I'm working on a predictive cost model where the patient's age (an integer quantity measured in years) is one of the predictor variables. A strong nonlinear relationship between age and risk of a hospital stay is evident:
I'm considering a penalized regression smoothing spline for patient age. According to The Elements of Statistical Learning (Hastie et al, 2009, p.151), the optimal knot placement is one knot per unique value of member age.
Given that I'm retaining age as an integer, is the penalized smoothing spline equivalent to running a ridge regression or lasso with 101 distinct age indicator variables, one per age value found in the dataset (minus one for reference)? Over parametrization is then avoided as the coefficients on each age indicator are shrunk towards zero.