SEVSELECT Procedure
RESTRICT Statement
RESTRICT restriction1 [, restriction2 …];
The RESTRICT statement imposes linear restrictions on the regression effect parameter estimates of the scale model that is specified in the SCALEMODEL statement. The restrictions are applied to all distributions that are specified in the DIST statement, including user-supplied distributions. The RESTRICT statement allows you to restrict only the parameters that are associated with the regression effects in the SCALEMODEL statement. If you want to restrict the distribution parameters, then you can define your own distribution function in the FCMP procedure and specify the desired restrictions. For more information about defining your own distributions, see the section Defining a Severity Distribution Model with the FCMP Procedure.
You can specify any number of RESTRICT statements. Each restriction is written either as a single linear equation or as a comma-separated list of two or more linear equations. A restriction equation consists of an expression, followed by an equality operator (=) or an inequality operator (<, >, <=, >=), followed by a second expression:
expression operator expression
The operator can be =, <, >, <=, or >=.
RESTRICT Statement Expressions
A restriction expression in a RESTRICT statement is composed of parameter names, constants, and the operators times (
), plus (
), and minus (
). Each restriction expression must be a linear function of the parameters in the model. In addition, no grouping symbols (such as parentheses) are allowed, and the constant factor in any product can appear only on the left-hand side of the times () operator.
In the following example, the assumption is that you have a data table in which y is the loss variable and x1–x3 are continuous variables. The PROC SEVSELECT program uses a RESTRICT statement to impose a restriction on the estimate for the parameter that is associated with the variable x2. Thus, in any solution that the optimizer finds, the solution must satisfy the condition that the parameter that is associated with the variable x2 is equal to 1.5:
proc sevselect data=mylib.exrestrict;
loss y;
scalemodel x1-x3;
dist stweedie;
restrict x2=l.5;
run;
It is important to keep in mind that the parameters that are associated with the variables, not the variables themselves, are restricted. Thus, in the preceding RESTRICT statement, the variable name "x2" refers to the parameter that is associated with the variable x2, not to the variable itself.
Parameter names are 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 in order to refer to that parameter in the RESTRICT statement. You can specify the PRINTINTERNALNAMES option in the PROC SEVSELECT statement if you want to see the internal names of the parameters. When you specify the PRINTINTERNALNAMES option, an extra column is added to the "Parameter Estimates" table to show the internal name of each parameter.
Restrictions should be consistent and not redundant. All restriction equations in all RESTRICT statements are applied jointly.
RESTRICT Statement Examples
Examples of valid RESTRICT statements include the following:
restrict x1=0.1;
restrict a+b=l;
restrict a-b=0, b+c=1.5;
restrict 2*f=g+h, f+g=0;
Examples of invalid RESTRICT statements include the following:
restrict x1^2=4;
restrict x1*x3=4;
restrict x1/x3=2;
restrict sin(a)=0;
restrict a*0.5=l;
restrict 2*(f+h)=1;
In the first four examples of invalid RESTRICT statements, the equation is nonlinear. The fifth example is invalid because the constant factor (0.5) cannot appear on the right-hand side of the times () operator. The last example is invalid because grouping symbols are not allowed.
The set of restrictions must be consistent. For example, you cannot specify the following statement because the three restrictions are not consistent:
restrict f-g=0,
f-h=0,
g-h=1;
Lagrange multipliers are reported in the "Parameter Estimates" table for all the active linear constraints along with a test of the null hypothesis that the restriction is satisfied. They are identified by the names Restrict1, Restrict2, and so on. The test statistic is the estimate divided by its standard error, and it is asymptotically normally distributed. This distribution is used to compute the p-value for the test. Nonactive (nonbinding) restrictions have no effect on the estimation results and are not included in the output.