Improving the quality classification using multiple choicelinear models
In this article we consider a classification problem and some methods for its solving based on the discrete choice models. Logit and Probit Models have been preferred to Discriminant Function Model because they less depend on the input factors. So, the question arises is it possible to introduce a new model based on a function which differs from the logit function for the Logit Model and the normal function for Probit Model respectively. In the "Problem Statement and Solution Methods" section it is described the mathematical model and also illustrated the possibility of introduction of a new model as it is presented existing restrictions preventing this action. Moreover, it is also written about a new method for parameters estimation for the classification function. The method is based on applying a new statistical distribution. The Laplace Law is introduced as a new distribution with unknown parameters. The new classification procedure is to solve the dual optimization problem. They are minimization of the likelihood function with the optimal coefficients fitting for a classification function and minimization of the classification error magnitude by varying the parameters value of the selected distribution. In order to make the study more comprehensive the computational experiments were performed with different sample sizes and varied number of income variables and the factors were distributed according to the standard normal law, asymmetric law based on the exponential distribution, as well as the distributions with heavy and light tails based on the double exponential law with the varied shape parameter value. The obtained results show the effectiveness of the proposed procedure. This is particularly well seen from the tests with the extended model (i.e., the model with many income variables). In "Conclusion" section, possible ways of further development the work have been noted. Due to the fact that the proposed method works well it is possible to study the magnitude of the classification error by choosing any other statistical distribution for creating the models with the certain conditions in the future. It should be noted, that the new method for solving the classification problem significantly improves the classification quality of existing procedures, so it can be successfully applied in practice.