A Bayesian Approach for Penalized Splines with Hierarchical Penalty

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Penalized spline has largely been applied in many research studies not limited to disease modeling and epidemiology. However, due to spatial heterogeneity of the data because different smoothing parameter leads to different amount of smoothing in different regions the penalized spline has not been exclusively appropriate to fit the data. The study assessed the properties of penalized spline hierarchical model; the hierarchy penalty improves the fit as well as the accuracy of inference. The simulation demonstrates the potential benefits of using the hierarchical penalty, which is obtained by modelling the global smoothing parameter as another spline. The results showed that mixed model with penalized hierarchical penalty had a better fit than the mixed model without hierarchy this was demonstrated by the rapid convergence of the model posterior parameters and the smallest DIC value of the model. Therefore hierarchical model with fifteen sub-knots provides a better fit of the data.