Quantile Regression

Implementation of quantile regression.

• Install using ]add QuantileRegressions
• Main author: Patrick Kofod Mogensen
• Contact: Use the https://github.com/pkofod/QuantileRegressions.jl/issues page
• License: BSD-3

Example

The file examples/qreg_example.jl shows how to use the functions provided here. It replicates part of the analysis in:

• Koenker, Roger and Kevin F. Hallock. "Quantile Regression". Journal of Economic Perspectives, Volume 15, Number 4, Fall 2001, Pages 143–156

We are interested in the relationship between income and expenditures on food for a sample of working class Belgian households in 1857 (the Engel data), so we estimate a least absolute deviation model.

julia> using QuantileRegressions

julia> # Load data
       url = "http://vincentarelbundock.github.io/Rdatasets/csv/quantreg/engel.csv"
"http://vincentarelbundock.github.io/Rdatasets/csv/quantreg/engel.csv"

julia> df = readtable(download(url))
235×3 DataFrames.DataFrame
│ Row │ x   │ income  │ foodexp │
├─────┼─────┼─────────┼─────────┤
│ 1   │ 1   │ 420.158 │ 255.839 │
│ 2   │ 2   │ 541.412 │ 310.959 │
│ 3   │ 3   │ 901.157 │ 485.68  │
│ 4   │ 4   │ 639.08  │ 402.997 │
│ 5   │ 5   │ 750.876 │ 495.561 │
│ 6   │ 6   │ 945.799 │ 633.798 │
│ 7   │ 7   │ 829.398 │ 630.757 │
│ 8   │ 8   │ 979.165 │ 700.441 │
⋮
│ 227 │ 227 │ 776.596 │ 485.52  │
│ 228 │ 228 │ 1230.92 │ 772.761 │
│ 229 │ 229 │ 1807.95 │ 993.963 │
│ 230 │ 230 │ 415.441 │ 305.439 │
│ 231 │ 231 │ 440.517 │ 306.519 │
│ 232 │ 232 │ 541.201 │ 299.199 │
│ 233 │ 233 │ 581.36  │ 468.001 │
│ 234 │ 234 │ 743.077 │ 522.602 │
│ 235 │ 235 │ 1057.68 │ 750.32  │

julia> # Fit least absolute deviation model (quantile  = .5)
       ResultQR = qreg(@formula(foodexp~income), df, .5)
StatsModels.TableRegressionModel{QuantileRegressions.QRegModel,Array{Float64,2}}

foodexp ~ 1 + income

Coefficients:
             Quantile Estimate Std.Error t value
(Intercept)       0.5  81.4822   14.6345 5.56783
income            0.5 0.560181 0.0131756 42.5164

The results look pretty close to Stata 12's qreg:

. insheet using engel.csv
. qreg foodexp income, vce(iid, kernel(epan2))
Median regression                                    Number of obs =       235
  Raw sum of deviations 46278.06 (about 582.54126)
  Min sum of deviations 17559.93                     Pseudo R2     =    0.6206

------------------------------------------------------------------------------
     foodexp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      income |   .5601805   .0131763    42.51   0.000     .5342206    .5861403
       _cons |   81.48233   14.63518     5.57   0.000     52.64815    110.3165
------------------------------------------------------------------------------

We can also compute and plot (using Julia's Winston) results for various quantiles. Full code to produce the figure is in the examples folder.

History

This package was originally created as a port of the reweighed least squares code by Vincent Arel-Bundock from the python project statsmodels. All contributions can be seen via the contributors page.