LINCON Statement

The CALIS Procedure

LINCON Statement

LINCON constraint < , constraint ... > ;

           where constraint represents
                number operator linear-term or
                linear-term operator number ,
           and linear-term is
                <+|-><coefficient*> parameter <<+|-><coefficient*> parameter... >

The LINCON statement specifies a set of linear equality or inequality constraints of the form

$\sum_{j=1}^n a_{ij} x_j \le b_i , i=1, ... ,m$

The constraints must be separated by commas. Each linear constraint i in the statement consists of a linear combination $\sum_j a_{ij} x_j$ of a subset of the n parameters x_j, j = 1, ... ,n, and a constant value b_i separated by a comparison operator. Valid operators are <=, <, >=, >, and = or, equivalently, LE, LT, GE, GT, and EQ. PROC CALIS cannot enforce the strict inequalities < or >. Note that the coefficients a_ij in the linear combination must be constant numbers and must be followed by an asterisk and the name of a parameter (for example, listed in the PARMS, STD or COV statement). The following is an example of the LINCON statement that sets a linear constraint on parameters x1 and x2:

   lincon       x1 + 3 * x2 <= 1;

Although you can easily express boundary constraints in LINCON statements, for many applications it is much more convenient to specify both the BOUNDS and the LINCON statements in the same PROC CALIS call.

The LINCON statement can contain only parameter names, operators, and numerical constants. If you need to compute the values of the coefficients a_ij or right-hand sides b_i, you can run a preliminary DATA step and create a TYPE=EST data set containing _TYPE_='LE', _TYPE_='GE', or _TYPE_='EQ' observations, then specify this data set as an INEST= or INVAR= data set in a following PROC CALIS run.

Chapter Contents
Previous
Next
Top