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.
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