Structured Factor Analysis: A Data Matrix-Based Alternative Approach to Structural Equation Modeling

References

• Adachi, K., & Trendafilov, N. T. (2018). Some mathematical properties of the matrix decomposition solution in factor analysis. Psychometrika, 83, 407–424. https://doi.org/10.1007/s11336-017-9600-y.
   PubMed Web of Science ®Google Scholar
• Anderson, T. W., & Rubin, H. (1956). Statistical inference in factor analysis. In J. Neyman (Ed.), Proceedings of the third Berkeley symposium on mathematical statistics and probability (5th ed., pp. 111–150). University of California Press.
   Google Scholar
• Bartholomew, D. J. (1981). Posterior analysis of the factor model. British Journal of Mathematical and Statistical Psychology, 34, 93–99. https://doi.org/10.1111/j.2044-8317.1981.tb00620.x
   Web of Science ®Google Scholar
• Bartlett, M. S. (1937). The statistical conception of mental factors. British Journal of Psychology, 28, 97–104. [Mismatch
   Google Scholar
• Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238–246. https://doi.org/10.1037/0033-2909.107.2.238.
   PubMed Web of Science ®Google Scholar
• Bentler, P. M. (1995). EQS structural equations program manual (Vol. 6). Multivariate Software.
   Google Scholar
• Bentler, P. M., & Chou, C.-P. (1987). Practical issues in structural modeling. Sociological Methods & Research, 16, 78–117. https://doi.org/10.1177/0049124187016001004
   Web of Science ®Google Scholar
• Bentler, P. M., & Speckart, G. (1979). Models of attitude–behavior relations. Psychological Review, 86, 452–464. https://doi.org/10.1037/0033-295X.86.5.452
   Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. Wiley.
   Google Scholar
• Bollen, K. A. (1996). An alternative two stage least squares (2SLS) estimator for latent variable equations. Psychometrika, 61, 109–121. https://doi.org/10.1007/BF02296961
   Web of Science ®Google Scholar
• Bollen, K. A. (2019). Model implied instrumental variables (MIIVs): An alternative orientation to structural equation modeling. Multivariate Behavioral Research, 54, 31–46. https://doi.org/10.1080/00273171.2018.1483224.
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., & Stine, R. (1993). Testing structural equation models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models. Sage Publications.
   Google Scholar
• Cassel, C., Hackl, P., & Westlund, A. H. (1999). Robustness of partial least-squares method for estimating latent variable quality structures. Journal of Applied Statistics, 26, 435–446. https://doi.org/10.1080/02664769922322
   Web of Science ®Google Scholar
• Chen, F., Bollen, K. A., Paxton, P. M., Curran, P. J., & Kirby, J. B. (2001). Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological Methods & Research, 29, 468–508. https://doi.org/10.1177/0049124101029004003
   Web of Science ®Google Scholar
• Cho, G., Sarstedt, M., & Hwang, H. (2022). A comparative evaluation of factor- and component-based structural equation modeling methods under (in)consistent model specifications. British Journal of Mathematical and Statistical Psychology, 75, 220–251. https://doi.org/10.1111/bmsp.12255
   PubMed Web of Science ®Google Scholar
• Croon, M. (2002). Using predicted latent scores in general latent structure models. In G. A. Marcoulides & I. Moustaki (Eds.), Latent variable and latent structure models (pp. 195–223). Erlbaum.
