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The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis.

Curran, Patrick J., West, Stephen G., Finch, John F.·1996·Psychological Methods

DOI 10.1037/1082-989x.1.1.16

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Abstract

Monte Carlo computer simulations were used to investigate the performance of three X 2 test statistics in confirmatory factor analysis (CFA). Normal theory maximum likelihood)~2 (ML), Browne's asymptotic distribution free X 2 (ADF), and the Satorra-Bentler rescaled X 2 (SB) were examined under varying conditions of sample size, model specification, and multivariate distribution. For properly specified models, ML and SB showed no evidence of bias under normal distributions across all sample sizes, whereas ADF was biased at all but the largest sample sizes. ML was increasingly overestimated with increasing nonnormality, but both SB (at all sample sizes) and ADF (only at large sample sizes) showed no evidence of bias. For misspecified models, ML was again inflated with increasing nonnormality, but both SB and ADF were underestimated with increasing nonnormality. It appears that the power of the SB and ADF test statistics to detect a model misspecification is attenuated given nonnormally distributed data. Confirmatory factor analysis (CFA) has become an increasingly popular method of investigating the structure of data sets in psychology. In contrast to traditional exploratory factor analysis that does not place strong a priori restrictions on the structure of the model being tested, CFA requires the investigator to specify both the number of factors

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Authors: Curran, P. J., West, S. G., & Finch, J. F.
Affiliations: University of California, Los Angeles (US)
Arizona State University (US)
Texas A&M University (US)
ORCID: Curran, Patrick J.
Venue: Psychological Methods
Publisher: American Psychological Association (APA)
Published: 1996-03
Volume: 1
Issue: 1
Pages: 16-29
ISSN: 1082-989X (ISSN-L)
1939-1463
DOI: 10.1037/1082-989x.1.1.16
OpenAlex: W1968524945
Cited by: 5,512
References: 1
Citations by year: 2026: 432 · 2025: 392 · 2024: 410 · 2023: 404 · 2022: 383 · 2021: 361 · 2020: 333 · 2019: 270 · 2018: 295 · 2017: 273 · 2016: 237 · 2015: 242 · 2014: 251 · 2013: 218 · 2012: 179
FWCI: 33.50
Type: journal article
Language: en
Open access: closed
Locations: Psychological Methods (publishedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords: confirmatory factor analysis, chi-square statistic, non-normality, model misspecification, robustness, sample size

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The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis.

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