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Modified Liu Parameters for Scaling Options of the Multiple Regression Model with Multicollinearity Problem

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  • Autcha Araveeporn

    (Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

Abstract

The multiple regression model statistical technique is employed to analyze the relationship between the dependent variable and several independent variables. The multicollinearity problem is one of the issues affecting the multiple regression model, occurring in regard to the relationship among independent variables. The ordinal least square is the standard method to evaluate parameters in the regression model, but the multicollinearity problem affects the unstable estimator. Liu regression is proposed to approximate the Liu estimators based on the Liu parameter, to overcome multicollinearity. In this paper, we propose a modified Liu parameter to estimate the biasing parameter in scaling options, comparing the ordinal least square estimator with two modified Liu parameters and six standard Liu parameters. The performance of the modified Liu parameter is considered, generating independent variables from the multivariate normal distribution in the Toeplitz correlation pattern as the multicollinearity data, where the dependent variable is obtained from the independent variable multiplied by a coefficient of regression and the error from the normal distribution. The mean absolute percentage error is computed as an evaluation criterion of the estimation. For application, a real Hepatitis C patients dataset was used, in order to investigate the benefit of the modified Liu parameter. Through simulation and real dataset analysis, the results indicate that the modified Liu parameter outperformed the other Liu parameters and the ordinal least square estimator. It can be recommended to the user for estimating parameters via the modified Liu parameter when the independent variable exhibits the multicollinearity problem.

Suggested Citation

  • Autcha Araveeporn, 2024. "Modified Liu Parameters for Scaling Options of the Multiple Regression Model with Multicollinearity Problem," Mathematics, MDPI, vol. 12(19), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3139-:d:1493583
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    References listed on IDEAS

    as
    1. Hu Yang & Jianwen Xu, 2009. "An alternative stochastic restricted Liu estimator in linear regression," Statistical Papers, Springer, vol. 50(3), pages 639-647, June.
    2. Muhammad Suhail & Iqra Babar & Yousaf Ali Khan & Muhammad Imran & Zeeshan Nawaz, 2021. "Quantile-Based Estimation of Liu Parameter in the Linear Regression Model: Applications to Portland Cement and US Crime Data," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-11, July.
    3. Druilhet, Pierre & Mom, Alain, 2008. "Shrinkage structure in biased regression," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 232-244, February.
    4. M. Hubert & P. Wijekoon, 2006. "Improvement of the Liu estimator in linear regression model," Statistical Papers, Springer, vol. 47(3), pages 471-479, June.
    5. Yuli Liang & Dietrich Rosen & Tatjana Rosen, 2021. "On properties of Toeplitz-type covariance matrices in models with nested random effects," Statistical Papers, Springer, vol. 62(6), pages 2509-2528, December.
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