Partitioning variance into constituents in multiple regression models: Commonality analysis

Abstract

Commonality analysis is a method of partitioning the explained variance in a multiple regression analysis into variance constituents associated with each independent variable uniquely and variance associated with common effects of one or more independent variables in various combinations. By partitioning variance, commonality analysis helps to determine accurately the degree of multicollinearity between the independent variables, suppressor variable and related importance of independent variables. In addition, commonality analysis provides regression effects (R2) of all possible simple and multiple regression models that can be constructed by the independent variables and thus helps researchers choose the most appropriate regression model. The purposes of this study are to (a) provide a general overview of multiple regression analysis and its application, (b) explain how to conduct commonality analysis in a regression model, and (c) determine the degree of multicollinearity between independent variables and suppressor variable in the model by means of commonality analysis results. For these purposes, OBBS data set which was collected during a project in Turkey was used to provide a heuristic example. In this example, three independent variables that are assumed to predict students’ academic performance were selected to create model and then multiple regression analysis and commonality analysis were conducted.