Model averaging and muddled multimodel inferences

Background/Question/Methods

Three common misuses of model-averaged estimates of parameters for predictors in regression models for making multimodel inferences based on Akaike Information Criterion (AIC) weights are identified in the ecological literature.  Model-averaged estimates of parameters for predictors are incorrectly used to make model-averaged predictions of the response when the models are not linear in the parameters; are unreasonably interpreted as if they are valid estimates of partial effects for individual parameters when there is multicollinearity among the predictors; and the associated AIC model weights are incorrectly used to assess the relative importance of individual predictors.  Although these procedures follow recommendations by Burnham and Anderson (2002, 2004) for incorporating model uncertainty into multimodel inferences, they lack a logical statistical foundation, are not generally useful, and can distract from addressing important statistical details relevant to every single candidate model.  Model averaging is reasonable for incorporating model uncertainty into quantities based on an entire model that have the same units in all candidate models, e.g. predicted responses, but is unreasonable for individual components of models, e.g. parameters for predictors, with units and interpretations that change among candidate models. 

Results/Conclusions

I illustrate these issues with a recent species distribution modeling technique developed by Rice et al. (2013) for predicting greater sage-grouse (Centrocercus urophasianus) distribution in northwestern Colorado.  Rice et al. (2013) used zero-truncated Poisson regression models of mean number of telemetry locations with cover type proportions in 1-km²areas as predictors for seasonal models.   Model-averaged predictions based on the model-averaged estimates for the predictors were incorrect because the models were nonlinear in the parameters for predictors.  The model-averaged estimates for predictors were not valid partial effects for the various cover type proportions because the compositional predictors had an inherent negative covariance structure.  The incorrect use of accumulated AIC model weights led to the unreasonable conclusion that sagebrush was the cover type with highest relative importance (1.0) simply because it was included in all candidate models.  The inferences in Rice et al. (2013) are all muddled as we do not know anything about the reliability of the predictions of sage-grouse distributions, how those predictions change with proportions of the various cover types, and which cover types contribute more strongly to the change in distribution.  The model averaging issues illustrated with Rice et al. (2013) are common in other recent ecological literature and ought to be discouraged from further use if we are to make effective scientific contributions to conservation and ecological understanding.