Construction of regression models with switching nonlinear transformations for the assigned explanatory variable

Often, when constructing regression models, it is necessary to resort to nonlinear transformations of explanatory variables. Both elementary and non-elementary functions can be used for this. This is done because many patterns in nature are complex and poorly described by linear dependencies. Usually, the transformations of explanatory variables in a regression model are constant for all observations of the sample. This work is devoted to constructing nonlinear regressions with switching transformations of the selected explanatory variable. In this case, the least absolute deviations method is used to estimate the unknown regression parameters. To form the rule for switching transformations, an integer function "floor" is used. A mixed 0–1 integer linear programming problem is formulated. The solution of this problem leads to both the identification of optimal estimates for nonlinear regression and the identification of a rule for switching transformations based on the values of explanatory variables. A problem of modeling the weight of aircraft fuselages is solved using this method. The nonlinear regression constructed with the proposed method using switching transformations turned out to be more accurate than the model using constant transformations over the entire sample. An advantage of the mechanism developed for constructing regression models is that thanks to the knowledge of the rules for switching transformations, the resulting regression can be used for forecasting.

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