Advertisement

Confirmatory Factor Analysis and Structural Equation Modeling

  • Aek Phakiti

Abstract

This chapter explains the core principles of confirmatory factor analysis (CFA) and structural equation modeling (SEM) that can be used in applied linguistics research. CFA and SEM are multivariate statistical techniques researchers use to test a hypothesis or theory. This chapter provides essential guidelines for not only how to read CFA and SEM reports but also how to perform CFA. CFA differs from exploratory factor analysis in many ways (e.g., statistical assumptions and procedures, assessment of model fit and methods for extracting factors). Researchers employ SEM to evaluate or test among observed variables and latent variables. In this chapter, EQS Program is used to illustrate how to perform CFA.

Keywords

Advanced statistics Confirmatory factor analysis (CFA) Structural equation modeling (SEM) EQS 

References

  1. Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52(3), 317–332.CrossRefGoogle Scholar
  2. Bentler, P. M. (1985–2018). EQS Version 6 for Windows [Computer software]. Encino, CA: Multivariate Software.Google Scholar
  3. Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238–246.CrossRefGoogle Scholar
  4. Bentler, P. M. (2006). EQS structural equation program manual. Encino, CA: Multivariate Software.Google Scholar
  5. Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness-of-fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606.CrossRefGoogle Scholar
  6. Bentler, P. M., & Wu, E. J. C. (2006). EQS for Windows user’s guide. Encino, CA: Multivariate Software.Google Scholar
  7. Bohrnstedt, G. W., & Carter, T. M. (1971). Robustness in regression analysis. In H. L. Costner (Ed.), Sociological methodology (pp. 118–146). San Fransisco: Jossey-Bass.Google Scholar
  8. Bozdogan, H. (1987). Model selection and Akaike’s information criteria (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345–370.CrossRefGoogle Scholar
  9. Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). New York and London: Guilford Press.Google Scholar
  10. Byrne, B. M. (2006). Structural equation modeling with EQS and EQS/Windows: Basic concepts, applications, and programming. New York and London: Psychology Press.Google Scholar
  11. Cliff, N. (1983). Some cautions concerning the application of causal modeling methods. Multivariate Behavioral Research, 18(1), 115–126.CrossRefGoogle Scholar
  12. Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159.CrossRefGoogle Scholar
  13. Grant, R., MacDonald, R., Phakiti, A., & Cook, H. (2014). The importance of writing in mathematics: Quantitative analysis of U.S. English learners’ academic language proficiency and mathematics achievement. In E. Stracke (Ed.), Intersections: Applied linguistics as a meeting place (pp. 208–232). Newcastle upon Tyne). London: Cambridge Scholars Publishing.Google Scholar
  14. Hancock, G. R., & Schoonen, R. (2015). Structural equation modelling: Possibilities for language learning researchers. Language Learning, 65(S1), 160–184.CrossRefGoogle Scholar
  15. In’nami, Y., & Koizumi, R. (2010). Can structural equation models in second language testing and learning research be successfully replicated? International Journal of Testing, 10, 262–273.CrossRefGoogle Scholar
  16. Jöreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika, 57, 239–257.Google Scholar
  17. Kaplan, D. (1995). Statistical power in structural equation modeling. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 100–117). Thousand Oaks: SAGE.Google Scholar
  18. Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). New York and London: The Guilford Press.Google Scholar
  19. Ockey, G. J. (2014). Exploratory factor analysis and structural equation modeling. In A. J. Kunnan (Ed.), The Companion to language assessment (pp. 1224–1444). Oxford: John Wiley & Sons.Google Scholar
  20. Ockey, G. J., & Choi, I. (2015). Structural equation modeling reporting practices for language assessment. Language Assessment Quarterly, 12(3), 305–319.CrossRefGoogle Scholar
  21. Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge: Cambridge University Press.Google Scholar
  22. Pedhazur, E. J., & Schmelkin, L. P. (1992). Measurement, design, and analysis: An integrated approach. Hillsdale, NJ: Holt, Rinehart and Winston.Google Scholar
  23. Phakiti, A. (2008). Strategic competence as a fourth-order factor model: A structural equation modeling approach. Language Assessment Quarterly, 5(1), 20–42.CrossRefGoogle Scholar
  24. Plonsky, L. (2013). Study quality in SLA: An assessment of designs, analyses, and reporting practices in quantitative L2 research. Studies in Second Language Acquisition, 35(4), 655–687.CrossRefGoogle Scholar
  25. Plonsky, L., & Oswald, F. L. (2014). How big is ‘big’? Interpreting effect sizes in L2 research. Language Learning, 64(4), 878–912.CrossRefGoogle Scholar
  26. Rubenfeld, S., & Clément, R. (2012). Intercultural conflict and mediation: An intergroup perspective. Language Learning, 62(4), 1205–1230.CrossRefGoogle Scholar
  27. Schoonen, R. (2015). Structural equation modelling in L2 research. In L. Plonsky (Ed.), Advancing quantitative methods in second language research (pp. 213–242). New York: Routledge.CrossRefGoogle Scholar
  28. Schumacker, R. E., & Lomax, R. G. (2016). A beginner’s guide to structural equation modeling (4th ed.). New York and London: Routledge.Google Scholar
  29. Thompson, B. (2000). Ten commandments of structural equation modeling. In L. G. Grimm & P. R. Yarnold (Eds.), Reading and understanding more multivariate statistics (pp. 261–283). Washington: American Psychological Association.Google Scholar
  30. Ullman, J. B. (1996). Structural equation modeling. In B. G. Tabachnick & L. S. Fidell (Eds.), Using multivariate statistics (3rd ed., pp. 709–811). New York: Harper Collins College Publishers.Google Scholar
  31. Vandergrift, L., & Baker, S. (2015). Learner variables in second language listening comprehension: An exploratory path analysis. Language Learning, 65(2), 390–416.CrossRefGoogle Scholar
  32. Weston, R., & Gore, P. A. (2006). A brief guide to structural equation modeling. The Counselling Psychologist, 34(5), 719–751.CrossRefGoogle Scholar
  33. Wheaton, B., Muthen, B., Alwin, D. F., & Summers, G. (1977). Assessing reliability and stability in panel models. Sociological Methodology, 8, 84–136.CrossRefGoogle Scholar
  34. Winke, P. (2014). Testing hypotheses about language learning using structural equation modeling. Annual Review of Applied Linguistics, 34, 102–122.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Sydney School of Education and Social WorkThe University of SydneySydneyAustralia

Personalised recommendations