Multinomial structuring in linear regression

摘要

Ordinary linear regression produces a good fit for the observations close to the mean point. To improve the fit for the values far from the mean point, an implement by the multinomial logit model is suggested. Segmenting the values of the dependent variable to several sections, it is possible to present a theoretical model via a linear aggregate of the chain regressions weighted by the multinomial logit shares. The paper considers several linear-multinomial hybrid models constructed by the objectives of maximum likelihood for the multinomial output and least squares for the segmented linear aggregates. Numerical estimations show that the hybrid models always outperform ordinary linear regressions, and demonstrate a better quality of fit and a more precise prediction. The suggested approach is convenient in application, and can enrich practical regression modeling.