Spatial smoothing revisited: An application to rental data in Munich

Spatial smoothing makes use of spatial information to obtain better estimates in regression models. In particular flexible smoothing with B-splines and penalties, which has been propagated by Eilers and Marx (1996) , provides strong tools that can be used to include available spatial information. We consider alternative smoothing methods in spatial additive regression and employ them for analysing rental data in Munich. The first method applies tensor product P-splines to the geolocation of apartments, measured on a continuous scale through the centroid of the quarter where an apartment is. The alternative approach exploits the neighbourhood structure of districts on a discrete scale, where districts consist of a set of neighbouring quarters. The discrete modelling approach yields smooth estimates when using ridge-type penalties but can also enforce spatial clustering of districts with a homogeneous structure when using Lasso-type penalties.