Assessing the Relationship Between Variance Decomposition and Model Fit in Multivariate Data Analysis

Posted: Aug 09, 2019

• Evelyn Perez
• Evelyn Scott
• Evelyn White

Abstract

This research addresses the methodological gap between variance decomposition techniques and model fit assessment in multivariate data analysis by developing an integrated framework called the Variance-Fit Nexus (VFN). The VFN framework establishes formal connections between decomposition patterns and fit assessment across principal component analysis, factor analysis, and multidimensional scaling, treating variance decomposition as an integral component of model evaluation rather than merely a preliminary step. Through simulation studies and empirical applications, the research demonstrates that specific patterns in eigenvalue distributions, component contributions, and variance allocation systematically predict model fit metrics, providing enhanced diagnostic capabilities and more nuanced understanding of model adequacy.