Generalized linear-quadratic model with a change point due to a covariate threshold

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. (C) 2021 Elsevier B.V. All rights reserved.