IDEAS home Printed from
   My bibliography  Save this article

Handling multicollinearity in quantile regression through the use of principal component regression


  • C. Davino

    (University of Naples Federico II)

  • R. Romano

    (University of Naples Federico II)

  • D. Vistocco

    (University of Naples Federico II
    University of Naples Federico II)


In many fields of applications, linear regression is the most widely used statistical method to analyze the effect of a set of explanatory variables on a response variable of interest. Classical least squares regression focuses on the conditional mean of the response, while quantile regression extends the view to conditional quantiles. Quantile regression is very convenient, whereas classical parametric assumptions do not hold and/or when relevant information lies in the tails and therefore the interest is in modeling the conditional distribution of the response at locations different from the mean. A situation common to most regression applications is the presence of strong correlations between predictors. This leads to the well-known problem of collinearity. While the effects of collinearity on least squares estimates are well investigated, this is not the case for quantile regression estimates. This paper aims to explore the collinearity problem in quantile regression. First, a simulation study analyses the problem concerning different degrees of collinearity and various response distributions. Then the paper proposes using regression on latent components as a possible solution to collinearity in quantile regression. Finally, a case study shows the assessment of the quality of service in the presence of highly correlated predictors.

Suggested Citation

  • C. Davino & R. Romano & D. Vistocco, 2022. "Handling multicollinearity in quantile regression through the use of principal component regression," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 153-174, August.
  • Handle: RePEc:spr:metron:v:80:y:2022:i:2:d:10.1007_s40300-022-00230-3
    DOI: 10.1007/s40300-022-00230-3

    Download full text from publisher

    File URL:
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL:
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Eide, Eric & Showalter, Mark H., 1998. "The effect of school quality on student performance: A quantile regression approach," Economics Letters, Elsevier, vol. 58(3), pages 345-350, March.
    2. Cristina Davino & Domenico Vistocco, 2007. "The evaluation of university educational processes: a quantile regression approach," Statistica, Department of Statistics, University of Bologna, vol. 67(3), pages 281-292.
    3. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    4. Rahim Alhamzawi & Keming Yu, 2012. "Variable selection in quantile regression via Gibbs sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 799-813, August.
    5. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    6. Tomohiro Ando & Ruey S. Tsay, 2011. "Quantile regression models with factor‐augmented predictors and information criterion," Econometrics Journal, Royal Economic Society, vol. 14, pages 1-24, February.
    7. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    8. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    9. Giglio, Stefano & Kelly, Bryan & Pruitt, Seth, 2016. "Systemic risk and the macroeconomy: An empirical evaluation," Journal of Financial Economics, Elsevier, vol. 119(3), pages 457-471.
    10. Bayer, Sebastian, 2018. "Combining Value-at-Risk forecasts using penalized quantile regressions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 56-77.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Huang, Luling & Nock, Destenie & Cong, Shuchen & Qiu, Yueming (Lucy), 2023. "Inequalities across cooling and heating in households: Energy equity gaps," Energy Policy, Elsevier, vol. 182(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Specification Choices in Quantile Regression for Empirical Macroeconomics," Working Papers 22-25, Federal Reserve Bank of Cleveland.
    2. Chen, Shi & Härdle, Wolfgang Karl & López Cabrera, Brenda, 2018. "Regularization Approach for Network Modeling of German Energy Market," IRTG 1792 Discussion Papers 2018-017, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Mert Demirer & Francis X. Diebold & Laura Liu & Kamil Yilmaz, 2018. "Estimating global bank network connectedness," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 1-15, January.
    4. Yongxia Zhang & Qi Wang & Maozai Tian, 2022. "Smoothed Quantile Regression with Factor-Augmented Regularized Variable Selection for High Correlated Data," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    5. Konrad Bogner & Florian Pappenberger & Massimiliano Zappa, 2019. "Machine Learning Techniques for Predicting the Energy Consumption/Production and Its Uncertainties Driven by Meteorological Observations and Forecasts," Sustainability, MDPI, vol. 11(12), pages 1-22, June.
    6. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    7. Georg Keilbar & Weining Wang, 2022. "Modelling systemic risk using neural network quantile regression," Empirical Economics, Springer, vol. 62(1), pages 93-118, January.
    8. Dengluan Dai & Anmin Tang & Jinli Ye, 2023. "High-Dimensional Variable Selection for Quantile Regression Based on Variational Bayesian Method," Mathematics, MDPI, vol. 11(10), pages 1-22, May.
    9. Qin, Yichen & Wang, Linna & Li, Yang & Li, Rong, 2023. "Visualization and assessment of model selection uncertainty," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    10. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    11. Oxana Babecka Kucharcukova & Jan Bruha, 2016. "Nowcasting the Czech Trade Balance," Working Papers 2016/11, Czech National Bank.
    12. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    13. Hou-Tai Chang & Ping-Huai Wang & Wei-Fang Chen & Chen-Ju Lin, 2022. "Risk Assessment of Early Lung Cancer with LDCT and Health Examinations," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    14. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    15. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    16. Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    17. Dmitriy Drusvyatskiy & Adrian S. Lewis, 2018. "Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 919-948, August.
    18. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    19. Jorge E. Galán & María Rodríguez Moreno, 2020. "At-risk measures and financial stability," Financial Stability Review, Banco de España, issue Autumn.
    20. Lucian Belascu & Alexandra Horobet & Georgiana Vrinceanu & Consuela Popescu, 2021. "Performance Dissimilarities in European Union Manufacturing: The Effect of Ownership and Technological Intensity," Sustainability, MDPI, vol. 13(18), pages 1-19, September.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metron:v:80:y:2022:i:2:d:10.1007_s40300-022-00230-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.