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Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error

Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error,10.1007/s00265-010-1045-6,Behavior

Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error   (Citations: 6)
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There has been a great deal of recent discussion of the practice of regression analysis (or more generally, linear modelling) in behaviour and ecology. In this paper, I wish to highlight two factors that have been under-considered, collinearity and measurement error in predictors, as well as to consider what happens when both exist at the same time. I examine what the consequences are for conventional regression analysis (ordinary least squares, OLS) as well as model averaging methods, typified by information theoretic approaches based around Akaike’s information criterion. Collinearity causes variance inflation of estimated slopes in OLS analysis, as is well known. In the presence of collinearity, model averaging reduces this variance for predictors with weak effects, but also can lead to parameter bias. When collinearity is strong or when all predictors have strong effects, model averaging relies heavily on the full model including all predictors and hence the results from this and OLS are essentially the same. I highlight that it is not safe to simply eliminate collinear variables without due consideration of their likely independent effects as this can lead to biases. Measurement error is also considered and I show that when collinearity exists, this can lead to extreme biases when predictors are collinear, have strong effects but differ in their degree of measurement error. I highlight techniques for dealing with and diagnosing these problems. These results reinforce that automated model selection techniques should not be relied on in the analysis of complex multivariable datasets.
Journal: Behavioral Ecology and Sociobiology - BEHAV ECOL SOCIOBIOL , vol. 65, no. 1, pp. 91-101, 2011
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    • ...Some other papers in the issue deal with specific questions raised by the IT technique, including the compilation of the set of models to be analyzed (Dochtermann and Jenkins 2010), the combination of information from different models (Richards et al. 2010), and dealing with collinearity and missing observations during this process (Freckleton 2010; Nakagawa and Freckleton 2010)...

    Gergely Hegyiet al. Using information theory as a substitute for stepwise regression in ec...

    • ...Model averaging has been advocated as an advantage of IT-AIC approaches (Burnham and Anderson 2002) despite wide acknowledgment that more work on model averaging is required (Buckland et al. 1997; Burnham and Anderson 2002, pp. 152–3; Richards 2005; Freckleton 2010; Nakagawa and Freckleton 2010)...
    • ...Further problems of stepwise approaches are that they can only be used to choose among a set of completely nested models and that they seldom deal well with collinear variables (Freckleton 2010)...
    • ...Our discussion recognises that model averaging remains an open research area, with further work required to understand fully its properties and limitations (Burnham and Anderson 2002, pp152–155; Stephens et al. 2007a; Freckleton 2010; Nakagawa and Freckleton 2010)...

    Shane A. Richardset al. Model selection and model averaging in behavioural ecology: the utilit...

    • ...Such robustness is even true in complex cases, for instance when there is collinearity among predictors (Freckleton 2010)...
    • ...These can include the possible correlations between the variables, which will be determined by the pattern of missingness, with consequences for parameter estimates and variances (Freckleton 2010)...
    • ...Also our morphological model may suffer from the problem of collinearity given correlations among morphological variables; the issue of collinearity is beyond the scope of this paper (we refer readers to Freckleton 2010)...

    Shinichi Nakagawaet al. Model averaging, missing data and multiple imputation: a case study fo...

    • ...When collinearity does exist, results tend to be unstable (small differences in the analysed data may lead to large changes in the parameters estimated), and estimates of parameters have large standard errors (implying that the estimated effect of a predictor variable is associated with large uncertainty; Freckleton 2010)...

    Roger Mundry. Issues in information theory-based statistical inference—a commentary ...

    • ...We omitted additive models including both of these variables together in the same model because we think they are redundant (see e.g., Freckleton 2010) Lastly, we considered interactions between pairs of the variables and added to our model set interactive models of body size with male dominance status, body size with territory quality, and food availability with territory quality (Table 3). For example, the thinking for the model with the ...

    Kenneth P. Burnhamet al. AIC model selection and multimodel inference in behavioral ecology: so...

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