In this article, we develop a generalized linear–quadratic model with a change point due to a covariate threshold, with one line segment and another quadratic segment intersecting at a change point. A two-step method is proposed to estimate the regression coefficients and the change point. The asymptotic properties of the proposed estimator are derived by modern empirical processes theory. A sup-likelihood ratio test statistic along with its limiting distribution is used to test the existence of the change point. Simulation studies demonstrate that the proposed estimator has good finite-sample performance for different link functions. The applications of the proposed method on Down Syndrome data and Heart failure clinical records data reveal interesting insights.
- Change point
- Generalized Linear-quadratic model
- Sup likelihood ratio test