Robust correlation scaled principal component regression

Authors : Aiman TAHİR, Maryam ILYAS

Pages : 459-486

Doi:10.15672/hujms.1122113

View : 15 | Download : 9

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :In multiple regression, different techniques are available to deal with the situation where the predictors are large in number, and multicollinearity exists among them. Some of these approaches rely on correlation and others depend on principal components. To cope with the influential observations insert ignore into journalissuearticles values(outliers, leverage, or both); in the data matrix for regression purposes, two techniques are proposed in this paper. These are Robust Correlation Based Regression insert ignore into journalissuearticles values(RCBR); and Robust Correlation Scaled Principal Component Regression insert ignore into journalissuearticles values(RCSPCR);. These proposed methods are compared with the existing methods, i.e., traditional Principal Component Regression insert ignore into journalissuearticles values(PCR);, Correlation Scaled Principal Component Regression insert ignore into journalissuearticles values(CSPCR);, and Correlation Based Regression insert ignore into journalissuearticles values(CBR);. Also, Macro insert ignore into journalissuearticles values(Missingness and cellwise and row-wise outliers); RCSPCR is proposed to cope with the problem of multicollinearity, the high dimensionality of the dataset, outliers, and missing observations simultaneously. The proposed techniques are assessed by considering several simulated scenarios with appropriate levels of contamination. The results indicate that the suggested techniques seem to be more reliable for analyzing the data with missingness and outlyingness. Additionally, real-life data applications are also used to illustrate the performance of the proposed methods.
Keywords : Principal component regression, influential observations, robust regression