`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 also the section RESTRICT Statement.

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 on. The probability of the Lagrange multipliers is computed using a beta distribution (LaMotte 1994). Nonactive (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;