Quickstart Guide

Installation

QuantReg.jl is available via the Julia general repository. To use it on your machine, you will need to run the following commands:

julia> using Pkg
julia> Pkg.add("QuantReg")

The Gurobi.jl dependency package may fail to build if Gurobi is not installed on the machine; this is okay. QuantReg.jl can now be loaded in the REPL with the following command:

julia> using QuantReg

Note that pre-compilation may take some time the first time the package is loaded; this is also to be expected.

Running your first model

The easiest way to generate, fit, and compute inference for a quantile regression model is via the rq command.

julia> using CSV, QuantReg
julia> df = CSV.read("/path/to/data.csv") # load dataset to fit
julia> model = rq(@formula(Y ~ X1 + X2 + X3), df; τ=0.50) # fit dataset

The resulting object model contains a median regression fitted and with inference computed according to default settings. For more information on default settings, see the QuantRegModel setting.

Within the result object, model.fit contains the results of fitting the model, including the coefficients, residuals, fitted values, and, for some fitting methods, the solution to the dual problem. For more information on how to access these values, see the QuantRegFit section.

model.inf contains the results of computing inference for the model, which encompasses confidence interval bounds if a rank test inversion is used to compute inference and encompasses standard errors, test statistics, p-values, and confidence interval bounds if inference is computed using asymptotic estimates of the covariance matrix. For more information on how to access these values, see the QuantRegInf section.

Running models at multiple quantiles

It is also possible to fit more than one model simultaneously by passing an array of τ values.

julia> models = rq(@formula(Y ~ X1 + X2 + X3), df; τ=[0.25, 0.50, 0.75])

This call yields a QuantRegModels object containing three quantile regression models, fit at the 0.25th, 0.50th, and 0.75th quantiles. The individual models can be accessed by using the τ values as indices. For example,

julia> models[0.25]

will return the quantile regression model fit at the 0.25th quantile. For more information on QuantRegModels objects, see the QuantRegModels section.

Configuring models

Users can provide more detailed model specifications as keyword arguments to the quantile regression command. Any specification field in the QuantRegModel type can be accepted as a keyword argument. The following command fits a quantile regression model at the 0.80th quantile using the Frisch-Newton and computes 80% confidence intervals under the assumption that the conditional quantile function is locally (in tau) linear (in x) (i.e. regression errors are not i.i.d.).

julia> rq(@formula(Y ~ X1 + X2 + X3), df; τ=0.80, fitmethod="fn", α=0.20, iid=false)

rq(formula::FormulaTerm, data::DataFrame; kwargs)

Under the hood of rq

In code, the rq function is really a wrapper for three functions that constitute a common workflow. It first constructs a new QuantRegModel object according to the specifications provided. Then, it fits the model in place according to the specifications in the model with fit!. This function call updates the QuantRegFit object stored in the model. Finally, it computes inference for the model according to the specifications in the model with compute_inf!. This function call updates the QuantRegInf object stored in the model.

For example, the call:

julia> model = rq(@formula(Y ~ X1 + X2 + X3), df; τ=0.80, fitmethod="fn", α=0.20, iid=false)

is equivalent to:

julia> model = QuantRegModel(@formula(Y ~ X1 + X2 + X3), df; τ=0.80, fitmethod="fn", α=0.20, 
                             iid=false)
julia> fit!(model)
julia> compute_inf!(model)