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Collinearity : a review of methods to deal with it and a simulation study evaluating their performance

Titelangaben

Dormann, Carsten F. ; Elith, Jane ; Bacher, Sven ; Buchmann, Carsten ; Carl, Gudrun ; Carré, Gabriel ; García Marquéz, Jaime R. ; Gruber, Bernd ; Lafourcade, Bruno ; Münkemüller, Tamara ; Osborne, Patrick E. ; Reineking, Björn ; Schröder, Boris ; Skidmore, Andrew K. ; Zurell, Damaris ; Lautenbach, Sven ; Leitão, Pedro ; McClean, Colin:
Collinearity : a review of methods to deal with it and a simulation study evaluating their performance.
In: Ecography. Bd. 36 (2013) Heft 1 . - S. 27-46.
ISSN 1600-0587
DOI: https://doi.org/10.1111/j.1600-0587.2012.07348.x

Abstract

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 ‘folklore’-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.

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Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Zusätzliche Informationen: BAYCEER106394
Institutionen der Universität: Forschungseinrichtungen > Zentrale wissenschaftliche Einrichtungen > Bayreuther Zentrum für Ökologie und Umweltforschung - BayCEER
Fakultäten > Fakultät für Biologie, Chemie und Geowissenschaften > Fachgruppe Geowissenschaften > Juniorprofessur Biogeographische Modellierung
Fakultäten
Fakultäten > Fakultät für Biologie, Chemie und Geowissenschaften
Fakultäten > Fakultät für Biologie, Chemie und Geowissenschaften > Fachgruppe Geowissenschaften
Forschungseinrichtungen
Forschungseinrichtungen > Zentrale wissenschaftliche Einrichtungen
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik
Eingestellt am: 29 Apr 2015 15:41
Letzte Änderung: 21 Nov 2023 14:51
URI: https://eref.uni-bayreuth.de/id/eprint/11595