Quantile Regression
Ordinary least squares regression models the relationship between one or more covariates X and the conditional mean of the
response variable Y given X=x. Quantile regression extends the regression model to conditional quantiles of the response
variable, such as the 90th percentile. Quantile regression is particularly useful when the rate of change in the conditional
quantile, expressed by the regression coefficients, depends on the quantile. The main advantage of quantile regression over
least squares regression is its flexibility for modeling data with heterogeneous conditional distributions. Data of this
type occur in many fields, including biomedicine, econometrics, and ecology.
The SAS/STAT quantile regression procedures include the following:
 QUANTLIFE — Quantile regression analysis for survival data with censored data
 QUANTREG — Quantile regression models
 QUANTSELECT — Effect selection for linear quantile regression models
QUANTLIFE Procedure
The QUANTLIFE procedure performs quantile regression analysis for survival data with censored data by using methods that are based
on generalizations of the KaplanMeier and the NelsonAalen estimators. The following are highlights of the QUANTLIFE procedure's features:
 supports hypothesis tests for the regression parameter
 supports semiparametric quantile regression that uses spline effects
 automatically creates survival plots, conditional quantile plots, and quantile process plots
 supports classification variables
 creates an output data set that contains predicted values and residuals
 creates an output data set that contains survival function estimates or the conditional quantile function estimates for every set of covariates

 supports an EFFECT statement that enables you to construct special collections of columns for design matrices
 supports weighted quantile regression
 computes confidence intervals for the quantile regression parameters by using resampling methods
 uses an interior point algorithm for parameter estimation, which uses parallel computing when multiple processors are available
 performs BY group processing, which enables you to obtain separate analyses of grouped observations

For further details, see
QUANTLIFE Procedure
QUANTREG Procedure
The QUANTREG procedure uses quantile regression to model the effects of covariates on the conditional quantiles of a response variable.
The following are highlights of the QUANTREG procedure's features:
 offers simplex, interior point, and smoothing algorithms for estimation
 provides sparsity, rank, and resampling methods for confidence intervals
 provides asymptotic and bootstrap methods for covariance and correlation matrices of the estimated parameters
 provides the Wald and likelihood ratio tests for the regression parameter estimates
 perform hypothesis tests for the estimable functions, construct confidence limits, and obtain specific nonlinear transformations
 enables you to construct special collections of columns for design matrices
 provides outlier and leveragepoint diagnostics
 supports parallel computing when multiple processors are available

 provides rowwise or columnwise output data sets with multiple quantiles
 provides regression quantile spline fits
 automatically produces fit plots, diagnostic plots, and quantile process plots by using ODS Graphics
 performs BY group processing, whcih enables you to obtain separate analyses on grouped observations
 perform weighted estimation
 creates an output data set that contains predicted values, residuals, estimated standard errors, and other statistics
 creates an output data set that contains the parameter estimates for all quantiles
 create a SAS data set that corresponds to any output table

For further details, see
QUANTREG Procedure
QUANTSELECT Procedure
The QUANTSELECT procedure performs effect selection in the framework of quantile regression. A variety of effect selection methods are
available, including greedy methods and penalty methods. PROC QUANTSELECT offers extensive capabilities for customizing the
effect selection processes with a variety of candidate selecting, effectselection stopping, and finalmodel choosing criteria.
It also provides graphical summaries for the effect selection processes.
The following are highlights of the QUANTSELECT procedure's features:
 supports the following model specifications:
 interaction (crossed) effects and nested effects
 constructed effects such as regression splines
 hierarchy among effects
 partitioning of data into training, validation, and testing roles
 provides the following selection controls:
 multiple methods for effect selection
 selection for quantile process and single quantile levels
 selection of individual or grouped effects
 selection based on a variety of selection criteria
 stopping rules based on a variety of model evaluation criteria

 provides graphical representations of the selection process
 provides output data sets that contain predicted values and residuals
 provides an output data set that contains the parameter estimates from a quantile process regression
 provides an output data set that contains the design matrix
 provides macro variables that contain selected effects

For further details, see
QUANTSELECT Procedure