Bazilevskiy M.P., Karaulova A.V. A method for measuring the nonlinearity degree of multivariate polynomial and posinomial regression models // 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], 2022. No. 4(16). P. 1-9. DOI: 10.26731/2658-3704.2022.4(16).1-9 [Accessed 17/12/22].
10.26731/2658-3704.2022.4(16).1-9
When constructing regression models, a balance should be struck between their accuracy and complexity. Complex models are often more accurate than simple ones, but they are more cumbersome, hard to see and inconvenient to use, which makes their interpretation very difficult. It becomes problematic to interpret models even if their structural specification is significantly non-linear. This article is devoted to the problem of estimating the degree of nonlinearity of regression models. Previously, the authors proposed a method for estimating the degree of nonlinearity for polynomial regressions with one explanatory variable. In this paper, this method is generalized for multivariate polynomial regressions. For the first time, a posinomial regression model has been introduced, which generalizes many known forms of relation between variables, in particular, a polynomial one. The proposed method for measuring the nonlinearity degree of polynomial regressions can also be applied to posinomial models.
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