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 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
The constraints must be separated by commas. Each linear constraint i in the statement consists of a linear combination of a subset of the n parameters xj, j = 1, ... ,n, and a constant value bi 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 aij 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 aij or right-hand sides bi, 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.

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