Generalized Models for Spatial Regression

• Activity Number: 560
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Isolated Statisticians
• Author(s): Matthieu Wilhelm*+ and Laura Maria Sangalli
• Companies: Universite de Neuchâtel and Politecnico di Milano
• Keywords: Generalized additive models ; Spatial regression ; Finite element ; Penalized regression

Abstract

We propose a novel method for the analysis of spatially distributed data occurring over irregularly shaped domains. This allows to estimate functions defined over domains characterized by concavities, complex boundaries or interior holes. We consider a generalized linear framework allowing for responses with distribution belonging to the exponential family. Specifically, we maximize a penalized log-likelihood function where the roughness penalty term involves a suitable differential operator of the spatial field over the domain of interest. This maximization is done via a penalized iterative least square approach. Space-varying covariate information can also be included in the model in a semi-parametric setting. The proposed models exploit advanced scientific computing techniques and specifically make use of the Finite Element Method. They provide a basis for piecewise polynomial surfaces and allows to impose boundary conditions. The models can deal with responses from any distribution in the exponential family, thus having a very broad applicability.