Nested piecewise linear regression models with continuous components 

Sergey I. Noskov, Doctor of engineering sciences, professor, professor of the sub-department of information systems and information security, Irkutsk State Transport University (15 Chernyshevskogo street, Irkutsk, Russia), E-mail: sergey.noskov.57@mail.ru
Egor S. Popov, Head of the laboratory of the subdepartment of information systems and information security, Irkutsk State Transport University (15 Chernyshevskogo street, Irkutsk, Russia),E-mail: eglir5732@mail.ru

Background. An approach is proposed to increase the flexibility of nested piecewise linear regression models proposed earlier by one of the authors due to the possibility of including continuous functions in them. It is noted that such an extension of the class of nested constructions is very relevant, since the wider the arsenal of forms of communication (types of approximating functions) between independent variables that is at the disposal of the researcher, the more adequate the analyzed object model he will eventually build. It is indicated that in the described models only the first nesting order is formalized, although it can also be the second, third, etc. In addition, multiplicative and additive nested piecewise linear regression models of the first and second types can be built. Results. It is shown that with the linearity of continuous functions included in embedded piecewise linear regression models and using as a loss function the sum of the modules of the differences between the calculated and actual values of the dependent variable, the problem of estimating model parameters is reduced to the problem of linear Boolean programming of a dimension acceptable for real situations. Effective software tools can be used to solve it, for example, the lpSolve program, which is freely available on the Internet. Conclusions. The proposed approach not only provides the possibility of calculating the values of unknown parameters of nested piecewise linear regression models with continuous components, but also allows us to identify the observation numbers on which the external and internal minima in the models worked.

piecewise linear regression, continuous functions, simple and homogeneous nested piecewise linear regression, linear Boolean programming problem, loss function

Noskov S.I., Popov E.S. Nested piecewise linear regression models with continuous components. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University proceedings. Volga region. Engineering sciences. 2024;(4):5–15. (In Russ.). doi: 10.21685/2072-3059-2024-4-1