Stability analysis of an additive spline model for respiratory health data by using knot removal

In many settings with possibly non-linear influence of covariates, such as in the present application with children's respiratory health data, generalized additive models are an attractive choice. Although techniques for fitting these have been extensively investigated, there are fewer results on stability of replication, i.e. stability of fitted model components with respect to perturbations in the data. Nevertheless, this aspect is essential for judging how useful the present model is for understanding predictors of lung function. We therefore investigate existing tools for stability analysis based on bootstrap samples, such as quantities for variability and bias, for our application. Furthermore, as the focus is on models based on B-splines, knot removal techniques are available. These can help to provide more insight into the stability of local features that are fitted in bootstrap samples. We analyse the bootstrap result matrix via log-linear models. Specifically, the relationship with respect to local features between the influence functions of potential lung function predictors is investigated.