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Reconsidering the Conditions for Conducting Confirmatory Factor Analysis

Published online by Cambridge University Press:  04 December 2020

Daniel Ondé Open the ORCID record for Daniel Ondé [Opens in a new window]  and
Jesús M. Alvarado Open the ORCID record for Jesús M. Alvarado [Opens in a new window]
Daniel Ondé*
Affiliation:
Universidad Complutense (Spain)
Jesús M. Alvarado
Affiliation:
Universidad Complutense (Spain)
*
Correspondence concerning this article should be addressed to Daniel Ondé Pérez. Universidad Complutense. Facultad de Psicología. Departamento de Psicobiología y Metodología en Ciencias del Comportamiento. 28040 Madrid (Spain). E-mail: [email protected]
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Abstract

There is a series of conventions governing how Confirmatory Factor Analysis gets applied, from minimum sample size to the number of items representing each factor, to estimation of factor loadings so they may be interpreted. In their implementation, these rules sometimes lead to unjustified decisions, because they sideline important questions about a model’s practical significance and validity. Conducting a Monte Carlo simulation study, the present research shows the compensatory effects of sample size, number of items, and strength of factor loadings on the stability of parameter estimation when Confirmatory Factor Analysis is conducted. The results point to various scenarios in which bad decisions are easy to make and not detectable through goodness of fit evaluation. In light of the findings, these authors alert researchers to the possible consequences of arbitrary rule following while validating factor models. Before applying the rules, we recommend that the applied researcher conduct their own simulation studies, to determine what conditions would guarantee a stable solution for the particular factor model in question.

Keywords

Confirmatory Factor AnalysisMonte Carlo studypractical significancevalidity
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 23 , 2020 , e55
Copyright
© Universidad Complutense de Madrid and Colegio Oficial de Psicólogos de Madrid 2020

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Footnotes

Conflicts of Interest: None

Funding Statement: This research received no specific grant from any funding agency, commercial or not-for-profit sectors

