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Three flawed practices associated with model averaging coefficients for predictor variables in regression models commonly occur when making multimodel inferences in analyses of ecological data. Model-averaged regression coefficients based on Akaike information criterion (AIC) weights have been recommended for addressing model uncertainty but they are not valid, interpretable estimates of partial effects for individual predictors when there is multicollinearity among the predictor variables. Multicollinearity implies that the scaling of units in the denominators of the regression coefficients may change across models such that neither the parameters nor their estimates have common scales, therefore averaging them makes no sense. The associated sums of AIC model weights recommended to assess relative importance of individual predictors are really a measure of relative importance of models, with little information about contributions by individual predictors compared to other measures of relative importance based on effects size or variance reduction. Sometimes the model-averaged regression coefficients for predictor variables are incorrectly used to make model-averaged predictions of the response variable when the models are not linear in the parameters. I demonstrate the issues with the first two practices using the college grade point average example extensively analyzed by Burnham and Anderson. I show how partial standard deviations of the predictor variables can be used to detect changing scales of their estimates with multicollinearity. Standardizing estimates based on partial standard deviations for their variables can be used to make the scaling of the estimates commensurate across models, a necessary but not sufficient condition for model averaging of the estimates to be sensible. A unimodal distribution of estimates and valid interpretation of individual parameters are additional requisite conditions. The standardized estimates or equivalently the t statistics on unstandardized estimates also can be used to provide more informative measures of relative importance than sums of AIC weights. Finally, I illustrate how seriously compromised statistical interpretations and predictions can be for all three of these flawed practices by critiquing their use in a recent species distribution modeling technique developed for predicting Greater Sage-Grouse ( Centrocercus urophasianus ) distribution in Colorado, USA. These model averaging issues are common in other ecological literature and ought to be discontinued if we are to make effective scientific contributions to ecological knowledge and conservation of natural resources.

A fundamental goal of scientific research is to identify the underlying variables that govern crucial processes of a system. This is especially difficult in ecology, which is intrinsically rich in candidate predictors. An efficient statistical procedure to evaluate the relative importance of predictors in regression models is highly desirable. However, previous studies criticised the most universally applicable method, by pointing out the low discriminating power of the importance index in simulated datasets. Here we proposed a new index, WiBB, which integrates the merits of several existing methods. WiBB combines a model‐weighting method from information theory (Wi), a standardised regression coefficient method measured by β* (B), and bootstrap resampling technique (B). We applied the WiBB in simulated datasets with known correlation structures, for both linear models (LM) and generalized linear models (GLM), to evaluate its performance. We also applied it to an empirical dataset of a plant genus Mimulus to select bioclimatic predictors of species' presence across the landscape. Results in the simulated datasets showed that the bootstrap resampling technique significantly improved the discriminant ability by correctly sorting the orders of relative importance of predictors. The WiBB method outperformed the β* and the relative sum of weights (SWi, a standardised version of sum of weights) methods in scenarios with small and large sample sizes, respectively. When testing WiBB in the empirical dataset with GLM, it sensibly identified four important predictors with high credibility out of six candidates in modelling geographical distributions of 71 Mimulus species. This integrated index has great advantages in evaluating predictor importance and hence reducing the dimensionality of data, without losing interpretive power. The simplicity of calculation of the new metric over more sophisticated statistical procedures makes it a handy method in the statistical toolbox.

Dominance analysis (DA) is a method used to evaluate the relative importance of predictors that was originally proposed for linear regression models. This article proposes an extension of DA that allows researchers to determine the relative importance of predictors in hierarchical linear models (HLM). Commonly used measures of model adequacy in HLM (i.e., deviance, pseudo-R 2 , and proportional reduction in prediction error) were evaluated in terms of their appropriateness as measures of model adequacy for DA. Empirical examples were used to illustrate the procedures for comparing the relative importance of Level-1 predictors and Level-2 predictors in a person-in-group design. Finally, a simulation study was conducted to evaluate the performance of the proposed procedures and develop recommendations.

This article advocates for the wider use of relative importance indices as a supplement to multiple regression analyses. The goal of such analyses is to partition explained variance among multiple predictors to better understand the role played by each predictor in a regression equation. Unfortunately, when predictors are correlated, typically relied upon metrics are flawed indicators of variable importance. To that end, we highlight the key benefits of two relative importance analyses, dominance analysis and relative weight analysis, over estimates produced by multiple regression analysis. We also describe numerous situations where relative importance weights should be used, while simultaneously cautioning readers about the limitations and misconceptions regarding the use of these weights. Finally, we present step-by-step recommendations for researchers interested in incorporating these analyses in their own work and point them to available web resources to assist them in producing these weights.

