Measures of predictor variable importance in multiple regression: An additional suggestion

Fabbris, Luigi

doi:10.1007/bf00145808

Cited by 21 publications

(27 citation statements)

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“…) even when the independent variables are correlated (see Fabbris, 1980;Genizi, 1993;Johnson, 2000). In this way, relative weights are easy to explain in the same way as general dominance weights because they sum to the model R 2 .…”

Section: Relative Weightsmentioning

confidence: 98%

Understanding the Results of Multiple Linear Regression

Nimon

Oswald

2013

Organizational Research Methods

282

226

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Multiple linear regression (MLR) remains a mainstay analysis in organizational research, yet intercorrelations between predictors (multicollinearity) undermine the interpretation of MLR weights in terms of predictor contributions to the criterion. Alternative indices include validity coefficients, structure coefficients, product measures, relative weights, all-possible-subsets regression, dominance weights, and commonality coefficients. This article reviews these indices, and uniquely, it offers freely available software that (a) computes and compares all of these indices with one another, (b) computes associated bootstrapped confidence intervals, and (c) does so for any number of predictors so long as the correlation matrix is positive definite. Other available software is limited in all of these respects. We invite researchers to use this software to increase their insights when applying MLR to a data set. Avenues for future research and application are discussed. Keywords multiple regression, quantitative research, exploratory, research designA continued goal of organizational researchers conducting regression analysis is to make inferences about the relative importance of predictor variables (cf. Nimon, Gavrilova, & Roberts, 2010;Zientek, Capraro, & Capraro, 2008), yet it is all too common to rely heavily (if not solely) on the regression coefficients from the analysis which optimize sample-specific prediction (minimize sum of squared errors). Instead, other metrics that operationalize relative importance in ways that are consistent with such researchers' goals would seem more appropriate, and a range of metrics and approaches exists. In addition to regression weights and zero-order correlation coefficients that researchers likely report, MLR interpretation may be further informed by considering structure

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Section: Relative Weightsmentioning

confidence: 98%

Understanding the Results of Multiple Linear Regression

Nimon

Oswald

2013

Organizational Research Methods

282

226

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“…These measures, however, are context dependent, and, when the predictors are correlated, they cannot be used to unambiguously determine the contribution of the predictor to the explained criterion variance (see, e.g., Budescu, 1993). To overcome this problem, several methods have been developed for assessing the RI of the predictors, among which are dominance analysis (Azen & Budescu, 2003;Budescu, 1993;Chevan & Sutherland, 1991) and Johnson's epsilon (ε; J. W. Johnson, 2000), initially proposed by Fabbris (1980). These RI indices are generally used to help determine importance when a researcher has no theoretical ordering of predictor variables (Baltes, Parker, Young, Huff, & Altmann, 2004).…”

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confidence: 99%

FIRE: an SPSS program for variable selection in multiple linear regression analysis via the relative importance of predictors

Lorenzo‐Seva

Ferrando

2010

Behav Res

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We provide an SPSS program that implements currently recommended techniques and recent developments for selecting variables in multiple linear regression analysis via the relative importance of predictors. The approach consists of: (1) optimally splitting the data for cross-validation, (2) selecting the final set of predictors to be retained in the equation regression, and (3) assessing the behavior of the chosen model using standard indices and procedures. The SPSS syntax, a short manual, and data files related to this article are available as supplemental materials from brm.psychonomic-journals.org/content/supplemental.Keywords Multiple linear regression . Variable selection . Relative importance . DUPLEX . SPSS Traditional regression analysis consists of fitting an "a priori" specified model in which the predictors are (ideally) uncorrelated. In contrast to this approach, however, most applications in contemporary regression belong to the exploratory data analysis framework (e.g., Box, 1983): An initial, tentative model, possibly with correlated predictors, is proposed and evolves throughout an iterative process that concludes with a final chosen equation. The central issue in this process is how to select the predictors that will be included in the final model. Mitchell and Beauchamp (1988) have provided some of the reasons for selecting a best (in some sense) set of predictors:(1) to express the relationship between the criterion and the predictors as simply as possible; (2) to reduce future prediction cost; (3) to identify the important and the negligible predictors; or (4) to increase the precision of statistical estimates and predictions. However, the procedures that we shall discuss here are designed to select the best set of predictors and are not intended to address more complex issues such as the assessment of directional influences among the predictors, interaction effects, or suppressor effects. This may be considered to be a limitation (for a further discussion, see Bring, 1994Bring, , 1995. These issues are usually dealt with by using structural equation models.Various procedures have been proposed for finding an optimal set of Q predictors from the P potential predictorsfor example, the Akaike information criterion (Akaike, 1973), the C p criterion (Mallows, 1973), or the Bayesian information criterion (Akaike, 1978;Schwarz, 1978). These procedures are based on a comparison of all 2 P possible sets. So, when P is large, the computational requirements can be prohibitive. As a practical solution, practitioners typically use heuristic methods to reduce the number of potential predictors: stepwise selection, forward selection, or backward elimination (see, e.g., Miller, 1990, for a detailed discussion). These methods sequentially include (or exclude) predictors based on the assessment of the significant changes in R 2 . An alternative and apparently simple approach to the selection problem is to choose the most important predictors. However, as Nunnally and Bernstein (1994, pp. 191-193) n...

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“…However, if we used standardized regression to solve this problem, standardized regression weights suffer from the weakness of inappropriately partitioning variance for addressing questions regarding relative importance . Therefore, before we conducted the paired t-test, we employed a relative weight analysis (Fabbris, 1980;Johnson, 2000), which allows for more accurate variance partitioning among correlated predictors. Because we suspect environmental change and previous firm performance both can influence the change in network size, we used relative weight analysis to identify the respective contribution of the two predictors to network tie size.…”

Section: Discussionmentioning

confidence: 99%

Boundaries of Network Ties in Entrepreneurship: How Large Is Too Large?

Qian

Kemelgor

2013

J. Dev. Entrepreneurship

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External environments can require entrepreneurs to adjust and maintain network ties to cope with environmental changes and turbulence. Although network ties can help entrepreneurs gain resources and support, researchers are becoming aware of some negative aspects of networks, such as information redundancy. We used relative weight analysis and identified that environmental munificence and uncertainty influence the size of one's network. In addition, we surveyed 44 entrepreneurial founders of firms in the bio-technology industry regarding their network composition, including number of ties and firm performance. We found that environmental factors led to increases in both business and social network size. In addition, we identified an optimal number of network ties prior to tie-additions becoming negatively related to firm performance.

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Measures of predictor variable importance in multiple regression: An additional suggestion

Cited by 21 publications

References 7 publications

Understanding the Results of Multiple Linear Regression

Understanding the Results of Multiple Linear Regression

FIRE: an SPSS program for variable selection in multiple linear regression analysis via the relative importance of predictors

Boundaries of Network Ties in Entrepreneurship: How Large Is Too Large?

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