CSPATIALREG Procedure

The RESTRICT statement imposes linear restrictions on the parameter estimates. You can specify any number of RESTRICT statements.

Each restriction is written as an expression, followed by an equality operator (=) or an inequality operator (<, >, <=, >=), followed by a second expression:

The operator can be =, <, >, <=, or >=.

Restriction expressions can be composed of parameter names; constants; and the operators times (), plus (), and minus (). The restriction expressions must be a linear function of the parameters.

Parameter names are as shown in the Parameter column of the "Parameter Estimates" table. If a parameter name contains a blank or some other special character (such as '*', '-', '(', or ')'), then you must use the internal name of the parameter to refer to that parameter in the RESTRICT statement. You can specify the PRINTINTERNALNAMES option in the PROC CSPATIALREG statement if you want to see the internal names of the parameters. When you specify the PRINTINTERNALNAMES option, the "Parameter Estimates" table includes an additional column that shows the internal name of each parameter.

For more information about how parameters are named in the RESTRICT statement, see the section Parameter Naming Conventions for RESTRICT, TEST, BOUNDS, and INIT Statements.

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 p-values of these Lagrange multipliers are computed using a beta distribution (LaMotte 1994). Nonactive (nonbinding) restrictions have no effect on the estimation results and are not noted in the output.

For example, the following RESTRICT statement constrains the spatial autoregressive coefficient to 0, which removes endogenous interaction effects:

restrict _rho = 0;