Recent studies have shown that relative permeability can be modeled as a state function which is independent of flow direction and dependent upon phase saturation (S), phase connectivity (X), and fluid–fluid interfacial area (A). This study evaluates the impact of each of the three state parameters (S, X, and A) in the estimation of relative permeability. The relative importance of the three state parameters in four separate quadrants of S-X-A space was evaluated using a machine learning algorithm (out-of-bag predictor importance method). The results show that relative permeability is sensitive to all the three parameters, S, X, and A, with varying magnitudes in each of the four quadrants at a constant value of wettability. We observe that the wetting-phase relative permeability is most sensitive to saturation, while the non-wetting phase is most sensitive to phase connectivity. Although the least important, fluid–fluid interfacial area is still important to make the relative permeability a more exact state function.

The purpose of the current study is to compare the extent to which general and specific abilities predict academic performances that are also varied in breadth (i.e., general performance and specific performance). The general and specific constructs were assumed to vary only in breadth, not order, and two data analytic approaches (i.e., structural equation modeling [SEM] and relative weights analysis) consistent with this theoretical assumption were compared. Conclusions regarding the relative importance of general and specific abilities differed based on data analytic approaches. The SEM approach identified general ability as the strongest and only significant predictor of general academic performance, with neither general nor specific abilities predicting any of the specific subject grade residuals. The relative weights analysis identified verbal reasoning as contributing more than general ability, or other specific abilities, to the explained variance in general academic performance. Verbal reasoning also contributed to most of the explained variance in each of the specific subject grades. These results do not provide support for the utility of predictor-criterion alignment, but they do provide evidence that both general and specific abilities can serve as useful predictors of performance.

The five articles in this special issue of Organizational Research Methods focus on various measures of global importance that rank and scale all p predictors in a multiple regression equation and compare their relative merits using a variety of real and simulated data sets. In this commentary, the authors describe several special features of dominance analysis that allow researchers to study more specific and narrowly focused aspects of relative importance. These analyses offer new insights into the pattern of importance that are not provided by any of the global measures of importance.

The purpose of this article is to examine the recent claims calling for abolishing domain importance weighting in quality of life (QoL) measures by considering the evidence conceptually and empirically. Based on a close review of evidence presented to date, it is suggested that using the range-of-affect hypothesis as a possible explanation of the poor performance of weighted satisfaction composite in predicting or correlating with global satisfaction or QoL measures can be beneficial to our understanding of the life satisfaction literature. However, given the conceptual focus and the empirical approach of the range-of-affect hypothesis presented in the life satisfaction context, using the range-of-affect hypothesis to argue against domain importance weighting raised more questions than answers. Calling for abolishing domain importance weighting in QoL measures, based on the evidence of range-of-affect hypothesis, is premature.

1. Functional traits are posited to explain interspecific differences in performance, but these relationships are difficult to describe for long-lived organisms such as trees, which exhibit strong ontogenetic changes in demographic rates. Here, we use a size-dependent model of tree growth to test the extent to which of 17 functional traits related to leaf and stem economics, adult stature and seed size predict the ontogenetic trajectory of tree growth. 2. We used a Bayesian modelling framework to parameterize and contrast three size-dependent diameter growth models using 16 years of census data from 5524 individuals of 50 rain forest tree species: a size-dependent model, a size-dependent model with species-specific parameters and a size-dependent model based on functional traits. 3. Most species showed clear hump-shaped ontogenetic growth trajectories and, across species, maximum growth rate varied nearly tenfold, from 0.58 to 5.51 mm year-1. Most species attained their maximum growth at 60% of their maximum size, whereas the magnitude of ontogenetic changes in growth rate varied widely among species. 4. The Trait-Model provided the best compromise between explained variance and model parsimony and needed considerably fewer parameters than the model with species terms. 5. Stem economics and adult stature largely explained interspecific differences in growth strategy. Maximum absolute diameter growth rates increased with increasing adult stature and leaf d13C and decreased with increasing wood density. Species with light wood had the greatest potential to modulate their growth, resulting in hump-shaped ontogenetic growth curves. Seed size and leaf economics, generally thought to be of paramount importance for plant performance, had no significant relationships with the growth parameters. 6. Synthesis. Our modelling approach offers a promising way to link demographic parameters to their functional determinants and hence to predict growth trajectories in species-rich communities with little parameter inflation, bridging the gap between functional ecology and population demography.

The topic of variable importance in linear regression is reviewed, and a measure first justified theoretically by Pratt (1987) is examined in detail. Asymptotic variance estimates are used to construct individual and simultaneous confidence intervals for these importance measures. A simulation study of their coverage properties is reported, and an example is provided.