Using Independent Components for Estimating Logistic Regression with High-Dimensional Multicollinear Data: Simulation and Application

Abstract

The logistic regression model is used to predict a binary response variable in terms of a set of explicative ones. In the presence of multicollinearity among predictor, the estimation of the model parameters is not very accurate and their interpretation in terms of odds ratios may be inaccurate. Another importantproblem is that usually a large number of predictors are required to explain the response. In order to improve the estimation of the logistic model parameters under multicollinearity and to reduce the dimensions of the data with continuous covariates, it is proposed to use as covariates of the logistic model a reduced set of optimum independent components of the original predictors. Breast cancer data is used as real data set. The performance of the proposed independent component logistic regression model is analyzed by developing a simulation study where different methods for selecting the optimum independent components are compared. We built up a simulation study to illustrate the performance of the model with different regressors, sample size, and correlation among the regressors. Independent component logistic regression compared with principal component logistic regression model and independent component logistic regression gives better results