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

Timothy Colin Bednall

No us346, OSF Preprints from Center for Open Science

Abstract: Understanding the variance explained by statistical models is crucial for data analysis and interpretation. Traditional measures such as R-Squared, coefficient omega, and Cronbach’s alpha provide insights into model performance, but they often lack consistency and comparability across 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 and simplifying reporting across various models. It also facilitates communication of results to nonacademic audiences, including policymakers and the public. The Vx index is straightforward to calculate using widely available software and provides a model-based approach that reflects hypothesized relationships among variables. This paper demonstrates the application of the Vx framework to multiple regression models, path and mediational models, and confirmatory factor analyses, using published datasets and providing accompanying R code and Excel spreadsheets for replication. The Vx framework offers a flexible and interpretable method for evaluating model performance, which can be applied to a range of different models within the structural equation modelling family.

Date: 2025-01-10
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:us346

DOI: 10.31219/osf.io/us346

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