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Title: Assessing robustness of factor ranking for supersaturated designs

Abstract

Supersaturated designs can potentially be a beneficial tool for efficiently exploring a large number of factors with a moderately sized design. However, because more factors are being considered than there are runs, the stability of the identified factors depends heavily on effect sparsity and the lack of highly influential observations. A helpful tool for the analysis of supersaturated designs is least absolute shrinkage and selection operation (LASSO), which is useful when the effects of many explanatory variables are sparse in a high-dimensional dataset. To understand the impact of individual observations on the selected factors, the LASSO influence plot was created. This work describes an application of this plot and its variants that can be used to identify influential points, increase understanding of the impact of individual observations on model parameters, and the robustness of results in analyses with supersaturated designs. These graphical methods can serve as a complement to other regression diagnostics techniques in the LASSO regression setting.

Authors:
 [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Pukyong National Univ., Busan (Korea). Dept. of Statistics
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE; USDOD; National Research Foundation of Korea (NRF)
OSTI Identifier:
1467262
Report Number(s):
LA-UR-17-24159
Journal ID: ISSN 0748-8017
Grant/Contract Number:  
AC52-06NA25396; 2017R1D1A3B03028648
Resource Type:
Accepted Manuscript
Journal Name:
Quality and Reliability Engineering International
Additional Journal Information:
Journal Volume: 34; Journal Issue: 3; Journal ID: ISSN 0748-8017
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Supersaturated designs; influential observations; LASSO influence plots; LASSO variable selection ranking plots; 3-D LASSO influence plots

Citation Formats

Jang, Dae-Heung, and Anderson-Cook, Christine M. Assessing robustness of factor ranking for supersaturated designs. United States: N. p., 2018. Web. doi:10.1002/qre.2262.
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Jang, Dae-Heung, & Anderson-Cook, Christine M. Assessing robustness of factor ranking for supersaturated designs. United States. https://doi.org/10.1002/qre.2262
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Jang, Dae-Heung, and Anderson-Cook, Christine M. Tue . "Assessing robustness of factor ranking for supersaturated designs". United States. https://doi.org/10.1002/qre.2262. https://www.osti.gov/servlets/purl/1467262.
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@article{osti_1467262,
title = {Assessing robustness of factor ranking for supersaturated designs},
author = {Jang, Dae-Heung and Anderson-Cook, Christine M.},
abstractNote = {Supersaturated designs can potentially be a beneficial tool for efficiently exploring a large number of factors with a moderately sized design. However, because more factors are being considered than there are runs, the stability of the identified factors depends heavily on effect sparsity and the lack of highly influential observations. A helpful tool for the analysis of supersaturated designs is least absolute shrinkage and selection operation (LASSO), which is useful when the effects of many explanatory variables are sparse in a high-dimensional dataset. To understand the impact of individual observations on the selected factors, the LASSO influence plot was created. This work describes an application of this plot and its variants that can be used to identify influential points, increase understanding of the impact of individual observations on model parameters, and the robustness of results in analyses with supersaturated designs. These graphical methods can serve as a complement to other regression diagnostics techniques in the LASSO regression setting.},
doi = {10.1002/qre.2262},
journal = {Quality and Reliability Engineering International},
number = 3,
volume = 34,
place = {United States},
year = {Tue Jan 23 00:00:00 EST 2018},
month = {Tue Jan 23 00:00:00 EST 2018}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1002/qre.2262
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Cited by: 1 work
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Figures / Tables:

Table 1 Table 1: Supersaturated design and response data demonstrated first by Lin
All figures and tables (22 total)
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Works referenced in this record:

Analysis of supersaturated designs via the Dantzig selector
journal, July 2009

  • Phoa, Frederick K. H.; Pan, Yu-Hui; Xu, Hongquan
  • Journal of Statistical Planning and Inference, Vol. 139, Issue 7
  • DOI: 10.1016/j.jspi.2008.10.023

Examining robustness of model selection with half-normal and LASSO plots for unreplicated factorial designs
journal, April 2017

  • Jang, Dae-Heung; Anderson-Cook, Christine M.
  • Quality and Reliability Engineering International, Vol. 33, Issue 8
  • DOI: 10.1002/qre.2156

Application of strategic sample composition to the screening of anti-inflammatory drugs in water samples using solid-phase microextraction
journal, October 2004

  • Carpinteiro, J.; Quintana, J. B.; Martı́nez, E.
  • Analytica Chimica Acta, Vol. 524, Issue 1-2
  • DOI: 10.1016/j.aca.2004.03.026

Bayesian D-optimal supersaturated designs
journal, January 2008

  • Jones, Bradley; Lin, Dennis K. J.; Nachtsheim, Christopher J.
  • Journal of Statistical Planning and Inference, Vol. 138, Issue 1
  • DOI: 10.1016/j.jspi.2007.05.021

Discussion: The Dantzig selector: Statistical estimation when p is much larger than n
journal, December 2007

Influence Plots for LASSO
journal, November 2016

  • Jang, Dae-Heung; Anderson-Cook, Christine M.
  • Quality and Reliability Engineering International, Vol. 33, Issue 7
  • DOI: 10.1002/qre.2106

Construction of supersaturated designs through partially aliased interactions
journal, January 1993

DASSO: connections between the Dantzig selector and lasso
journal, January 2009

  • James, Gareth M.; Radchenko, Peter; Lv, Jinchi
  • Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 71, Issue 1
  • DOI: 10.1111/j.1467-9868.2008.00668.x
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    Figures / Tables found in this record:

    Table 1 (p. 3)table
    Table 2 (p. 4)table
    Figure 1 (p. 5)figure
    Figure 2 (p. 5)figure
    Figure 3 (p. 6)figure
    Figure 4 (p. 7)figure
    Table 3 (p. 7)table
    Figure 5 (p. 8)figure
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    Table 4 (p. 9)table
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    Figure 11 (p. 13)figure
    Figure 12 (p. 14)figure
    Table 5 (p. 14)table
    Figure 13 (p. 15)figure
    Figure 14 (p. 15)figure
    Table 6 (p. 16)table
    Figure 15 (p. 17)figure
    Figure 16 (p. 18)figure
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