On estimating the change point in generalized linear models

TL;DR

This paper introduces a new estimation method for change points in generalized linear models, overcoming non-differentiability issues, and demonstrates its effectiveness through simulations and a real case study on myocardial infarction risk.

Contribution

It proposes an estimator for change points in GLMs that achieves standard asymptotic properties despite the non-differentiability challenge.

Findings

Estimator is consistent and asymptotically normal.

Simulation results show good performance.

Applied successfully to a myocardial infarction case-control study.

Abstract

Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable relating to a particular independent variable of interest. The statistical challenge one encounters is that the likelihood function is not differentiable with respect to this change point parameter. Consequently, the conventional asymptotic properties for the maximum likelihood estimators fail to hold in this situation. In this paper, we propose an estimating procedure for estimating the change point along with other regression coefficients under the generalized linear model framework. We show that the proposed estimators enjoy the conventional asymptotic properties including consistency and normality. Simulation work we conducted suggests that it performs well for the situations considered. We applied the proposed method to a case-control study aimed to examine the relationship between the risk of myocardial infarction and alcohol intake.