Semiparametric change points detection using single index spatial random effects model in environmental epidemiology study

Environmental health studies are of great interest in research to evaluate the mortality-temperature relationship by adjusting spatially correlated random effects as well as identifying significant change points in temperature. However, this relationship is often not expressed using parametric models, which makes identifying change points an even more challenging problem. This paper proposes a unified semiparametric approach to simultaneously identify the nonlinear mortality-temperature relationship and detect spatially-dependent change points. A unified method is proposed for the model estimation, spatially dependent change points detection, and testing whether they are significant simultaneously by a permutation-based test. We operate under the assumption that change points remain constant, yet acknowledge the uncertainty regarding their precise number. These change points are influenced by the smoothing of an unknown function, which in turn relies on a smoothing variable and spatial random effects. Consequently, the detection of change points may be influenced by spatial effects. In this paper, several simulation studies are conducted to evaluate the performance of our proposed approach. The advantages of this unified approach are demonstrated using epidemiological data on mortality and temperature.