This study presents a novel procedure for handling potential non-linear effects of continuous predictors within the framework of generalized linear models. Focused on detecting departure points from linearity, the method employs linear spline functions with truncated basis expansion, enabling direct interpretation of knots as change points in predictor effects. Estimating the number and positions of spline knots poses a compelling yet non-trivial challenge due to the varying dimensions of the parameter space and identifiability issues. Our methodology addresses this challenge, incorporating their estimation in two steps within a Bayesian framework. First, the number of knots is selected using the stochastic search variable selection method. Subsequently, the final model is fitted with fixed but free knot locations, employing the Bayesian approach for estimation. To validate our approach, we conduct a simulation study exploring its performance under varied conditions and demonstrating its effectiveness in capturing non-linear effects. We showcase the method’s applicability and interpretability in modeling non-linear relationships within GLMs through two real data examples.
