QLIM Procedure

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, and so on. 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 _Lambdai, where i increments from 1, or as specified by the user. The limits for the discrete dependent variable are named _Limiti. If the LIMIT=varying option is specified, then _Limiti starts from 1. If the LIMIT=varying option is not specified, then _Limit1 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.x, where x is the name of the independent variable. You can form the name of the parameter associated with an interaction regressor by concatenating the interacting variables with an underscore. 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>0;
run;

When there are multiple equations in the estimation, the parameters in the main equation are named in the format of y.x, where y is the name of the dependent variable and x is the name of the independent variable. The standard deviation of the errors is called _Sigma.y. The correlation of the errors is called _Rho for bivariate model. For the model with three variables it is _Rho.y1.y2, _Rho.y1.y3, _Rho.y2.y3. The construction of correlation names for multivariate models is analogous. Box-Cox parameters are called _Lambdai.y and limit variables are called _Limiti.y. Parameters in the HETERO statement are named as _H.y.x. In the OUTEST= data set, all variables are changed from '.' to '_'.

Table 11 shows the option in the OUTPUT statement, with the corresponding variable names and their explanation.

Table 11: OUTPUT Statement Options and Variable Names

Option	Name	Explanation
PREDICTED	P_y	Predicted value of y
RESIDUAL	RESID_y	Residual of y, (y-PredictedY)
XBETA	XBETA_y	Structure part () of y equation
ERRSTD	ERRSTD_y	Standard deviation of error term
PROB	PROB_y	Probability that y is taking the observed value in this observation (discrete y only)
PROBALL	PROBi_y	Probability that y is taking the ith value (discrete y only)
MILLS	MILLS_y	Inverse Mills ratio for y
EXPECTED	EXPCT_y	Unconditional expected value of y
CONDITIONAL	CEXPCT_y	Conditional expected value of y, condition on the truncation.
MARGINAL	MEFF_x	Marginal effect of x on y () with single equation
	MEFF_y_x	Marginal effect of x on y () with multiple equations
	MEFF_Pi_x	Marginal effect of x on y () with single equation and discrete y
	MEFF_Pi_y_x	Marginal effect of x on y () with multiple equations and discrete y
TE1	TE1	Technical efficiency estimate for each producer proposed by Battese and Coelli (1988)
TE2	TE2	Technical efficiency estimate for each producer proposed by Jondrow et al. (1982)

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 y as Resid:

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