Test Statistics for Confirmatory Factor Analysis Under Non-Normality and Large p/n Ratios

A Comment on Muda and Yangxuan (2026)

Bibliographic Data

ID21641904
AuthorsNjål Foldnes (0000-0001-6889-6067, University of Stavanger, corresponding author), Steffen Grønneberg (0000-0003-2785-6530, BI Norwegian Business School)
Year2026
Pages1-5
Publication date2026-06-01
Open AccessYes
TypeARTICLE
VenueStructural Equation Modeling: A Multidisciplinary Journal (JOURNAL)
Journal identifiersISSN: 1070-5511 • E-ISSN: 1532-8007
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/10705511.2026.2651100
OpenAlexW7163001661
LanguageEN
References cited12

Muda and Yangxuan recommended a ridge-calibrated test statistic for controlling Type I error inflation in confirmatory factor analysis under non-normality. Although improving finite-sample inference is an important goal, their empirical evaluation is undermined by incorrectly implemented benchmark statistics, misattributed comparison methods, and a simulation design restricted to asymptotically robust conditions. Using corrected code, we reanalyze the original conditions and replace the misattributed benchmarks with the penalized eigenvalue procedures pEBA4RLS and pOLS2RLS. Under the original conditions, the best-performing procedures are the ridge-calibrated TCsFCr statistic and the penalized eigenvalue methods. However, under additional non-asymptotically robust conditions, including high-dimensional models, pEBA4RLS provides the most reliable Type I error control and outperforms the ridge-calibrated competitors

Confirmatory factor analysis · Statistical analysis · Statistical hypothesis testing · Data Analysis with R · Psychometric Methodologies and Testing · Statistical Methods in Clinical Trials

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Open DOIOpen Access