Comparison of Robustness between Linear Regression and Logistic Regression in Dichotomous Criterion

Abstract

As "Big data" has arisen, simplicity and robustness for analysis have been emphasized. Therefore, we focus on the model which is relatively simpler and more robustness against fluctuation of data. Accurate classifcation is one of the most important things to decide a model for decision making in practice. Logistic model is known as an accurate model to estimate the probabilities of dependent categories. However, focusing on the goal of classifcation in practical use, we assume that linear regression can be more efficient in using practical decision making. We start this study to identify the linear regression analysis is better in robustness than the logistic regression analysis. In simulation, by increasing the number of independent variables, we observe the performances of each method. We try diverse data generated by different models to see the robustness of linear regression analysis. Based on the two conjectures, we analyze the prediction errors of each method. By comparing prediction errors, we conclude the linear regression analysis is the most robust method in our simulation. However, because wee only simulate the equal proportioned two classes, the further study is needed.