CQLIM Procedure
RESTRICT Statement
RESTRICT restriction1 <, restriction2 …> ;
The RESTRICT statement imposes linear restrictions on the parameter estimates. You can specify any number of RESTRICT statements, but the number of restrictions that are imposed is limited by the number of regressors.
Each restriction is written as an expression, followed by an equality operator (=) or an inequality operator (<, >, <=, >=), followed by a second expression:
expression operator expression
The operator can be =, <, >, <= , or >=. The operator and second expression are optional.
Restriction expressions can be composed of parameter names; multiplication (), addition (
), and subtraction (
) operators; and constants. Parameters that are named in restriction expressions must be among the parameters that are estimated by the model. Parameters that are associated with a regressor variable are referred to by the name of the corresponding regressor variable. The restriction expressions must be a linear function of the parameters.
The following statements illustrate the use of the RESTRICT statement:
proc cqlim data=mylib.dataset;
model y = x1-x10 / censored(lb=0);
restrict x1*2 <= x2 + x3;
run;
The RESTRICT statement can also be used to impose cross-equation restrictions in multivariate models. The following RESTRICT statement imposes an equality restriction on coefficients of in equation
and
in equation
:
proc cqlim data=mylib.dataset;
model y1 = x1-x10 / discrete;
model y2 = x1-x4 / discrete;
restrict y1.x1=y2.x1;
run;
Lagrange multipliers are reported in the "Parameter Estimates" table for all the active linear constraints. They are identified by the names Restrict1, Restrict2, and so on. The test statistics and p-values for these restrictions are computed using the Lagrange multiplier test that is described in the section Tests on Parameters. Nonactive (nonbinding) restrictions have no effect on the estimation results and are not noted in the output.
The RESTRICT statement is not supported if a BAYES statement is also specified. In Bayesian analysis, the restrictions on parameters are usually introduced through the prior distribution.