Estimation of Regression Models with Regressors in the Explanatory Variables Linear Combinations Modules Form

This article is devoted to the study of the constructing process a new structural specification of regression models containing module signs. Earlier, similar simpler forms of relationships between variables were introduced by the author and were called modular regressions. The regression with regressors in the explanatory variables linear combinations modules form proposed in this article generalizes the previously considered forms. The least absolute deviations method is used to estimate the proposed regressions. Two problems of mixed 0-1 integer linear programming are formulated for estimating modular regressions. In the first of them, the signs in front of the modules must be specified manually, and in the second, the signs in front of the modules are determined automatically. Computational experiments were conducted using real data on the unemployment rate in the Russian Federation. The LPSolve package was chosen as a solver for optimization problems. It was found that with one possible way of declaring unlimited variables in this package, the resulting solution may be suboptimal. It is shown that the known method of declaring unlimited parameters as the difference of two non-negative variables will be correct. During the experiments, modular regressions of the unemployment rate with five variables, containing one and two modules, and with two variables, containing one, two and three modules, were constructed. The resulting regressions by the residuals modules sum were better than linear models. In one case, a regression with all zero residuals was identified. The experiments showed that with an increase in the number of modules, the time for estimating modular regressions increases.