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Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators

Author

Listed:
  • Massimiliano Giacalone

    (University of Naples ‘Federico II’, Complesso Universitario di Monte Sant’Angelo)

  • Demetrio Panarello

    (Parthenope University of Naples)

  • Raffaele Mattera

    (University of Naples ‘Federico II’, Complesso Universitario di Monte Sant’Angelo)

Abstract

Multicollinearity is one of the most important issues in regression analysis, as it produces unstable coefficients’ estimates and makes the standard errors severely inflated. The regression theory is based on specific assumptions concerning the set of error random variables. In particular, when errors are uncorrelated and have a constant variance, the ordinary least squares estimator produces the best estimates among all linear estimators. If, as often happens in reality, these assumptions are not met, other methods might give more efficient estimates and their use is therefore recommendable. In this paper, after reviewing and briefly describing the salient features of the methods, proposed in the literature, to determine and address the multicollinearity problem, we introduce the Lpmin method, based on Lp-norm estimation, an adaptive robust procedure that is used when the residual distribution has deviated from normality. The major advantage of this approach is that it produces more efficient estimates of the model parameters, for different degrees of multicollinearity, than those generated by the ordinary least squares method. A simulation study and a real-data application are also presented, in order to show the better results provided by the Lpmin method in the presence of multicollinearity.

Suggested Citation

  • Massimiliano Giacalone & Demetrio Panarello & Raffaele Mattera, 2018. "Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1831-1859, July.
  • Handle: RePEc:spr:qualqt:v:52:y:2018:i:4:d:10.1007_s11135-017-0571-y
    DOI: 10.1007/s11135-017-0571-y
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    1. Claes Cassel & Peter Hackl & Anders Westlund, 1999. "Robustness of partial least-squares method for estimating latent variable quality structures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 435-446.
    2. Mineo, Angelo & Ruggieri, Mariantonietta, 2005. "A Software Tool for the Exponential Power Distribution: The normalp Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i04).
    3. Chatelain, Jean-Bernard & Ralf, Kirsten, 2014. "Spurious regressions and near-multicollinearity, with an application to aid, policies and growth," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 39(A), pages 85-96.
    4. Jörg Blasius & John Gower, 2005. "Multivariate Prediction with Nonlinear Principal Components Analysis: Application," Quality & Quantity: International Journal of Methodology, Springer, vol. 39(4), pages 373-390, August.
    5. Tanja Krone & Casper J. Albers & Marieke E. Timmerman, 2017. "A comparative simulation study of AR(1) estimators in short time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(1), pages 1-21, January.
    6. Alexis Lazaridis, 2007. "A Note Regarding the Condition Number: The Case of Spurious and Latent Multicollinearity," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(1), pages 123-135, February.
    7. Giulio Bottazzi & Angelo Secchi, 2011. "A new class of asymmetric exponential power densities with applications to economics and finance," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 20(4), pages 991-1030, August.
    8. Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 164-175.
    9. John Gower & Jörg Blasius, 2005. "Multivariate Prediction with Nonlinear Principal Components Analysis: Theory," Quality & Quantity: International Journal of Methodology, Springer, vol. 39(4), pages 359-372, August.
    10. Theo Dijkstra, 2014. "Ridge regression and its degrees of freedom," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3185-3193, November.
    11. Griffiths, William E. & Hajargasht, Gholamreza, 2016. "Some models for stochastic frontiers with endogeneity," Journal of Econometrics, Elsevier, vol. 190(2), pages 341-348.
    12. András Vargha & Lars Bergman & Harold Delaney, 2013. "Interpretation problems of the partial correlation with nonnormally distributed variables," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(6), pages 3391-3402, October.
    13. Sergio Destefanis & Giovanni C. Porzio, 1999. "Dynamic graphics and model validation: an application to best‐practice production functions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 15(4), pages 259-267, October.
    14. Feng-Jenq Lin, 2008. "Solving Multicollinearity in the Process of Fitting Regression Model Using the Nested Estimate Procedure," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(3), pages 417-426, June.
    15. David J. Armor & Chenna Reddy Cotla & Thomas Stratmann, 2017. "Spurious relationships arising from aggregate variables in linear regression," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(3), pages 1359-1379, May.
    16. Catalina Garcia & José Pérez & José Liria, 2011. "The raise method. An alternative procedure to estimate the parameters in presence of collinearity," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(2), pages 403-423, February.
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