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

Title data

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. Vol. 36 (January 2013) Issue 1 . - pp. 27-46.
ISSN 1600-0587
DOI: https://doi.org/10.1111/j.1600-0587.2012.07348.x

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: BAYCEER106394
Institutions of the University: Research Institutions > Research Centres > Bayreuth Center of Ecology and Environmental Research- BayCEER
Faculties > Faculty of Biology, Chemistry and Earth Sciences > Department of Earth Sciences > Junior Professorship Biogeographical Modelling
Faculties
Faculties > Faculty of Biology, Chemistry and Earth Sciences
Faculties > Faculty of Biology, Chemistry and Earth Sciences > Department of Earth Sciences
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 500 Science
Date Deposited: 29 Apr 2015 15:41
Last Modified: 29 Apr 2015 15:41
URI: https://eref.uni-bayreuth.de/id/eprint/11595