Estimating Outliers Using the Iterative Method in Partial Least Squares Regression Analysis for Linear Models.
Abstract
Outliers affect the accuracy of the estimated parameters of the partial least squares regression model and give unacceptably large residual values. Traditional robust methods (used in ordinary least squares) cannot be used to treat outliers in estimating partial least squares regression model, due to the number of independent variables greater than the sample size, therefore, it was proposed to use an iterative method to treat outliers and estimation of partial least squares regression model parameters. The iterative method relies on identifying outliers and then estimating them using the initial estimated values and the residual and determining the optimal value that gives the least sum of squares error for the partial least square regression model. To illustrate the proposed method, simulated and real data were used based on a program MATLAB designed for this purpose. The proposed method provided accurate results for the partial squares regression model parameters depending on MSE criteria and addressed the problem of outliers.
References
- Abdi, H., (2010). Partial least squares regression and projection on latent structure regression (PLS Regression).Wiley Interdisciplinary Reviews: computational statistics,2(1), pp.97-106.
- Ali, T. H., Sedeeq, B. S., Saleh, D. M., & Rahim, A. G. (2024). Robust multivariate quality control charts for enhanced variability monitoring. Quality and Reliability Engineering International, 40(3), 1369-1381. https://doi.org/10.1002/qre.3472
- Ali, Taha Hussein & Awaz Shahab M. "Uses of Waveshrink in Detection and Treatment of Outlier Values in Linear Regression Analysis and Comparison with Some Robust Methods", Journal of Humanity Sciences 21.5 (2017): 38-61.
- Ali, Taha Hussein, 2018, Solving Multi-collinearity Problem by Ridge and Eigenvalue Regression with Simulation, Journal of Humanity Sciences, 22.5: 262-276.
- Ali, Taha Hussein, and Saleh, Dlshad Mahmood, "Proposed Hybrid Method for Wavelet Shrinkage with Robust Multiple Linear Regression Model: With Simulation Study" QALAAI ZANIST JOURNAL 7.1 (2022): 920-937.
- Ali, Taha Hussein, Heyam Abd Al-Majeed Hayawi, and Delshad Shaker Ismael Botani. "Estimation of the bandwidth parameter in Nadaraya-Watson kernel non-parametric regression based on universal threshold level." Communications in Statistics-Simulation and Computation 52.4 (2023): 1476-1489.
- Ali, Taha Hussein, Nasradeen Haj Salih Albarwari, and Diyar Lazgeen Ramadhan. Using the hybrid proposed method for Quantile Regression and Multivariate Wavelet in estimating the linear model parameters. Iraqi Journal of Statistical Sciences 20.1 (2023): 9-24.
- Boulesteix, A.L. and Strimmer, K., (2007). Partial least squares: a versatile tool for the analysis of high-dimensional genomic data.Briefings in bioinformatics,8(1), pp.32-44.
- Cousineau D., Chartier, S. (2010). Outliers detection and treatment: a review. International Journal of Psychological Research,3(1), 58-67.58
- Geladi, P. and Kowalski, B.R., 1986. Partial least-squares regression: a tutorial.Analytica chimica acta,185, pp.1-17.
- Kareem, Nazeera Sedeek and Mohammad, Awaz Shahab, and Ali, Taha Hussein, Construction robust simple linear regression profile Monitoring Journal of Kirkuk University for Administrative and Economic Sciences, 9.1. (2019): 242-257.
- Kettaneh, N., Berglund, A. and Wold, S., (2005). PCA and PLS with very large data sets.Computational Statistics & Data Analysis,48(1), pp.69-85.
- Omer, A. W., Sedeeq, B. S., & Ali, T. H. (2024). A proposed hybrid method for Multivariate Linear Regression Model and Multivariate Wavelets (Simulation study). Polytechnic Journal of Humanities and Social Sciences, 5(1), 112-124. https://doi.org/10.25156/ptjhss.v5n1y2024.pp112-124
- Pirouz, D. M. (2006). An Overview of Partial Least Squares. Irvine: Business Publications.
- Rosipal, R. and Krmer, N., (2005), February. Overview and recent advances in partial least squares. InInternational Statistical and Optimization Perspectives Workshop" Subspace, Latent Structure and Feature Selection"(pp. 34-51). Berlin, Heidelberg: Springer Berlin Heidelberg.
