Reconsidering the Conditions for Conducting Confirmatory Factor Analysis

  1. Daniel Ondé 1
  2. Jesús M. Alvarado 1
  1. 1 Universidad Complutense (Spain)
Revista:
The Spanish Journal of Psychology

ISSN: 1138-7416

Año de publicación: 2020

Número: 23

Páginas: 1-15

Tipo: Artículo

DOI: 10.1017/SJP.2020.56 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: The Spanish Journal of Psychology

Resumen

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.

Referencias bibliográficas

  • Bollen, K. A. (1989). Structural equations with latent variables. John Wiley & Sons. http://doi.org/10.1002/9781118619179
  • Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford Publications.
  • Cattell, R. B. (Ed.). (1978). The scientific use of factor analysis in behavioral and life sciences. Plenum Press. http://doi.org/10.1007/978-1-4684-2262-7
  • 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.1.1.16
  • 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/10.1080/00273170902794206
  • 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_5
  • 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.4.3.272
  • 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/a0015808
  • 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.
  • 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/10.1080/10705510903203573
  • 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_5
  • 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/a0024917
  • 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/a0014694
  • Jöreskog, K. G., & Sörbom, D. (1989). LISREL 7: A guide to the program and applications. Scientific Software International.
  • Jöreskog, K. G., & Sörbom, D. (1993). LISREL 8: Structural equation modeling with the SIMPLIS command language. Scientific Software International.
  • Jöreskog, K. G., & Sörbom, D. (1996). PRELIS 2: User’s reference guide. Scientific Software International.
  • Kline, R. B. (2015). Principles and practice of structural equation modeling. Guilford Publications.
  • 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.4.2.192
  • 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.30.3.199361
  • 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.51.1.201
  • 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.1.2.130
  • 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.4.1.84
  • 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_1
  • McDonald, R. P. (1985). Factor analysis and related methods. Psychology Press.
  • 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.7.1.64
  • 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.50.9.741
  • Mulaik, S. A. (2009). Linear causal modeling with structural equations. CRC Press. http://doi.org/10.1201/9781439800393
  • 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_8
  • 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.2018.00751
  • 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/
  • Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36.
  • 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.2005.05.001
  • Stevens, J. (2009). Applied multivariate statistics for the social sciences. Erlbaum.
  • 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/10.1177/0013164413495237
  • 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_5
Fuente de los datos: Dialnet