t* statistic
reported for the Lagrangian parameters does not follow a Student's *t*
distribution, but its square follows a beta distribution
(LaMotte 1994). The *p*-value for these parameters is computed
using the beta distribution.

The Lagrangian parameter measures the
sensitivity of the SSE to the restriction constant.
If the restriction constant is changed by a small amount
, the SSE is changed by .
The *t* ratio tests the significance of the restrictions.
If is zero, the restricted estimates are the
same as the unrestricted estimates, and a change in the
restriction constant in either direction increases the SSE.

RESTRICT statements are ignored if the PCOMIT= or RIDGE= option is specified in the PROC REG statement.

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