For citation:
Bazilevskiy M. P. Multi-criteria approach to pair-multiple linear regression models constructing. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 1, pp. 88-99. DOI: 10.18500/1816-9791-2021-21-1-88-99, EDN: AVRVDN
Multi-criteria approach to pair-multiple linear regression models constructing
A pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear regression model. In this case, pair-multiple regression models retain the ability to interpret the coefficients and predict the values of the explained variable. An aggregated quality criterion of regression models based on four well-known indicators: the coefficient of determination, Darbin – Watson, the consistency of behaviour and the average relative error of approximation is proposed. Using this criterion, the problem of multi-criteria construction of a pair-multiple linear regression model is formalized as a nonlinear programming problem. An algorithm for its approximate solution is developed. The results of this work can be used to improve the overall qualitative characteristics of multiple linear regression models.
- Montgomery D. C., Peck E. A., Vining G. G. Introduction to Linear Regression Analysis. Wiley, 2012. 672 p.
- Kleinbaum D. G., Kupper L. L., Nizam A., Rosenberg E. S. Applied Regression Analysis and Other Multivariable Methods. Cengage Learning, 2013. 1072 p.
- Harrell Jr., Frank E. Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis. Springer Series in Statistics, 2015. 582 p.
- Kuhn M., Johnson K. Applied Predictive Modeling. Springer, 2018. 600 p.
- Gillard J. An overview of linear structural models in errors in variables regression. REVSTAT – Statistical Journal, 2010, vol. 8, no. 1, pp. 57–80.
- Xu K., Ma Y., Wang L. Instrument assisted regression for errors in variables models with binary response. Scandinavian Journal of Statistics, 2015, vol. 42, iss. 1, pp. 104–117. https://doi.org/10.1111/sjos.12097
- Rudelson M., Zhou S. Errors-in-variables models with dependent measurements. Electronic Journal of Statistics, 2017, vol. 11, no. 1, pp. 1699–1797. https://doi.org/10.1214/17-EJS1234
- Gospodinov N., Komunjer I., Ng S. Simulated minimum distance estimation of dynamic models with errors-in-variables. Journal of Econometrics, 2017, vol. 200, iss. 2, pp. 181– 193. https://doi.org/10.1016/j.jeconom.2017.06.004
- Soderstrom T., Soverini U. Errors-in-variables identification using maximum likelihood estimation in the frequency domain. Automatica, 2017, vol. 79, pp. 131–143. https://doi.org/10.1016/j.automatica.2017.01.016
- Bianco A. M., Spano P. M. Robust estimation in partially linear errors-in-variables models. Computational Statistics & Data Analysis, 2017, vol. 106, pp. 46–64. https://doi.org/10.1016/j.csda.2016.09.002
- Deming W. E. Statistical Adjustment of Data. Wiley, 1943. 273 p.
- Wu C., Yu J. Z. Evaluation of linear regression techniques for atmospheric applications: The importance of appropriate weighting. Atmospheric Measurement Techniques, 2018, vol. 11, pp. 1233–1250. https://doi.org/10.5194/amt-11-1233-2018
- Henderson C. M., Shulman N. J., MacLean B., MacCoss M. J., Hoofnagle A. N. Skyline performs as well as vendor software in the quantitative analysis of serum 25-hydroxy vitamin D and vitamin D binding globulin. Clinical Chemistry, 2018, vol. 64, iss. 2, pp. 408–410. https://doi.org/10.1373/clinchem.2017.282293
- Reverter-Branchat G., Bosch J., Vall J., Farre M., Papaseit E., Pichini S., Segura J. Determination of recent growth hormone abuse using a single dried blood spot. Clinical Chemistry, 2016, vol. 62, iss. 10, pp. 1353–1360. https://doi.org/10.1373/clinchem.2016.257592
- Bazilevskiy M. P. Synthesis of the multiple linear regression and deming regression model. Informatsionnye tekhnologii v modelirovanii i upravlenii: podkhody, metody, resheniya: materialy II Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem [Information Technologies in Modeling and Management: Approaches, Methods, Solutions: Materials of the II All-Russian Scientific Conference with International Participation: in 2 pt.]. Tolyatti, 2019, pt. 1, pp. 64–69 (in Russian).
- Bazilevskiy M. P. Synthesis of multiple linear regression and Deming regression model’s: investigation the dependences of parameter estimates and adequacy criteria on the ratio of variance error variables. Informacionnye tehnologii i matematicheskoe modelirovanie v upravlenii slozhnymi sistemami: ehlektronnyj nauchnyj zhurnal [Information technology and mathematical modeling in the management of complex systems: electronic scientific journal], 2019, no. 2, pp. 18–25 (in Russian). Available at: http://ismmirgups.ru/toma/23-2019 (accessed 19 June 2019).
- Noskov S. I., Bazilevskiy M. P. Postroyenie regressionnykh modeley s ispol’zovaniem apparata lineino-bulevogo programmirovaniya [Construction of Regression Models Using Linear Boolean Programming]. Irkutsk, IrGUPS, 2018. 176 p. (in Russian).
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