Correction of regression model parameters based on expert information on changes in the significance of predictors in the background
https://doi.org/10.55648/1998-6920-2025-19-1-11-19
Abstract
The paper proposes an algorithmic method of accounting for regression modeling of complex objects of any nature, along with statistical expert information on changes in the significance of predictors in the background. The method of mixed estimation and the continuous form of the maximum consistency method are used as methods for calculating unknown parameters of the model. The first of them is based on a combination of the methods of smallest modules and anti-robust estimation, each of which "works" on "its own" subsample of the original data sample. The second one is designed to increase consistency in changing the calculated and set values of the dependent variable. The implementation of the joint use of
statistical and expert information in modeling for these methods is reduced to solving the corresponding linear programming problems. The proposed method is implemented in the construction of a linear regression model of patent activity in Russia
Keywords
About the Authors
Sergei Ivanovich NoskovRussian Federation
Daniel Evgenyevich Bayanov
Russian Federation
References
1. Adulaimi A. A. A. Traffic Noise Modelling Using Land Use Regression Model Based on Machine Learning, Statistical Regression and GIS // Energies, Basel, 2021, vol. 14, no. 16, 5095 p.
2. Shahabi H., Hashim M., Ahmad B. B. Remote sensing and GIS-based landslide susceptibility mapping using frequency ratio, logistic regression, and fuzzy logic methods at the central Zab basin // Iran. Environmental Earth Sciences, 2015, vol. 73, pp. 8647–8668.
3. Nosek, Konrad. Schwarz Information Criterion Based Tests for a Change-Point in Regression Models // Statistical papers, Berlin, Germany, 2010, vol. 51, pp. 915–929.
4. Wang, Liang-Jie et al. Landslide Susceptibility Mapping in Mizunami City, Japan: A Comparison between Logistic Regression, Bivariate Statistical Analysis and Multivariate Adaptive Regression Spline Models // Catena, Giessen, 2015, vol. 135, pp. 271–282.
5. Yang, G., Zheng, C. Y., Zhai, X. Q. Influence analysis of building energy demands on the optimal design and performance of CCHP system by using statistical analysis. // Energy and Buildings, 2017, vol. 153, pp. 297–316.
6. Zheng, J., Song, Z. Two-level independent component regression model for multivariate spectroscopic calibration // Chemometrics and Intelligent Laboratory Systems, 2016, vol. 155, pp. 160–169.
7. Shalabh, Garg, G., Misra, N. Consistent estimation of regression coefficients in ultrastructural measurement error model using stochastic prior information // Statistical Papers, Berlin, Germany, 2010, vol. 51, pp. 717–748.
8. Fouad G., Skupin A., Tague C. L. Regional regression models of percentile flows for the contiguous United States: Expert versus data-driven independent variable selection // Journal of Hydrology. Regional Studies, 2018, vol. 17, pp. 64-82.
9. Szymanowski, M., Kryza, M. Local regression models for spatial interpolation of urban heat island—an example from Wrocław // Theoretical and Applied Climatology, SW Poland, 2012, vol. 108, pp. 53–71.
10. Draper N., Smith H. Prikladnoj regressionnyj analiz [Applied regression analysis]. М.: Dialektika. 912 p.
11. Sizjakov N.P., Shestopalova O.L. Prognozirovanie sootvetstvija harakteristik kosmicheskih sredstv predjavljaemym trebovanijam na osnove ispolzovanija nechetkoj regressionnoj modeli [Forecasting the compliance of the characteristics of space assets with the requirements based on the use of a fuzzy regression model]. Informacija i kosmos. 2010, no. 1, pp. 133-135.
12. Bojko N.S., Loshakov A.V. Prognozirovanie pokazatelej bezopasnosti poljotov s uchjotom vnedrenija upravlencheskogo reshenija na osnove regressionnyh modelej [Forecasting flight safety indicators, taking into account the implementation of a management solution based on regression models]. Vestnik Ul'janovskogo gosudarstvennogo tehnicheskogo universiteta. 2022, no. 2 (98), pp. 74-76.
13. Gerashhenko I.P. Metody prognozirovanija v regressionnyh i adaptivnyh modeljah pri analize dinamicheskih rjadov [Forecasting methods in regression and adaptive models in the analysis of dynamic series]. Matematicheskie struktury i modelirovanie. 2000, no. 5, pp. 140-154.
14. Golovchenko V.B., Noskov S.I. Vybor klassa linejnoj po parametram regressii na osnove jekspertnyh vyskazyvanij [Choosing a linear regression class based on expert statements]. Kibernetika i sistemnyj analiz. 1992, no. 5, pp.109-115.
15. Golovchenko V.B., Noskov S.I. Kombinirovanie prognozov s uchetom jekspertnoj informacii [Combining forecasts with expert information]. Avtomatika i telemehanika. 1992, no. 11, pp. 109-117.
16. Noskov S.I., Postroenie linejnoj regressii s uchetom jekspertnoj informacii otnositelno sravnitelnoj znachimosti peremennyh [The construction of a linear regression taking into account expert information on the comparative significance of variables]. Vestnik Tehnologicheskogo universiteta. 2021, Vol. 24, no. 2, pp. 83-86.
17. Noskov S.I. Metod smeshannogo ocenivanija parametrov linejnoj regressii: osobennosti primenenija [The method of mixed estimation of linear regression parameters: application features]. Vestnik Voronezhskogo gosudarstvennogo universiteta. Serias: Sistemnyj analiz i informacionnye tehnologii. 2021, no. 1, pp. 126-132.
18. Noskov S.I. Metod maksimalnoj soglasovannosti v regressionnom analize [The method of maximum consistency in regression analysis]. Izvestija Tul'skogo gosudarstvennogo universiteta. Tehnicheskie nauki. 2021, no. 10, pp. 380-385.
19. Noskov S.I., Pashkov D.V. Realizacija konkursa regressionnyh modelej jeffektivnosti intellektual'noj dejatel'nosti [Implementation of the competition for regression models of intellectual activity efficiency]. Jelektronnyj setevoj politematicheskij zhurnal «Nauchnye trudy KubGTU». 2022, no. 6, pp. 40–51.
20. Shipicyna R.E., Vitvickij E.E. Sravnenie udobstva ispol''zovanija programmnyh produktov pri reshenii transportnoj zadachi linejnogo programmirovanija: LPSolve IDE i Microsoft Excel [Comparison of the usability of software products in solving the transport problem of linear programming: LPSolve IDE and Microsoft Excel]. Obrazovanie. Transport. Innovacii. Stroitel'stvo. Sbornik materialov V Nacional'noj nauchno-prakticheskoj konferencii. Omsk, 2022, pp. 250-254.
21. Arslanov M.Z. Matematicheskie modeli zadachi ob upakovke edinichnyh kvadratov [Mathematical models of the problem of packing unit squares]. Problemy informatiki. 2015, no. 4 (29), pp. 5-13.
22. Pervun O.E. Optimizacija i issledovanie zadach linejnogo programmirovanija sredstvami prilozhenija R [Optimization and research of linear programming problems by means of the R application]. Informacionno-komp'juternye tehnologii v jekonomike, obrazovanii i social'noj sfere. 2022, no. 4 (38), pp. 87-92.
Supplementary files
Review
For citations:
Noskov S.I., Bayanov D.E. Correction of regression model parameters based on expert information on changes in the significance of predictors in the background. The Herald of the Siberian State University of Telecommunications and Information Science. 2025;19(1):11-19. (In Russ.) https://doi.org/10.55648/1998-6920-2025-19-1-11-19