References

Bollen, K. A. (1989). Structural equations with latent variables. John Wiley & Sons. http://doi.org/10.1002/9781118619179CrossRefGoogle Scholar
Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford Publications.Google Scholar
Cattell, R. B. (Ed.). (1978). The scientific use of factor analysis in behavioral and life sciences. Plenum Press. http://doi.org/10.1007/978-1-4684-2262-7CrossRefGoogle Scholar
Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1(1), 16–29. https://doi.org/10.1037/1082-989X.1.1.16CrossRefGoogle Scholar
de Winter, J. C. F., Dodou, D., & Wieringa, P. A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44(2), 147–181. https://doi.org/10.1080/00273170902794206CrossRefGoogle ScholarPubMed
Enders, C., & Bandalos, D. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 8(3), 430–457. https://doi.org/10.1207/S15328007SEM0803_5CrossRefGoogle Scholar
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299. https://doi.org/10.1037/1082-989X.4.3.272CrossRefGoogle Scholar
Ferguson, C. J. (2009). An effect size primer: A guide for clinicians and researchers. Professional Psychology: Research and Practice, 40(5), 532–538. https://doi.org/10.1037/a0015808CrossRefGoogle Scholar
Ferrando, P. J., & Anguiano-Carrasco, C. (2010). El análisis factorial como técnica de investigación en psicología [Factor analysis as a technique in psychological research]. Papeles del Psicólogo, 31(1), 18–33.Google Scholar
Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling: A Multidisciplinary Journal, 16(4), 625–641. https://doi.org/10.1080/10705510903203573CrossRefGoogle Scholar
Gagné, P., & Hancock, G. R. (2006). Measurement model quality, sample size, and solution propriety in confirmatory factor models. Multivariate Behavioral Research, 41(1), 65–83. https://doi.org/10.1207/s15327906mbr4101_5CrossRefGoogle ScholarPubMed
Heene, M., Hilbert, S., Draxler, C., Ziegler, M., & Bühner, M. (2011). Masking misfit in confirmatory factor analysis by increasing unique variances: A cautionary note on the usefulness of cutoff values of fit indices. Psychological Methods, 16(3), 319–336. https://doi.org/10.1037/a0024917CrossRefGoogle ScholarPubMed
Jackson, D. L., Gillaspy, J. A., & Purc-Stephenson, R. (2009). Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychological Methods, 14(1), 6–23. https://doi.org/10.1037/a0014694CrossRefGoogle ScholarPubMed
Jöreskog, K. G., & Sörbom, D. (1989). LISREL 7: A guide to the program and applications. Scientific Software International.Google Scholar
Jöreskog, K. G., & Sörbom, D. (1993). LISREL 8: Structural equation modeling with the SIMPLIS command language. Scientific Software International.Google Scholar
Jöreskog, K. G., & Sörbom, D. (1996). PRELIS 2: User’s reference guide. Scientific Software International.Google Scholar
Kline, R. B. (2015). Principles and practice of structural equation modeling. Guilford Publications.Google Scholar
Little, T. D., Lindenberger, U., & Nesselroade, J. R. (1999). On selecting indicators for multivariate measurement and modeling with latent variables: When “good” indicators are bad and “bad” indicators are good. Psychological Methods, 4(2), 192–211. https://doi.org/10.1037/1082-989X.4.2.192CrossRefGoogle Scholar
Lloret-Segura, S., Ferreres-Traver, A., Hernández-Baeza, A., & Tomás-Marco, I. (2014). El análisis factorial exploratorio de los ítems: Una guía práctica, revisada y actualizada [Exploratory item factor analysis: A practical guide revised and updated]. Anales de Psicología/Annals of Psychology, 30(3), 1151–1169. https://doi.org/10.6018/analesps.30.3.199361Google Scholar
MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual Review of Psychology, 51(1), 201–226. https://doi.org/10.1146/annurev.psych.51.1.201CrossRefGoogle ScholarPubMed
MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130–149. https://doi.org/10.1037/1082-989X.1.2.130CrossRefGoogle Scholar
MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4(1), 84–99. https://doi.org/10.1037/1082-989X.4.1.84CrossRefGoogle Scholar
Marsh, H. W., Hau, K.-T., Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33(2), 181–220. https://doi.org/10.1207/s15327906mbr3302_1CrossRefGoogle ScholarPubMed
McDonald, R. P. (1985). Factor analysis and related methods. Psychology Press.Google Scholar
McDonald, R. P., & Ho, M.-H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7(1), 64–82. http://doi.org/10.1037//1082-989X.7.1.64CrossRefGoogle ScholarPubMed
Messick, S. (1995). Validity of psychological assessment: Validation of inferences from persons’ responses and performances as scientific inquiry into score meaning. American Psychologist, 50(9), 741–749. https://doi.org/10.1037/0003-066X.50.9.741CrossRefGoogle Scholar
Mulaik, S. A. (2009). Linear causal modeling with structural equations. CRC Press. http://doi.org/10.1201/9781439800393CrossRefGoogle Scholar
Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling: A Multidisciplinary Journal, 9(4), 599–620. https://doi.org/10.1207/S15328007SEM0904_8CrossRefGoogle Scholar
Ondé, D., & Alvarado, J. M. (2018). Scale validation conducting confirmatory factor analysis: A Monte Carlo simulation study with LISREL. Frontiers in Psychology, 9, Article e751. https://doi.org/10.3389/fpsyg.2018.00751CrossRefGoogle ScholarPubMed
R Development Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing [Computer software]. http://www.R-project.org/Google Scholar
Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36.CrossRefGoogle Scholar
Shah, R., & Goldstein, S. M. (2006). Use of structural equation modeling in operations management research: Looking back and forward. Journal of Operations Management, 24(2), 148–169. https://doi.org/10.1016/j.jom.2005.05.001CrossRefGoogle Scholar
Stevens, J. (2009). Applied multivariate statistics for the social sciences. Erlbaum.Google Scholar
Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for structural equation models: An evaluation of power, bias, and solution propriety. Educational and Psychological Measurement, 73(6), 913–934. https://doi.org/10.1177/0013164413495237CrossRefGoogle Scholar
Ximénez, C. (2006). A Monte Carlo study of recovery of weak factor loadings in confirmatory factor analysis. Structural Equation Modeling: A Multidisciplinary Journal, 13(4), 587–614. https://doi.org/10.1207/s15328007sem1304_5CrossRefGoogle Scholar