The HPQUANTSELECT Procedure

Fit Statistics

The "Fit Statistics" table displays fit statistics for the selected model. The statistics include the following:

  • Objective Function, total sum of check losses. Objective Function is denoted as $D(\tau )$ in Table 14.6.

  • R1, a measure between 0 and 1 that indicates the portion of the (corrected) total check losses attributed to the fit rather than left to residuals. It is calculated as $1-{\frac{D(\tau )}{D_0(\tau )}}$. It is the quantile regression counterpart of the linear regression R square.

  • Adj R1, the adjusted R1, a version of R1 that has been adjusted for degrees of freedom. It is calculated as

    \[ \mbox{Adj R1} = 1 - \frac{n-i}{n-p}(1-\mbox{R1}) \]

    where $i=1$ if the intercept is forced in and $i=0$ otherwise , n is the number of observations used to fit the model, and p is the number of parameters in the model.

  • the fit criteria AIC, AICC, and SBC if they are used in the selection process. For the formulas to evaluate these criteria, see Table 14.6.

  • the average check loss (ACL) on the training, validation, and test data

You can request the "Fit Statistics" tables for the model at each step of the selection process by specifying the DETAILS= option in the SELECTION statement.