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Predictor relative importance and matching regression parameters

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  • Stan Lipovetsky
  • W. Michael Conklin

Abstract

Predictor importance in applied regression modeling gives the main operational tools for managers and decision-makers. The paper considers estimation of predictors' importance in regression using measures introduced in works by Gibson and R. Johnson (GJ), then modified by Green, Carroll, and DeSarbo, and developed further by J. Johnson (JJ). These indices of importance are based on the orthonormal decomposition of the data matrix, and the work shows how to improve this approximation. Using predictor importance, the regression coefficients can also be adjusted to reach the best data fit and to be meaningful and interpretable. The results are compared with the robust to multicollinearity, but computationally difficult, Shapley value regression (SVR). They show that the JJ index is good for importance estimation, but the GJ index outperforms it if both predictor importance and coefficients of regression are needed; hence, this index (GJ) can be used in place of the more computationally intensive estimation by SVR. The results can be easily estimated by the considered approach that is very useful in practical regression modeling and analysis, especially for big data.

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  • Stan Lipovetsky & W. Michael Conklin, 2015. "Predictor relative importance and matching regression parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 1017-1031, May.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:5:p:1017-1031
    DOI: 10.1080/02664763.2014.994480
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    References listed on IDEAS

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    1. Stan Lipovetsky & Michael Conklin, 2001. "Analysis of regression in game theory approach," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(4), pages 319-330, October.
    2. Stan Lipovetsky & W. Michael Conklin, 2010. "Reply to the paper ‘Do not adjust coefficients in Shapley value regression’ by U. Gromping, S. Landau, Applied Stochastic Models in Business and Industry, 2009; DOI: 10.1002/asmb.773," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(2), pages 203-204, March.
    3. Conklin, Michael & Powaga, Ken & Lipovetsky, Stan, 2004. "Customer satisfaction analysis: Identification of key drivers," European Journal of Operational Research, Elsevier, vol. 154(3), pages 819-827, May.
    4. Richard Johnson, 1966. "The minimal transformation to orthonormality," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 61-66, March.
    5. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    6. Joachim Büschken & Thomas Otter & Greg M. Allenby, 2013. "The Dimensionality of Customer Satisfaction Survey Responses and Implications for Driver Analysis," Marketing Science, INFORMS, vol. 32(4), pages 533-553, July.
    7. Soofi, E. S. & Retzer, J. J., 2002. "Information indices: unification and applications," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 17-40, March.
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    Cited by:

    1. Stan Lipovetsky, 2021. "Predictor Analysis in Group Decision Making," Stats, MDPI, vol. 4(1), pages 1-14, February.
    2. Stan Lipovetsky & Michael Conklin, 2018. "Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles," Stats, MDPI, vol. 1(1), pages 1-7, November.

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