Strategy for node placement for penalized spline regression

We present a new method for the selection of node sequences for P-spline regression curves. The method assumes that the data themselves determine the number and position of the nodes. Thus, this new node placement scheme assumes that nodes are a random variable across a thin grid of possible candidate nodes in the covariate range. Thus, through a grid search, we determine the knot that maximizes the correlation in each iteration. This new node placement scheme has obtained excellent results compared to conventional node allocation methods in a simulation study and, furthermore, our simulation study shows that this strategy makes the model more parsimonious. The results provide guidance in selecting the number of nodes not necessarily equidistant in a penalized spline regression model.