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SAS/STAT Software

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 Procedure


The QUANTLIFE procedure performs quantile regression analysis for survival data with censored data by using methods that are based on generalizations of the Kaplan-Meier and the Nelson-Aalen 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 leverage-point diagnostics
  • supports parallel computing when multiple processors are available
  • provides row-wise or column-wise 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, effect-selection stopping, and final-model 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