Dichotomous Proportional Hazard Regression Model: A Case Study on Students’ Dropout

Abstract

In problems involving binary classification, researchers often encounter data suitable for modeling dichotomous responses. These scenarios include medical diagnostics, where outcomes are classified as “disease” or “no disease”, and credit scoring in finance, determining whether a loan applicant is “high risk” or “low risk”. Dichotomous response models are also useful in many other areas for estimating binary responses. The logistic regression model is one option for modeling dichotomous responses; however, other statistical models may be required to improve the quality of fits. In this paper, a new regression model is proposed for cases where the response variable is dichotomous. This novel, non-linear model is derived from the cumulative distribution function of the proportional hazard distribution, and is suitable for modeling binary responses. Statistical inference is performed using a classical approach with the maximum likelihood method for the proposed model. Additionally, it is demonstrated that the introduced model has a non-singular information matrix. The results of a simulation study, along with an application to student dropout data, show the great potential of the proposed model in practical and everyday situations.

Keywords

• dichotomous response
• logistic regression
• maximum likelihood estimation
• proportional hazard distribution