A comparison of Thin Plate Splines and P-splines in the Generalized Additive Model for Discrete-Choice Data

The utility functions used in the Multinomial Logit model for to describe consumer brand choice data are usually specified as linear-in-parameter. Due to nonlinear price functions, it can be more realistic to implement nonparametric functions instead, which can be done by spline smoothing techniques. This research compares a knot-based approximation of Thin Plate Splines to P-splines with second order difference penalties, as the latter could be more suitable in brand choice related context. The results, however, show that one technique is not significantly better than the other. Furthermore, the influence of the number of knots on the estimation accuracy is investigated. The results show that when including more knots, the performance of the _t increases. However, after a certain point, the computation time increases significantly, while the performance does hardly improve anymore.