Relative Importance of Predictors in Multilevel Modeling (original) (raw)
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Regular Articles: Relative Importance of Predictors in Multilevel Modeling
2014
The Pratt index is a useful and practical strategy for day-to-day researchers when ordering predictors in a multiple regression analysis. The purposes of this study are to introduce and demonstrate the use of the Pratt index to assess the relative importance of predictors for a random intercept multilevel model.
Interpreting Multiple Linear Regression: A Guidebook of Variable Importance
Multiple regression (MR) analyses are commonly employed in social science fields. It is also common for interpretation of results to typically reflect overreliance on beta weights (cf. Courville & Thompson, 2001; Nimon, Roberts, & Gavrilova, 2010; Zientek, Capraro, & Capraro, 2008), often resulting in very limited interpretations of variable importance. It appears that few researchers employ other methods to obtain a fuller understanding of what and how independent variables contribute to a regression equation.
This paper aims to introduce multilevel logistic regression analysis in a simple and practical way. First, we introduce the basic principles of logistic regression analysis (conditional probability, logit transformation, odds ratio). Second, we discuss the two fundamental implications of running this kind of analysis with a nested data structure: In multilevel logistic regression, the odds that the outcome variable equals one (rather than zero) may vary from one cluster to another (i.e. the intercept may vary) and the effect of a lower-level variable may also vary from one cluster to another (i.e. the slope may vary). Third and finally, we provide a simplified three-step " turnkey " procedure for multilevel logistic regression modeling: • Preliminary phase: Cluster-or grand-mean centering variables • Step #1: Running an empty model and calculating the intraclass correlation coefficient (ICC) • Step #2: Running a constrained and an augmented intermediate model and performing a likelihood ratio test to determine whether considering the cluster-based variation of the effect of the lower-level variable improves the model fit • Step #3 Running a final model and interpreting the odds ratio and confidence intervals to determine whether data support your hypothesis Command syntax for Stata, R, Mplus, and SPSS are included. These steps will be applied to a study on Justin Bieber, because everybody likes Justin Bieber. 1
Organizational Research Methods, 2014
Determining independent variable relative importance is a highly useful practice in organizational science. Whereas techniques to determine independent variable importance are available for normally distributed and binary dependent variable models, such techniques have not been extended to multicategory dependent variables (MCDVs). The current work extends previous research on binary dependent variable relative importance analysis to provide a methodology for conducting relative importance analysis on MCDV models from a dominance analysis (DA) perspective. Moreover, the current work provides a set of comprehensive data analytic examples that demonstrate how and when to use MCDV models in a DA and the advantages general DA statistics offer in interpreting MCDV model results. Moreover, the current work outlines best practices for determining independent variable relative importance for MCDVs using replicable examples on data from the publicly available General Social Survey. The present work then contributes to the literature by using in-depth data analytic examples to outline best practices in conducting relative importance analysis for MCDV models and by highlighting unique information DA results provide about MCDV models.
Using Pratt\u27s Importance Measures in Confirmatory Factor Analyses
2017
When running a confirmatory factor analysis (CFA), users specify and interpret the pattern (loading) matrix. It has been recommended that the structure coefficients, indicating the factors’ correlation with the observed indicators, should also be reported when the factors are correlated (Graham, Guthrie, & Thompson, 2003; Thompson, 1997). The aims of this article are: (1) to note the structure coefficient should be interpreted with caution if the factors are specified to correlate. Because the structure coefficient is a zero-order correlation, it may be partially or entirely a reflection of factor correlations. This is elucidated by the matrix algebra of the structure coefficients based on the example in Graham et al. (2003). (2) The second aim is to introduce the method of Pratt’s (1987) importance measures to be used in a CFA. The method uses the information in the structure coefficients, along with the pattern coefficients, into unique measures that are not confounded by the fact...
Behavior Research Methods, 2011
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.
Using Pratt's Importance Measures in Confirmatory Factor Analyses
Journal of Modern Applied Statistical Methods, 2017
When running a confirmatory factor analysis (CFA), users specify and interpret the pattern (loading) matrix. It has been recommended that the structure coefficients, indicating the factors' correlation with the observed indicators, should also be reported when the factors are correlated (Graham, Guthrie, & Thompson, 2003; Thompson, 1997). The aims of this article are: (1) to note the structure coefficient should be interpreted with caution if the factors are specified to correlate. Because the structure coefficient is a zero-order correlation, it may be partially or entirely a reflection of factor correlations. This is elucidated by the matrix algebra of the structure coefficients based on the example in Graham et al. (2003). (2) The second aim is to introduce the method of Pratt's (1987) importance measures to be used in a CFA. The method uses the information in the structure coefficients, along with the pattern coefficients, into unique measures that are not confounded by the factor correlations. These importance measures indicate the proportions of the variation in an observed indicator that are attributable to the factorsan interpretation analogous to the effect size measure of eta-squared. The importance measures can further be transformed to eta correlations, a measure of unique directional correlation of a factor with an observed indicator. This is illustrated with a real data example.
History and Use of Relative Importance Indices In Organizational Research
Organizational Research Methods, 2004
The search for a meaningful index of the relative importance of predictors in multiple regression has been going on for years. This type of index is often desired when the explanatory aspects of regression analysis are of interest. The authors define relative importance as the proportionate contribution each predictor makes to R2, considering both the unique contribution of each predictor by itself and its incremental contribution when combined with the other predictors. The purposes of this article are to introduce the concept of relative importance to an audience of researchers in organizational behavior and industrial/organizational psychology and to update previous reviews of relative importance indices. To this end, the authors briefly review the history of research on predictor importance in multiple regression and evaluate alternative measures of relative importance. Dominance analysis and relative weights appear to be the most successful measures of relative importance currently available. The authors conclude by discussing how importance indices can be used in organizational research.
Influential Cases in Multilevel Modeling: A Methodological Comment
American Sociological Review, 2010
A large number of cross-national survey datasets have become available in recent decades. Consequently, scholars frequently apply multilevel models to test hypotheses on both the individual and the country level. However, no currently available cross-national survey project covers more than 54 countries (GESIS 2009). Multilevel modeling therefore runs the risk that higher-level slope estimates (and the substantial conclusions drawn from