Comparison of Subspace Dimension Reduction Methods in Logistic Regression

Abstract

Regression models are very useful in describing and predicting real world phenomena. The Logistic regression is an extremely robust and flexible method for dichotomous classification prediction. This model is a classification model rather than regression model. When the number of predictors in regression models is high, data analysis is difficult. Dimension reduction has become one of the most important issues in regression analysis because of its importance in dealing with problems with high-dimensional data. In this paper, the methods of diminishing the dimension of variables in logistic regression, which include the estimation of central subspace based on the inverse regression, the likelihood acquisition method and principal component analysis are considered. Using a real data associated with the dental problems the Logistic regression is fitted and the correct classification of the data computed. At the end, The simulation study is presented to compare the sufficient dimension reduction methods with each other. In the simulation, MATLAB software is used and the Programs are attached at the end of the article in appendix.