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The MDC Procedure

BOUNDS Statement

BOUNDS bound1 <, bound2 ...> ;

The BOUNDS statement imposes simple boundary constraints on the parameter estimates. BOUNDS statement constraints refer to the parameters estimated by the MDC procedure. You can specify any number of BOUNDS statements.

Each bound is composed of parameters, constants, and inequality operators:

item operator item < operator item < operator item ...> >

Each item is a constant, parameter, or list of parameters. Parameters associated with a regressor variable are referred to by the name of the corresponding regressor variable. Each operator is ’<’, ’>’, ’<=’, or ’>=’.

You can use both the BOUNDS statement and the RESTRICT statement to impose boundary constraints; however, the BOUNDS statement provides a simpler syntax for specifying these kinds of constraints. See the section RESTRICT Statement as well.

Lagrange multipliers are reported for all the active boundary constraints. In the displayed output, the Lagrange multiplier estimates are identified with the names Restrict1, Restrict2, and so forth. The probability of the Lagrange multipliers is computed using a beta distribution (LaMotte 1994). Nonactive, or nonbinding, bounds have no effect on the estimation results and are not noted in the output.

The following BOUNDS statement constrains the estimates of the coefficient of ttime to be negative and the coefficients of x1 through x10 to be between zero and one. This example illustrates the use of parameter lists to specify boundary constraints.

   bounds ttime < 0,
          0 < x1-x10 < 1;
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