Abstract
Spatially structured additivemodels offer the flexibility to estimate regression relationships for spatially and temporally correlated data. Here, we focus on the estimation of conditional deer browsing probabilities in the National Park “Bayerischer Wald”. The models are fitted using a componentwise boosting algorithm. Smooth and non-smooth base learners for the spatial component of the models are compared. A benchmark comparison indicates that browsing intensities may be best described by non-smooth base learners allowing for abrupt changes in the regression relationship.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ammer, C. (1996). Impact of ungulates on structure and dynamics of natural regeneration of mixed mountain forests in the Bavarian Alps, Forest Ecology and Management 88: 43–53.
Augustin, N., Musio, M., von Wilpert E, K., Kublin, Wood, S. & Schumacher, M. (2009). Modelling spatio-temporal forest health monitoring data.
Breiman, L. (1996). Bagging predictors, Machine Learning 24: 123–140.
Breiman, L. (2001). Random forests, Machine Learning 45: 5–32.
Breiman, L., Friedman, J., Olshen, R. & Stone, C. (1983). Classification and regression trees, Wadsworth, Belmont, California .
Bühlmann, P. (2004). Bagging, boosting and ensemble methods, in J. Gentle, W. Härdle & Y.Mori (eds), Handbook of Computational Statistics: Concepts and Methods, Springer.
Bühlmann, P. & Hothorn, T. (2007). Boosting algorithms: Regularization, prediction and model fitting, Statistical Science 22(4): 477–505.
Bühlmann, P. & Yu, B. (2003). Boosting with the l 2 loss: Regression and classification, Journal of the American Statistical Association 98: 324–339.
Efron, B. (1979). Bootstrap methods: another look at the jackknife, Annals of Statistics 7: 1–26.
Eiberle, K. (1989). Über den Einfluss des Wildverbisses auf die Mortalität von jungen Waldbämen in der oberen Montanstufe, Schweizer Zeitschrift für Forstwesen 140: 1031–1042.
Eiberle, K. & Nigg, H. (1987). Grundlagen zur Beurteilung des Wildverbisses im Gebirgswald, Schweizer Zeitschrift für Forstwesen 138: 474–785.
Eilers, P. & Marx, B. (1996). Flexible smoothing with B-splines and penalties, Statistical Science 11: 89–102.
Fahrmeir, L., Kneib, T. & Lang, S. (2004). Penalized structured additive regression for space-time data: A Bayesian perspective, Statistica Sinica 14: 731–761.
Forstliches Gutachten (2006). Forstliche Gutachten zur Situation der Waldverjungung 2006, Bayerische Staatsministerium für Landwirtschaft und Forsten.
Friedman, J. (2001). Greedy function approximation: A gradient boosting machine, The Annals of Statistics 29: 1189–1232.
Fritz, P. (2006). Ökologischer Waldumbau in Deutschland - Fragen, Antworten, Perspektiven, Oekom, München.
Hastie, T. & Tibshirani, R. (1990). Generalized Additive Models, Chapman & Hall/CRC.
Hastie, T., Tibshirani, R. & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer.
Hothorn, T., Hornik, K. & Zeileis, A. (2006). Unbiased recursive partitioning: A conditional inference framework, Journal of Computational and Graphical Statistics 15: 651–674.
Kneib, T., Hothorn, T. & Tutz, G. (2009). Variable selection and model choice in geoadditive regression models, Biometrics 65: 626–634.
Knoke, T., Ammer, C., Stimm, B. & Mosandl, R. (2008). Admixing broad-leaved to coniferous tree species–A review on yield, ecological stability and economics, European Journal of Forest Research 127: 89–101.
Knoke, T. & Seifert, T. (2008). Integrating selected ecological effects of mixed european beech–Norway spruce stands in bioeconomic modelling, Ecological Modelling 210: 487–498.
Lutz, R., Kalisch, M. & Bühlmann, P. (2008). Robustified l 2 boosting, Computational Statistics & Data Analysis 52: 3331–3341.
Moog, M. (2008). Bewertung von Wildschäden im Wald, Neumann-Neudamm, Melsungen.
Motta, R. (2003). Ungulate impact on rowan (Sorbus aucuparia l) and norway spruce (Picea abies (l) karst) height structure in mountain forests in the italian alps, Forest Ecology and Management 181: 139–150.
Prien, S. (1997). Wildschäden im Wald, Paul Parey, Berlin.
Rüegg, D. (1999). Zur Erhebung des Einflusses von Wildtieren auf die Waldverüngung, Schweizer Zeitschrift für Forstwesen 150: 327–331.
Schmid, M. & Hothorn, T. (2008). Boosting additive models using component-wise P-splines, Computational Statistics & Data Analysis 53: 298–311.
Weisberg, P., Bonavia, F. & Bugmann, H. (2005). Modeling the interacting effects of browsing and shading on mountain forest regeneration (Picea abies), Ecological Modelling 185: 213–230.
Wood, S. (2006). Generalized Additive Models: An Introduction with R, Chapman & Hall/CRC.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Robinzonov, N., Hothorn, T. (2010). Boosting for Estimating Spatially Structured Additive Models. In: Kneib, T., Tutz, G. (eds) Statistical Modelling and Regression Structures. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2413-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2413-1_10
Published:
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2412-4
Online ISBN: 978-3-7908-2413-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)