Abstract
In geostatistics, both kriging and smoothing splines are commonly used to generate an interpolated map of a quantity of interest. The geoadditive model proposed by Kammann and Wand (J R Stat Soc: Ser C (Appl Stat) 52(1):1–18, 2003) represents a fusion of kriging and penalized spline additive models. Complex data issues, including non-linear covariate trends, multiple measurements at a location and clustered observations are easily handled using the geoadditive model. We propose a likelihood based estimation procedure that enables the estimation of the range (spatial decay) parameter associated with the penalized splines of the spatial component in the geoadditive model. We present how the spatial covariance structure (covariogram) can be derived from the geoadditive model. In a simulation study, we show that the underlying spatial process and prediction of the spatial map are estimated well using the proposed likelihood based estimation procedure. We present several applications of the proposed methods on real-life data examples.
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Acknowledgements
Support from a doctoral Grant of Hasselt University is acknowledged (BOF11D04FAEC to YV). Support from the National Institutes of Health is acknowledged [award number R01CA172805 to CF]. Support from the University of Antwerp scientific chair in Evidence-Based Vaccinology, financed in 2009–2014 by a gift from Pfizer, is acknowledged [to NH]. Support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) is gratefully acknowledged. For the simulation study we used the infrastructure of the VSC - Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government - department EWI.
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Vandendijck, Y., Faes, C. & Hens, N. Estimating the spatial covariance structure using the geoadditive model. Environ Ecol Stat 24, 341–361 (2017). https://doi.org/10.1007/s10651-017-0373-3
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DOI: https://doi.org/10.1007/s10651-017-0373-3