README.md

LinRegOutliers

A Julia package for outlier detection in linear regression.

Implemented Methods

• Ordinary Least Squares, Weighted Least Squares, Basic diagnostics
• Hadi & Simonoff (1993)
• Kianifard & Swallow (1989)
• Sebert & Montgomery & Rollier (1998)
• Least Median of Squares
• Least Trimmed Squares
• Minimum Volume Ellipsoid (MVE)
• MVE & LTS Plot
• Billor & Chatterjee & Hadi (2006)
• Pena & Yohai (1995)
• Satman (2013)
• Satman (2015)
• Setan & Halim & Mohd (2000)
• Least Absolute Deviations (LAD)
• Least Trimmed Absolute Deviations (LTA)
• Hadi (1992)
• Marchette & Solka (2003) Data Images
• Satman's GA based LTS estimation (2012)
• Fischler & Bolles (1981) RANSAC Algorithm
• Minimum Covariance Determinant Estimator
• Imon (2005) Algorithm
• Barratt & Angeris & Boyd (2020) CCF algorithm
• Atkinson (1994) Forward Search Algorithm
• BACON Algorithm (Billor & Hadi & Velleman (2000))
• Hadi (1994) Algorithm
• Chatterjee & Mächler (1997)
• Summary

Unimplemented Methods

• Depth based estimators (Regression depth, deepest regression, etc.)
• Theil & Sen estimator for mutliple regression

Installation

julia> ]
(@v1.5) pkg> add LinRegOutliers

or

julia> using Pgk
julia> Pkg.add("LinRegOutliers")

then

julia> using LinRegOutliers

to make all the stuff be ready!

Examples

julia> using LinRegOutliers
julia> # Regression setting for Hawkins & Bradu & Kass data
julia> reg = createRegressionSetting(@formula(y ~ x1 + x2 + x3), hbk)
julia> smr98(reg)
14-element Array{Int64,1}:
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14

julia> py95(reg)["outliers"]
14-element Array{Int64,1}:
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14

julia> reg = createRegressionSetting(@formula(calls ~ year), phones);
julia> lms(reg)
Dict{Any,Any} with 6 entries:
  "stdres"    => [2.42593, 1.62705, 0.550525, 0.584612, 0.155943, -0.272726, -0.608843, -1.03751, -0.448118, -0.228929  …  93.4182, 96.9692, 112.552, 127.209, 147.419, 174.108…
  "S"         => 1.08048
  "outliers"  => [14, 15, 16, 17, 18, 19, 20, 21]
  "objective" => 0.43276
  "coef"      => [-56.3796, 1.16317]
  "crit"      => 2.5 

julia> reg = createRegressionSetting(@formula(calls ~ year), phones);

julia> lts(reg)
Dict{Any,Any} with 6 entries:
  "betas"            => [-56.5219, 1.16488]
  "S"                => 1.10918
  "hsubset"          => [11, 10, 5, 6, 23, 12, 13, 9, 24, 7, 3, 4, 8]
  "outliers"         => [14, 15, 16, 17, 18, 19, 20, 21]
  "scaled.residuals" => [2.41447, 1.63472, 0.584504, 0.61617, 0.197052, -0.222066, -0.551027, -0.970146, -0.397538, -0.185558  …  91.0312, 94.4889, 109.667, 123.943, 143.629, …
  "objective"        => 3.43133

julia> # Matrix of independent variables of Hawkins & Bradu & Kass data
julia> data = hcat(hbk.x1, hbk.x2, hbk.x3);
julia> dataimage(data)

julia> using LinRegOutliers
julia> reg = createRegressionSetting(@formula(calls ~ year), phones);
julia> atkinsonstalactiteplot(reg)
m           1         2
   123456789012345678901234
 2              ********   
 3              ********   
 4 +            ********   
 5 +            ********   
 6 +            ********   
 7 +            ********   
 8 +            ********   
 9 +            ********+  
10 +            ********+  
11 +            ********   
12              ********   
13 +            ********   
14              ********   
15              ********   
16              ********   
17              ********   
18               *******+  
19               ****** +++
20               ****** +++
21               ****** +++
22               ****** +++
23               +++*** +++
24                  ++* +++
   123456789012345678901234
            1         2

News

• We implemented algorithm(X, y) style calls for all of the algorithms where X is the design matrix and y is the response vector.
• We implemented ~25 outlier detection algorithms which covers a high percentage of the literature.

Want to have contributions?

You are probably the right contributor

• If you have statistics background
• If you like Julia

However, the second condition is more important because an outlier detection algorithm is just an algorithm. Reading the implemented methods is enough to implement new ones. Please follow the issues. Here is the a bunch of first shot introductions for new comers. Welcome and thank you in advance!

Contact & Communication

• Please use issues for a new feature request or bug reports
• We are in #linregoutliers channel on Julia Slack for any discussion requires online chatting.