МЕТОД ОЦЕНИВАНИЯ ЛОГИСТИЧЕСКИХ РЕГРЕССИЙ С ПОМОЩЬЮ АППАРАТА ЛИНЕЙНОГО ПРОГРАММИРОВАНИЯ

Abstract

The article is devoted to the problem of estimating logistic regressions where the explanatory variable has only two values, 0 and 1. The predicted values of the explanatory variable of the estimated logistic regression are interpreted as the probabilities of the occurrence of some event. As a result, such models are widely used to solve classifi cation problems. In practice, the maximum likelihood estimation, which is implemented in many modern statistical packages, is mainly used to estimate logistic regressions. One of its disadvantages, for example, is that it does not provide unique estimates when grouping objects into two separate classes. The study proposes a new method for estimating logistic regressions. Conventionally, it can be divided into two stages. The fi rst stage consists of solving a specially formulated linear programming problem. As a result, the weighting coeffi cients of the linear combination of explanatory variables are found. In fact, classifi cation is already carried out at this stage. The second stage is to calibrate the probability scale. Computational experiments were carried out based on a real sample of volume 100. The new method has proven its effi ciency when objects are completely separable into two classes. In addition, in terms of the number of correctly predicted cases, the new method was never inferior to the maximum likelihood estimation, and even surpassed the latter in one of the experiments.