Percentage of variance accounted for in structural equation models: The rediscovery of the goodness of fit index.

Abstract

This article delves into the often-overlooked metric of percentage of variance accounted for in structural equation models (SEM). The goodness of fit index (GFI) provides the percentage of variance of the sum of squared covariances explained by the model. Despite being introduced over four decades ago, the GFI has been overshadowed in favor of fit indices that prioritize distinctions between close and nonclose fitting models. Similar to R² in regression, the GFI should not be used to this aim but rather to quantify the model's utility. The central aim of this study is to reintroduce the GFI, introducing a novel approach to computing the GFI using mean and mean-and-variance corrected test statistics, specifically designed for nonnormal data. We use an extensive simulation study to evaluate the precision of inferences on the GFI, including point estimates and confidence intervals. The findings demonstrate that the GFI can be very accurately estimated, even with nonnormal data, and that confidence intervals exhibit reasonable accuracy across diverse conditions, including large models and nonnormal data scenarios. The article provides methods and code for estimating the GFI in any SEM, urging researchers to reconsider the reporting of the percentage of variance accounted for as an essential tool for model assessment and selection. (PsycInfo Database Record (c) 2024 APA, all rights reserved).