Related Experiment Video
Updated: May 30, 2026

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
Published on: September 27, 2019
Masking misfit in confirmatory factor analysis by increasing unique variances: a cautionary note on the usefulness of
Moritz Heene1, Sven Hilbert, Clemens Draxler
1Department of Psychology, Karl Franzens University of Graz, Graz A-8010, Austria. moritz.heene@unigraz.at
Abstract:
Fit indices are widely used in order to test the model fit for structural equation models. In a highly influential study, Hu and Bentler (1999) showed that certain cutoff values for these indices could be derived, which, over time, has led to the reification of these suggested thresholds as "golden rules" for establishing the fit or other aspects of structural equation models. The current study shows how differences in unique variances influence the value of the global chi-square model test and the most commonly used fit indices: Root-mean-square error of approximation, standardized root-mean-square residual, and the comparative fit index. Using data simulation, the authors illustrate how the value of the chi-square test, the root-mean-square error of approximation, and the standardized root-mean-square residual are decreased when unique variances are increased although model misspecification is present. For a broader understanding of the phenomenon, the authors used different sample sizes, number of observed variables per factor, and types of misspecification. A theoretical explanation is provided, and implications for the application of structural equation modeling are discussed.
Related Concept Videos
Expected Frequencies in Goodness-of-Fit Tests
One-Way ANOVA: Equal Sample Sizes
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
Confounding in Epidemiological Studies
One-Way ANOVA: Unequal Sample Sizes
Compacting Factor test
The procedure begins by placing concrete into the upper hopper without any compaction. Once filled, the bottom door of this hopper is opened,...
Friedman Two-way Analysis of Variance by Ranks

