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Simultaneous raise regression: a novel approach to combating collinearity in linear regression models

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  • Jinse Jacob

    (SRM Institute of Science and Technology)

  • R. Varadharajan

    (SRM Institute of Science and Technology)

Abstract

The effect of multicollinearity deems the estimation and interpretation of regression coefficients by the method of Ordinary Least Squares (OLS) as burdensome. Even if there are alternate techniques like Ridge Regression (RR) and Liu Regression (LR) for providing a model, the statistical inference is impaired. In this study, we present the Simultaneous Raise Regression (SRR) approach, which is based on QR decomposition and reduces multicollinearity while preserving statistical inference. In contrast to the classical raise approach, the proposed strategy attains the number of variables to be raised and their corresponding raise parameter with a single step. We have designed Sequential Variation Inflation Factor for this purpose (SVIF). The performance of SRR has been compared with OLS, Ridge Regression and Liu Regression through Predictive Root Mean Square Error (PRMSE), Predictive Mean Absolute Error (PMAE) and Standard Error of the coefficients. To validate the suggested approach, a simulation study and a real-life example are presented; both outcomes imply that our proposed method outperforms the competition.

Suggested Citation

  • Jinse Jacob & R. Varadharajan, 2023. "Simultaneous raise regression: a novel approach to combating collinearity in linear regression models," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(5), pages 4365-4386, October.
    • Handle: RePEc:spr:qualqt:v:57:y:2023:i:5:d:10.1007_s11135-022-01557-9
    DOI: 10.1007/s11135-022-01557-9
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Sergio Perez-Melo & B. M. Golam Kibria, 2020. "On Some Test Statistics for Testing the Regression Coefficients in Presence of Multicollinearity: A Simulation Study," Stats, MDPI, vol. 3(1), pages 1-16, March.
    4. 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.
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