Using Dominance Analysis to Determine Predictor Importance in Logistic Regression

This article proposes an extension of dominance analysis that allows researchers to determine the relative importance of predictors in logistic regression models. Criteria for choosing logistic regression R2 analogues were determined and measures were selected that can be used to perform dominance analysis in logistic regression. A simulation study, using both simple random sampling from a known population and bootstrap sampling from a single (parent) random sample, was performed to evaluate the bias, sampling distribution, and confidence intervals of quantitative dominance measures as well as the reproducibility of qualitative dominance measures. Results indicated that the bootstrap procedure is feasible and can be used in applied research to generalize logistic regression dominance analysis results to the population of interest. The procedures for determining and interpreting the general dominance of predictors in a logistic regression context are illustrated with an empirical example.

[1]  A. Agresti.  An introduction to categorical data analysis , 1997 .

[2]  Jr. Louis A. Cox,et al.  A New Measure of Attributable Risk for Public Health Applications , 1985 .

[3]  U. Grömping.  Estimators of Relative Importance in Linear Regression Based on Variance Decomposition , 2007 .

[4]  D. Budescu.  Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. , 1993 .

[5]  D. Budescu,et al.  The dominance analysis approach for comparing predictors in multiple regression. , 2003, Psychological methods.

[6]  Richard G. Lomax,et al.  A Beginner's Guide to Structural Equation Modeling , 2022 .

[7]  Comparing the squared multiple correlation coefficients of non-nested models: an examination of confidence intervals and hypothesis testing. , 2008, The British journal of mathematical and statistical psychology.

[8]  J. Elashoff,et al.  Multiple Regression in Behavioral Research. , 1975 .

[9]  T. Amemiya.  QUALITATIVE RESPONSE MODELS: A SURVEY , 1981 .

[10]  J. Liao,et al.  Adjusted Coefficients of Determination for Logistic Regression , 2003 .

[11]  Arturo Estrella,et al.  A new measure of fit for equations with dichotomous dependent variables , 1998 .

[12]  Robert A. Stine,et al.  An Introduction to Bootstrap Methods , 1989 .

[13]  S. Menard.  Six Approaches to Calculating Standardized Logistic Regression Coefficients , 2004 .

[14]  M Schemper,et al.  Explained variation for logistic regression. , 1996, Statistics in medicine.

[15]  E. Soofi.  Capturing the Intangible Concept of Information , 1994 .

[16]  J. Bring.  How to Standardize Regression Coefficients , 1994 .

[17]  N. Nagelkerke,et al.  A note on a general definition of the coefficient of determination , 1991 .

[18]  A Agresti,et al.  Summarizing the predictive power of a generalized linear model. , 2000, Statistics in medicine.

[19]  D. McFadden.  MEASUREMENT OF URBAN TRAVEL DEMAND , 1974 .

[20]  Erich Barke,et al.  Hierarchical partitioning , 1996, Proceedings of International Conference on Computer Aided Design.

[21]  James M. LeBreton,et al.  History and Use of Relative Importance Indices in Organizational Research , 2004 .

[22]  S. Menard.  Coefficients of Determination for Multiple Logistic Regression Analysis , 2000 .

[23]  Willem van den Burg,et al.  Some properties of two measures of multivariate association , 1988 .

[24]  Ehsan S. Soofi,et al.  A Framework for Measuring the Importance of Variables with Applications to Management Research and Decision Models , 2000, Decis. Sci..

[25]  T. O. Kvålseth.  Cautionary Note about R 2 , 1985 .