   Google Scholar
• De Jonckere, J., & Rosseel, Y. (2022). Using bounded estimation to avoid nonconvergence in small sample structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 29(3), 412–417. https://doi.org/10.1080/10705511.2021.1982716
   Web of Science ®Google Scholar
• de Leeuw, J. (2004). Least squares optimal scaling of partially observed linear systems (pp. 121–134). Springer. https://doi.org/10.1007/978-1-4020-1958-6_7
   Google Scholar
• de Leeuw, J. (2017). Factor analysis as matrix decomposition and approximation: Theory. http://deleeuwpdx.net/pubfolders/factor/factor.pdf
   Google Scholar
• de Leeuw, J., Young, F. W., & Takane, Y. (1976). Additive structure in qualitative data: An alternating least squares method with optimal scaling features. Psychometrika, 41, 471–503. https://doi.org/10.1007/BF02296971
   Web of Science ®Google Scholar
• Devlieger, I., & Rosseel, Y. (2017). Factor score path analysis: an alternative for SEM? Methodology, 13, 31–38. https://doi.org/10.1027/1614-2241/a000130
   Web of Science ®Google Scholar
• Dijkstra, T. K. (2011). Consistent Partial Least Squares Estimators for Linear and Polynomial Factor Models. https://doi.org/10.13140/RG.2.1.3997.0405
   Google Scholar
• Dijkstra, T. K. (2013). The Simplest Possible Factor Model Estimator. https://doi.org/10.13140/RG.2.1.3605.6809
   Google Scholar
• Dijkstra, T. K. (2017). A perfect match between a model and a mode. In H. Latan & R. Noonan (Eds.), Partial least squares path modeling: Basic concepts, methodological issues and applications (pp. 55–80). Springer. https://doi.org/10.1007/978-3-319-64069-3_4
   Google Scholar
• Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7, 1–26. https://doi.org/10.1214/aos/1176344552
   Web of Science ®Google Scholar
• Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Siam. https://doi.org/10.1137/1.9781611970319
   Google Scholar
• Fomby, T. B., Johnson, S. R., & Hill, R. C. (2012). Advanced econometric methods. Springer. https://doi.org/10.1007/978-1-4419-8746-4
   Google Scholar
• Fornell, C., Johnson, M. D., Anderson, E. W., Cha, J., & Bryant, B. E. (1996). The American customer satisfaction index: Nature, purpose, and findings. Journal of Marketing, 60, 7–18. https://doi.org/10.2307/1251898
   Web of Science ®Google Scholar
• Gu, F., Yung, Y.-F., & Cheung, M. W.-L. (2019). Four covariance structure models for canonical correlation analysis: A COSAN modeling approach. Multivariate Behavioral Research, 54, 192–223. https://doi.org/10.1080/00273171.2018.1512847
   PubMed Web of Science ®Google Scholar
• Hwang, H., Cho, G., Jung, K., Falk, C. F., Flake, J. K., Jin, M. J., & Lee, S. H. (2021). An approach to structural equation modeling with both factors and components: Integrated generalized structured component analysis. Psychological Methods, 26, 273–294. https://doi.org/10.1037/met0000336.
   PubMed Web of Science ®Google Scholar
• Hwang, H., Malhotra, N. K., Kim, Y., Tomiuk, M. A., & Hong, S. (2010). A comparative study on parameter recovery of three approaches to structural equation modeling. Journal of Marketing Research, 47, 699–712. https://doi.org/10.2139/ssrn.1585305
   Web of Science ®Google Scholar
• Hwang, H., Takane, Y., & Jung, K. (2017). Generalized structured component analysis with uniqueness terms for accommodating measurement error. Frontiers in Psychology, 8, 2137. https://doi.org/10.3389/fpsyg.2017.02137
   PubMed Web of Science ®Google Scholar
• Jöreskog, K. G. (1978). Structural analysis of covariance and correlation matrices. Psychometrika, 43, 443–477. https://doi.org/10.1007/BF02293808
   Web of Science ®Google Scholar
• Jöreskog, K. G., & Sorbom, D. (1986). PRELIS: A program for multivariate data screening and data summarization. Scientific Software.
   Google Scholar
• Lance, C. E., Cornwell, J. M., & Mulaik, S. A. (1988). Limited information parameter estimates for latent or mixed manifest and latent variable models. Multivariate Behavioral Research, 23, 171–187. https://doi.org/10.1207/s15327906mbr2302_3.
   PubMed Web of Science ®Google Scholar
• Leong, F. T. L., & Huang, J. L. (2016). