Variance Explained (Vx): A General, Model-Based Approach for Explaining and Partitioning Variance

Understanding the variance explained by statistical models and their predictors is crucial for data analysis and interpretation. Traditional measures such as R-squared (R2), coefficient omega, and Cronbach’s alpha provide insights into model performance, but they lack a consistent approach despite having a common mathematical foundation. Measures of variables’ importance, such as Pratt’s measure, have been applied to regression models, but have seldom been extended beyond this context. This paper introduces a general index for variance explained (Vx), which encompasses predictive model evaluation, reliability analysis, and variable importance. The Vx framework synthesizes previous approaches, providing a unifying framework that replicates other measures while offering new insights. The paper demonstrates how Vx can be applied to regression models, path and mediational models, and confirmatory and exploratory factor analysis using published datasets. The Vx framework offers a more flexible and general method for model evaluation, which has the potential to improve the consistency and clarity of scientific reporting.