TY - JOUR A1 - Dormann, Carsten F. A1 - Elith, Jane A1 - Bacher, Sven A1 - Buchmann, Carsten M. A1 - Carl, Gudrun A1 - Carre, Gabriel A1 - Garcia Marquez, Jaime R. A1 - Gruber, Bernd A1 - Lafourcade, Bruno A1 - Leitao, Pedro J. A1 - Münkemüller, Tamara A1 - McClean, Colin A1 - Osborne, Patrick E. A1 - Reineking, Bjoern A1 - Schröder-Esselbach, Boris A1 - Skidmore, Andrew K. A1 - Zurell, Damaris A1 - Lautenbach, Sven T1 - Collinearity a review of methods to deal with it and a simulation study evaluating their performance JF - Ecography : pattern and diversity in ecology ; research papers forum N2 - Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the folk lore'-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them. Y1 - 2013 U6 - https://doi.org/10.1111/j.1600-0587.2012.07348.x SN - 0906-7590 SN - 1600-0587 VL - 36 IS - 1 SP - 27 EP - 46 PB - Wiley-Blackwell CY - Hoboken ER - TY - JOUR A1 - Häring, Tim A1 - Reger, Birgit A1 - Ewald, Jörg A1 - Hothorn, Torsten A1 - Schröder-Esselbach, Boris T1 - Predicting Ellenberg's soil moisture indicator value in the Bavarian Alps using additive georegression JF - Applied vegetation science : official organ of the International Association for Vegetation Science N2 - Questions Can forest site characteristics be used to predict Ellenberg indicator values for soil moisture? Which is the best averaged mean value for modelling? Does the distribution of soil moisture depend on spatial information? Location Bavarian Alps, Germany. Methods We used topographic, climatic and edaphic variables to model the mean soil moisture value as found on 1505 forest plots from the database WINALPecobase. All predictor variables were taken from area-wide geodata layers so that the model can be applied to some 250 000 ha of forest in the target region. We adopted methods developed in species distribution modelling to regionalize Ellenberg indicator values. Therefore, we use the additive georegression framework for spatial prediction of Ellenberg values with the R-library mboost, which is a feasible way to consider environmental effects, spatial autocorrelation, predictor interactions and non-stationarity simultaneously in our data. The framework is much more flexible than established statistical and machine-learning models in species distribution modelling. We estimated five different mboost models reflecting different model structures on 50 bootstrap samples in each case. Results Median R2 values calculated on independent test samples ranged from 0.28 to 0.45. Our results show a significant influence of interactions and non-stationarity in addition to environmental covariates. Unweighted mean indicator values can be modelled better than abundance-weighted values, and the consideration of bryophytes did not improve model performance. Partial response curves indicate meaningful dependencies between moisture indicator values and environmental covariates. However, mean indicator values <4.5 and >6.0 could not be modelled correctly, since they were poorly represented in our calibration sample. The final map represents high-resolution information of site hydrological conditions. Conclusions Indicator values offer an effect-oriented alternative to physically-based hydrological models to predict water-related site conditions, even at landscape scale. The presented approach is applicable to all kinds of Ellenberg indicator values. Therefore, it is a significant step towards a new generation of models of forest site types and potential natural vegetation. KW - Boosting KW - Mboost KW - Non-stationarity KW - Predictive vegetation mapping KW - Site ecology KW - Species distribution modelling Y1 - 2013 U6 - https://doi.org/10.1111/j.1654-109X.2012.01210.x SN - 1402-2001 VL - 16 IS - 1 SP - 110 EP - 121 PB - Wiley-Blackwell CY - Hoboken ER - TY - JOUR A1 - Jeltsch, Florian A1 - Bonte, Dries A1 - Peer, Guy A1 - Reineking, Björn A1 - Leimgruber, Peter A1 - Balkenhol, Niko A1 - Schröder-Esselbach, Boris A1 - Buchmann, Carsten M. A1 - Müller, Thomas A1 - Blaum, Niels A1 - Zurell, Damaris A1 - Böhning-Gaese, Katrin A1 - Wiegand, Thorsten A1 - Eccard, Jana A1 - Hofer, Heribert A1 - Reeg, Jette A1 - Eggers, Ute A1 - Bauer, Silke T1 - Integrating movement ecology with biodiversity research - exploring new avenues to address spatiotemporal biodiversity dynamics Y1 - 2013 UR - http://download.springer.com/static/pdf/827/art%253A10.1186%252F2051-3933-1- 6.pdf?auth66=1394891271_f1a4cb74d6be42ee3f8872ef2ca22c24&ext=.pdf U6 - https://doi.org/10.1186/2051-3933-1-6 ER -