Quantifying variable importance in a multimodel inference framework

Abstract

SummaryThe sum of Akaike weights (SW) is often used to quantify relative variable importance (RVI) within the information‐theoretic (IT) multimodel inference framework. A recent study (Galipaudet al. 2014,Methods in Ecology and Evolution5: 983) questioned the validity of the SW approach. Regrettably, this study is flawed because SW was evaluated with an inappropriate benchmark. Irrespective of this study's methodological issues, RVI metrics based on the relative contribution of explanatory variables in explaining the variance in the response variable (partitionedR2‐based) are lacking in multimodel inference.We re‐evaluated the validity of SW by repeating Galipaudet al.'s experiment but with an appropriate benchmark. When explanatory variables are uncorrelated, the quantity that SW estimates (i.e. the probability that a variable is included in the actual best IT model) is monotonically related to squared zero‐order correlation coefficients (r2) between explanatory variables and the response variable. The degree of correspondence between SW andr2rankings(notvalues) of variables in data sets with uncorrelated explanatory variables was therefore used as a benchmark to evaluate the validity of SW as a RVI metric. To address the lack of partitionedR2‐based RVI metrics in multimodel inference, we proposed 2 metrics: (a)Iweighted, the average model probability‐weighted partitionedR2; and (b)Ibest, the partitionedR2derived from the best IT model. We performed Monte Carlo simulations to evaluate the utility ofIweightedandIbestversus partitionedR2derived from the global model (Iglobal).SW rankings matchedr2rankings of variables; therefore, SW is a valid measure of RVI. Among partitionedR2‐based metrics,IweightedandIglobalwere generally more accurate in estimating the population partitionedR2.Iweightedperformed better when explanatory variables were uncorrelated, whereasIglobalwas better in smaller data sets with correlated explanatory variables. To improve the utility ofIweightedin such data sets, we proposed approaches to eliminate or reduce the influence of correlated variables.Despite recent criticisms, our results show that SW is a valid RVI metric. To quantify RVI in terms of theR2explained by each variable,IweightedandIglobalare the preferred RVI metrics.