Relative importance analysis with multivariate models: Shifting the focus from independent variables to parameter estimates

Abstract

Conclusions regarding the relative importance of different independent variables in a statistical model have meaningful implications for theory and practice. However, methods for determining relative importance have yet to extend beyond statistical models with a single dependent variable and a limited set of multivariate models. To accommodate multivariate models, the current work proposes shifting away from the concept of independent variable relative importance toward that of parameter estimate relative importance (PERI). This paper illustrates the PERI approach by comparing it to the evaluation of regression slopes and independent variable relative importance (IVRI) statistics to show the interpretive and methodological advantages of the new concept and associated methods. PERI’s advantages above standardized slopes stem from the same fit metric that is used to compute PERI statistics; this makes them more comparable to one another than standardized slopes. PERI’s advantages over IVRI stem from situations where independent variables do not predict all dependent variables; hence, PERI permits importance determination in situations where independent variables are nested in dependent variables they predict. We also provide recommendations for implementing PERI using dominance analysis with statistical models that can be estimated with maximum likelihood estimation combined with a series of model constraints using two examples.