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

Understanding the variance explained by statistical models is crucial for data analysis andinterpretation. Traditional measures such as R-Squared, coefficient omega, and Cronbach’s alphaprovide insights into model performance, but they often lack consistency and comparabilityacross different contexts. This paper introduces a general index for variance explained (Vx),which encompasses predictive model evaluation, reliability analysis, and variable importance.The Vx framework offers a unified approach, enhancing consistency in assessing model fit andsimplifying reporting across various models. It also facilitates communication of results to nonacademicaudiences, including policymakers and the public. The Vx index is straightforward tocalculate using widely available software and provides a model-based approach that reflectshypothesized relationships among variables. This paper demonstrates the application of the Vxframework to multiple regression models, path and mediational models, and confirmatory factoranalyses, using published datasets and providing accompanying R code and Excel spreadsheetsfor replication. The Vx framework offers a flexible and interpretable method for evaluatingmodel performance, which can be applied to a range of different models within the structuralequation modelling family.