The QUANTREG Procedure

TEST Statement

Testing Effects of Covariates
Testing for Heteroscedasticity

<label:> TEST effects </ options> ;

In quantile regression analysis, you might be interested in testing whether a covariate effect is statistically significant for a given quantile. In other situations, you might be interested in testing whether the coefficients of a covariate are the same across a set of quantiles. You can use the TEST Statement to perform these tests.

Testing Effects of Covariates

You can use TEST statement to obtain a test for the canonical linear hypothesis concerning the parameters of the tested effects

$\beta _{j} = 0, \ \ j=i_1,\ldots ,i_ q$

where q is the total number of parameters of the tested effects. The tested effects can be any set of effects in the MODEL statement. Three types of tests (Wald, likelihood ratio, and rank methods) are available for testing effects of covariates by the following options in the TEST statement after a slash (/):

WALD: requests Wald tests.
LR: requests likelihood ratio tests.
RANKSCORE <(NORMAL | WILCOXON | SIGN | TAU)>: requests rank tests. The NORMAL, WILCOXON, and SIGN functions are implemented and suitable for iid error models, and the TAU score function is implemented and appropriate for non-iid error models. By default, the TAU score function is used. See Koenker (2005) for more information about the score functions.

Testing for Heteroscedasticity

You can test whether there is any difference among the estimated coefficients across quantiles if several quantiles are specified in the MODEL statement. The test for such heteroscedasticity can be requested by the option QINTERACT after a slash (/) in the TEST statement. See Example 77.5.

You can submit multiple TEST statements, provided that they appear after the MODEL statement. The optional label, which must be a valid SAS name, is used to identify output from the corresponding TEST statement. See the section Linear Test for details about these tests.