The QLIM Procedure

### Naming of Parameters

When there is only one equation in the estimation, parameters are named in the same way as in other SAS procedures such as REG, PROBIT, etc. The constant in the regression equation is called Intercept. The coefficients on independent variables are named by the independent variables. The standard deviation of the errors is called _Sigma. If there are Box-Cox transformations, the coefficients are named _Lambda, where increments from 1, or as specified by the user. The limits for the discrete dependent variable are named _Limit. If the LIMIT=varying option is specified, then _Limit starts from 1. If the LIMIT=varying option is not specified, then _Limit is set to 0 and the limit parameters start from . If the HETERO statement is included, the coefficients of the independent variables in the hetero equation are called _H., where is the name of the independent variable. If the parameter name includes interaction terms, it needs to be enclosed in quotation marks followed by . The following example restricts the parameter that includes the interaction term to be greater than zero:

```   proc qlim data=a;
model y = x1|x2;
endogenous y ~ discrete;
restrict "x1*x2"N>0;
run;
```

When there are multiple equations in the estimation, the parameters in the main equation are named in the format of ., where is the name of the dependent variable and is the name of the independent variable. The standard deviation of the errors is called _Sigma.. The correlation of the errors is called _Rho for bivariate model. For the model with three variables it is _Rho.., _Rho.., _Rho... The construction of correlation names for multivariate models is analogous. Box-Cox parameters are called _Lambda. and limit variables are called _Limit.. Parameters in the HETERO statement are named as _H... In the OUTEST= data set, all variables are changed from ’.’ to ’_’.

### Naming of Output Variables

The following table shows the option in the OUTPUT statement, with the corresponding variable names and their explanation.

Option

Name

Explanation

PREDICTED

P_y

Predicted value of

RESIDUAL

RESID_y

Residual of , (y-PredictedY)

XBETA

XBETA_y

Structure part () of equation

ERRSTD

ERRSTD_y

Standard deviation of error term

PROB

PROB_y

Probability that is taking the observed value in this observation (discrete only)

PROBALL

PROB_y

Probability that is taking the th value (discrete only)

MILLS

MILLS_y

Inverse Mills ratio for

EXPECTED

EXPCT_y

Unconditional expected value of

CONDITIONAL

CEXPCT_y

Conditional expected value of , condition on the truncation.

MARGINAL

MEFF_x

Marginal effect of on () with single equation

MEFF_y_x

Marginal effect of on () with multiple equations

MEFF_P_x

Marginal effect of on () with single equation and discrete

MEFF_P_y_x

Marginal effect of on () with multiple equations and discrete

If you prefer to name the output variables differently, you can use the RENAME option in the data set. For example, the following statements rename the residual of as Resid:

```   proc qlim data=one;
model y = x1-x10 / censored;
output out=outds(rename=(resid_y=resid)) residual;
run;
```
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