The HPQUANTSELECT Procedure

MODEL Statement

  • MODEL dependent=<effects> / <options>;

The MODEL statement names the dependent variable and the explanatory effects, including covariates, main effects, interactions, and nested effects. If you omit the explanatory effects, PROC HPQUANTSELECT fits an intercept-only model.

After the keyword MODEL, the dependent (response) variable is specified, followed by an equal sign. The explanatory effects follow the equal sign. For information about constructing the model effects, see the section Parameterization of Model Effects.

You can specify the following options in the MODEL statement after a slash (/):

CLB

requests the 100 left-parenthesis 1 minus alpha right-parenthesis% upper and lower confidence limits for the parameter estimates. By default, the 95% limits are computed; you can use the ALPHA= option in the PROC HPQUANTSELECT statement to change the alpha level.

INCLUDE=n
INCLUDE=single-effect
INCLUDE=(effects)

forces effects to be included in all models. If you specify INCLUDE=n, then the first n effects that are listed in the MODEL statement are included in all models. If you specify INCLUDE=single-effect or if you specify a list of effects within parentheses, then the specified effects are forced into all models. The effects that you specify in the INCLUDE= option must be explanatory effects that are defined in the MODEL statement.

NOINT

suppresses the intercept term that is otherwise included in the model.

ORDERSELECT

specifies that, for the selected model, effects be displayed in the order in which they first entered the model. If you do not specify this option, then effects in the selected model are displayed in the order in which they appear in the MODEL statement.

QUANTILES=number-list
QUANTILE=number-list

specifies the quantile levels for the quantile regression. You can specify any number of quantile levels in left-parenthesis 0 comma 1 right-parenthesis. If you do not specify this option, the HPQUANTSELECT procedure performs median regression effect selection that corresponds to QUANTILE=0.5.

SPARSITY(<BF | HS> <IID>)

specifies the suboptions for estimating the sparsity function. You can specify the Bofinger method by using the BF suboption or the Hall-Sheather method by using the HS suboption. By default, the Hall-Sheather method is used. You can also specify the IID suboption to assume that the quantile regression errors satisfy the independently and identically distributed (iid) assumption. Let f Subscript i and upper F Subscript i, respectively, denote the probability density function and the cumulative distribution function of the ith error for i equals 1 comma ellipsis comma n. The iid assumption means that there exist f and F such that f equals f 1 equals midline-horizontal-ellipsis equals f Subscript n and upper F equals upper F 1 equals midline-horizontal-ellipsis equals upper F Subscript n. If you specify the IID option, the covariance matrix of the parameter estimates, omega squared left-parenthesis tau comma upper F right-parenthesis left-parenthesis bold upper X prime bold upper X right-parenthesis Superscript minus, is adopted for computing the confidence limits and the Wald statistics, where omega squared left-parenthesis tau comma upper F right-parenthesis equals tau left-parenthesis 1 minus tau right-parenthesis slash f squared left-parenthesis upper F Superscript negative 1 Baseline left-parenthesis tau right-parenthesis right-parenthesis. By default, the covariance matrix of the parameter estimates is non-iid and takes the sandwich form: n Superscript negative 2 Baseline tau left-parenthesis 1 minus tau right-parenthesis bold upper H Subscript n Superscript minus Baseline left-parenthesis bold upper X prime bold upper X right-parenthesis bold upper H Subscript n Superscript minus Baseline comma where bold upper H Subscript n Baseline equals n Superscript negative 1 Baseline sigma-summation Underscript i equals 1 Overscript n Endscripts f Subscript i Baseline left-parenthesis upper F Subscript i Superscript negative 1 Baseline left-parenthesis tau right-parenthesis right-parenthesis bold x Subscript i Baseline bold x Subscript i Superscript prime Baseline period For more information, see the section Details: HPQUANTSELECT Procedure.

START=n
START=single-effect
START=(effects)

begins the effect-selection process in the forward and stepwise selection methods from the initial model that you designate. If you specify START=n, then the starting model consists of the first n effects listed in the MODEL statement. If you specify START=single-effect or if you specify a list of effects within parentheses, then the starting model consists of these specified effects. The effects that you specify in the START= option must be explanatory effects defined in the MODEL statement. The START= option is not available when you specify METHOD=BACKWARD in the SELECTION statement.

STB

produces standardized regression coefficients. A standardized regression coefficient is computed by dividing a parameter estimate by the ratio of the sample standard deviation of the dependent variable to the sample standard deviation of the regressor. If you use the INCLUDE= option to force some effects to be in the model, then the QTRSELECT procedure computes the sample standard deviation against all the effects that are forced in, as follows. Let bold upper X 1 denote the design submatrix of p 1 regressors that consists of all the effects that are forced in, and let bold z denote the dependent variable or any regressor. Then the sample standard deviation of bold z is computed as

s Subscript z Baseline equals StartRoot StartFraction bold z prime left-bracket bold upper I minus bold upper X 1 left-parenthesis bold upper X prime 1 bold upper X 1 right-parenthesis Superscript negative 1 Baseline bold upper X prime 1 right-bracket bold z Over n minus p 1 EndFraction EndRoot
TOL

produces tolerance values for the estimates. Tolerance for a parameter is defined as 1 minus upper R squared, where upper R squared is obtained from the ordinary least squares regression of the parameter on all other parameters in the model.

VIF

produces variance inflation factors in the parameter estimates table. Variance inflation is the reciprocal of tolerance.

Last updated: December 09, 2022