CQLIM Procedure

HETERO Statement

HETERO dependent-variables exogenous-variables </ options > ;

The HETERO statement specifies variables that are related to the heteroscedasticity of the residuals and the way that these variables are used to model the error variance. PROC CQLIM supports the following heteroscedastic regression model:

y Subscript i Baseline equals bold x prime Subscript i Baseline bold-italic beta plus epsilon Subscript i

epsilon Subscript i Baseline tilde normal upper N left-parenthesis 0 comma sigma Subscript i Superscript 2 Baseline right-parenthesis

For more information about the specification of functional forms, see the section Heteroscedasticity.

The HETERO statement is currently not supported with a BAYES statement.

You can use the HETERO statement only for univariate models.

The following options specify the functional forms of heteroscedasticity:

LINK=EXP | LINEAR

specifies the functional form. You can specify the following values:

EXP: specifies the exponential link function:
LINEAR: specifies the linear link function:

By default, LINK=EXP.

NOCONST

specifies that no constant appear in the exponential heteroscedasticity model:

SQUARE

estimates the model by using the square of the linear heteroscedasticity function. For example, you can specify the heteroscedasticity function

by using the following code:

model y = x1 x2 / censored(lb=0);
hetero y ~ z1 / link=linear square;

The SQUARE option does not apply to the exponential heteroscedasticity function, because the square of an exponential function of is the same as the exponential of . Hence, the only difference is that all estimates are divided by two.

This option is ignored if you do not specify the LINK= option.

Last updated: November 24, 2025