Comparison between Linear Regression and Robust Regression Models by Using Error Criteria and Information Criteria Applied to Human Sample

Authors

  • Ismat Mousa Ibrahim Technical College of Duhok, Department of Dental Technology, Duhok Polytechnic University, Duhok, Iraq

DOI:

https://doi.org/10.21271/zjhs.29.2.14

Keywords:

Robust Method, Least Trimmed Square, Maximum Likelihood.

Abstract

Hypertension is a common and serious disease, and for this reason, a sample of patients was chosen from Azadi Teaching Hospital in Duhok. In this study a comparison was made between Ordinary Least Squares (OLS) with two robust methods Least Trimmed Square Estimator (LTS) and the Modified Maximum likelihood type estimator (MM), they were evaluated using two types of criteria represented by error criteria (MSE, MAPE, MSAE, SAZ1, SAZ2,) and information criteria (AIC, BIC). Criteria have played a fundamental role in the statistics field and at the same time have applied to obtain the lowest rate of errors as well as to get the optimal solutions. The Modified Maximum likelihood type estimator method showed high efficiency in calculating values by most criteria, with exception of the SAS2 criteria, which recorded as the best value using the Least Trimmed Square Estimator method, and the (MSE) criteria, which showed best value using the Ordinary least squares method.”

References

-Acquah, H. de-G. (2010) “Comparison of Akaike information criterion (AIC) and Bayesian information criterion (BIC) in selection of an asymmetric price relationship”.

- Alma, O. G. (2011): Comparison of Robust Regression Methods in Linear Regression. Int. J. Contemp. Math. Sciences, Vol. 6. Mugla University, Turkey.

- Bai, X. (2010): Robust Linear Regression. B. S., Mathematics and Applied Mathematics China. 5/11/2013.

- Bianco, A. M. & Ben, M. G. & Yohai, V. J. (2003): Robust Estimation for Linear Regression with asymmetric Errors with applications to log-gamma regression. Universidad de Buenps Aires.

-Bollen, K. A. , Harden, J. J. , Ray, S., and Zavisca, J. (2014) “BIC and alternative Bayesian information criteria in the selection of structural equation models,” Struct. Equ. Model. a Multidiscip. J., vol. 21, no. 1, pp. 1–19.

-Bozdogan, H. (1987) “Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions,” Psychometrika, vol. 52, no. 3, pp. 345– 370,

- DeForest, D.K., Ryan, A.C., Tear, L.M. and Brix, K.V., 2023. Comparison of multiple linear regression and biotic ligand models for predicting acute and chronic zinc toxicity to freshwater organisms. Environmental toxicology and chemistry, 42(2), pp.393-413.

- Heritier, S. & Copt, S. (2006): Robust MM-Estimation and Inference In Mixed Linear Models.Universite de Geneve.

-Hodson, T.O., Over, T.M. and Foks, S.S., (2021). Mean squared error, deconstructed. Journal of Advances in Modeling Earth Systems, 13(12), p. e2021MS002681.

- Isazade, V., Qasimi, A.B., Dong, P., Kaplan, G. and Isazade, E., 2023. Integration of Moran’s I, geographically weighted regression (GWR), and ordinary least square (OLS) models in spatiotemporal modeling of COVID-19 outbreak in Qom and Mazandaran provinces, Iran. Modeling Earth Systems and Environment, 9(4), pp.3923-3937.

- Ismat mousa Ibrahim, “Using New Criteria to Compare between Some Robust Method and Ordinary Least Squares in Multiple Regression with Application on Wheat Data in Iraq”, Sofia University "ST. KLIMENT OHRIDSKI", 2016.

- Kahwachi, Wasfi (2014). Some Statistical Functions for Model Accuracy Measuring, Unpublished papar. Salahaddin University.

- Lee, M., & Han, C. (2024). Ordinary least squares and instrumental-variables estimators for any outcome and heterogeneity. The Stata Journal, 24(1), 72-92. https://doi.org/10.1177/1536867X241233645.

- Muhbauer, A. & Spichtinger. & Lohmann, U. (2009): Application and Comparison of Robust Linear Regression Methods for Trend Estimation. Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland.

-Nabillah, I. and Ranggadara, I., (2020). Mean absolute percentage error untuk evaluasi hasil prediksi komoditas laut. Journal of Information System, 5(2), pp.250-255.

- Rousseeuw, P.J. & Van Driessen, K. (1999): A Fast Algorithm for the Minimum Covariance Determinat Estimator, Technometrics, No. 41, pp. 212 – 223.

- Rousseeuw, P. J. (1984): Least Median of Squares Regression. Journal of the American Statistical Association 79: 871-880.

- Rousseeuw, P. & Yohai, V. (1984): Robust Regression by Means of S-estimates. In Robust and nonlinear time series, J. Franke, W. Hardle and R. Martin (eds.). Lecture Notes in Statistics,26, 256 - 272.

- Sahu, S.K., 2023. Simple Linear Regression Model. In Introduction to Probability, Statistics & R: Foundations for Data-Based Sciences (pp. 361-404). Cham: Springer International Publishing.

- Sanford, W. (2005): Applied Linear Regression, 3rd edition, John Wiley & Sons, Inc. Hoboken, New Jersey, Canada.

- Schumann, D.: Robust Variable Selection. Raleigh, North

Carolina.http://repository.lib.ncsu.edu/ir/bitstream/1840.16/4764/1/etd.pdf 4/2/2014.

-Shareef, A.A. and Ibrahim, I.M., (2020). Comparison of mistakes criteria using multiple linear regressions applied to cotton data. Periodicals of Engineering and Natural Sciences, 8(1), pp.231-241.

- Shi, Y., 2023. Application of Improved Linear Regression Algorithm in Business Behavior Analysis. Procedia Computer Science, 228, pp.1101-1109.

- Wang, Y., Guo, Z., Zhang, Y., Hu, X. and Xiao, J., 2023. Iron Ore Price Prediction Based on Multiple Linear Regression Model. Sustainability, 15(22), p.15864.

-Yang, D., Yang, H.M., Wang, P. and Li, S.J., (2020). MSAE: a multitask learning approach for traffic flow prediction using deep neural network. In Advances in Intelligent Information Hiding and Multimedia Signal Processing: Proceedings of the 15th International Conference on IIH-MSP in conjunction with the 12th International

Conference on FITAT, July 18-20, Jilin, China, Volume 1 (pp. 153-161). Springer Singapore.

- Yohai, V. J. (1987): High Breakdown Point and High Efficiency Robust Estimates for Regression. Annals of Statistics 15, 642-656.

Published

2025-04-15

How to Cite

Ismat Mousa Ibrahim. (2025). Comparison between Linear Regression and Robust Regression Models by Using Error Criteria and Information Criteria Applied to Human Sample. Zanco Journal of Human Sciences, 29(2), 298–313. https://doi.org/10.21271/zjhs.29.2.14

Issue

Section

Original Articles