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

Ecography - Tập 36 Số 1 - Trang 27-46 - 2013
Carsten F. Dormann1,2, Jane Elith3, Sven Bacher4, Carsten M. Buchmann5, Gudrun Carl1, Gabriel Carré6, Jaime Márquez7, Bernd Gruber1,8, Bruno Lafourcade9, Pedro J. Leitão10,11, Tamara Münkemüller9, Colin J. McClean12, Patrick E. Osborne13, Björn Reineking14, Boris Schröder15,5, Andrew K. Skidmore16, Damaris Zurell15,5, Sven Lautenbach1,17
1Helmholtz Zentrum für Umweltforschung = Helmholtz Centre for Environmental Research
2University of Freiburg [Freiburg]
3Sch Bot
4Université de Fribourg = University of Fribourg
5University of Potsdam = Universität Potsdam
6Services déconcentrés d'appui à la recherche Provence-Alpes-Côte d'Azur
7Senckenberg Museum [Frankfurt]
8University of Canberra
9Université Joseph Fourier - Grenoble 1
10Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
11Universidade Técnica de Lisboa
12University of York
13University of Southampton *
14 University of Bayreuth
15Technische Universität Munchen - Technical University Munich - Université Technique de Munich
16University of Twente,
17Rheinische Friedrich-Wilhelms-Universität Bonn

Tóm tắt

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.

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Ecography

Tập 36 Số 1

27-46

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