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A Model Implied Instrumental Variable Approach to Exploratory Factor Analysis (MIIV-EFA)

Author

Listed:
  • Kenneth A. Bollen

    (University of North Carolina at Chapel Hill
    University of North Carolina)

  • Kathleen M. Gates

    (University of North Carolina at Chapel Hill)

  • Lan Luo

    (University of North Carolina at Chapel Hill)

Abstract

Spearman (Am J Psychol 15(1):201–293, 1904. https://doi.org/10.2307/1412107 ) marks the birth of factor analysis. Many articles and books have extended his landmark paper in permitting multiple factors and determining the number of factors, developing ideas about simple structure and factor rotation, and distinguishing between confirmatory and exploratory factor analysis (CFA and EFA). We propose a new model implied instrumental variable (MIIV) approach to EFA that allows intercepts for the measurement equations, correlated common factors, correlated errors, standard errors of factor loadings and measurement intercepts, overidentification tests of equations, and a procedure for determining the number of factors. We also permit simpler structures by removing nonsignificant loadings. Simulations of factor analysis models with and without cross-loadings demonstrate the impressive performance of the MIIV-EFA procedure in recovering the correct number of factors and in recovering the primary and secondary loadings. For example, in nearly all replications MIIV-EFA finds the correct number of factors when N is 100 or more. Even the primary and secondary loadings of the most complex models were recovered when the sample sizes were at least 500. We discuss limitations and future research areas. Two appendices describe alternative MIIV-EFA algorithms and the sensitivity of the algorithm to cross-loadings.

Suggested Citation

  • Kenneth A. Bollen & Kathleen M. Gates & Lan Luo, 2024. "A Model Implied Instrumental Variable Approach to Exploratory Factor Analysis (MIIV-EFA)," Psychometrika, Springer;The Psychometric Society, vol. 89(2), pages 687-716, June.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:2:d:10.1007_s11336-024-09949-6
    DOI: 10.1007/s11336-024-09949-6
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    References listed on IDEAS

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    1. Zachary F. Fisher & Kenneth A. Bollen, 2020. "An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 660-683, September.
    2. Joshua D. Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 69-85, Fall.
    3. Kenneth Bollen, 1996. "An alternative two stage least squares (2SLS) estimator for latent variable equations," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 109-121, March.
    4. Christopher J. Urban & Daniel J. Bauer, 2021. "A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 1-29, March.
    5. Albert Madansky, 1964. "Instrumental variables in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 105-113, June.
    6. Masamori Ihara & Yutaka Kano, 1986. "A new estimator of the uniqueness in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 563-566, December.
    7. Thomas Mroz & Kenneth Bollen & Ilene Speizer & Dominic Mancini, 1999. "Quality, accessibility, and contraceptive use in rural tanzania," Demography, Springer;Population Association of America (PAA), vol. 36(1), pages 23-40, February.
    8. Robert Jennrich, 1987. "Tableau algorithms for factor analysis by instrumental variable methods," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 469-476, September.
    9. Shaobo Jin & Fan Yang-Wallentin & Kenneth A. Bollen, 2021. "A unified model-implied instrumental variable approach for structural equation modeling with mixed variables," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 564-594, June.
    10. Joshua Angrist & Alan Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Working Papers 834, Princeton University, Department of Economics, Industrial Relations Section..
    11. Kenneth Bollen & Albert Maydeu-Olivares, 2007. "A Polychoric Instrumental Variable (PIV) Estimator for Structural Equation Models with Categorical Variables," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 309-326, September.
    12. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    13. Yutaka Kano, 1990. "Noniterative estimation and the choice of the number of factors in exploratory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 277-291, June.
    14. Kenneth Bollen & Stanislav Kolenikov & Shawn Bauldry, 2014. "Model-Implied Instrumental Variable—Generalized Method of Moments (MIIV-GMM) Estimators for Latent Variable Models," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 20-50, January.
    15. Allison J. Sovey & Donald P. Green, 2011. "Instrumental Variables Estimation in Political Science: A Readers’ Guide," American Journal of Political Science, John Wiley & Sons, vol. 55(1), pages 188-200, January.
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