Selection of Informative Operations in the Construction of Linear Non-elementary Regression Models

Abstract

This article is devoted to one of the main problems of regression analysis – the choice of regression model structural specification. The work is based on the linear non-elementary regressions proposed earlier by the author, which, in addition to explanatory variables, include binary operations of all their possible pairs. In such models, with an increase in the number of explanatory variables, the number of binary operations increases significantly. The aim of this work is to develop selection algorithms in linear non-elementary regressions of the most informative variables and operations. An algorithm for approximate estimation of linear non-elementary regressions using the ordinary least squares is considered. The problem of selection of informative operations is formulated. Two strategies for constructing linear non-elementary regressions are proposed. In the first of them there are no restrictions on the number of occurrences of explanatory variables in the model and on the number of binary operations. In the second, the model contains the largest number of binary operations, and each explanatory variable is included in it only once. Using combinatorics, the computational complexity of each of these strategies was determined. It turned out that the problem of constructing a linear non-elementary model based on the second strategy is solved in practice much faster than a similar problem based on the first strategy. The proposed algorithms were implemented using the Gretl package as a special program. With the help of it, high-quality linear non-elementary regression models of freight rail transportation in the Irkutsk region were built