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))
Summary

Unimplemented Methods

Hadi (1994) Algorithm
Depth based estimators (Regression depth, deepest regression, etc.)
Theil & Sen estimator for mutliple regression

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

detectOutliersImage

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

detectOutliersImage

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.