Theory of Ridge Regression Estimation with Applications

8Logistic Regression Model

In this chapter, we discuss the shrinkage and penalty estimators related to logistic regression models. Logistic regression is often used when the response variable encodes a binary outcome. Logistic regression is a widely used tool for the statistical analysis of observed proportions or rates. Methods for fitting logistic multiple regression models have been available through standard statistical packages for the past several years.

8.1 Introduction

Logistic regression is a popular method to model binary data in biostatistics and health sciences. It has extensive applications in many different spheres of life. A classic area of application of logistic regression is biomedical studies. There are other areas like the prediction of loan returning behavior of bank clients or whether a company would or would not reach a bankruptcy situation in the future (Beaver 1966; Martin 1977; Tam and Kiang 1992). Another popular example is to investigate the occurrence of a disease as related to different characteristics of the patients, such as age, sex, food habit, daily exercise, and others. Fitting a model with appropriate significant predictors is a challenging job. When selecting the variables for a linear model, we generally look at individual ‐values. This procedure can be deceptive. If the variables are highly correlated, the ‐values may also be high, motivating ...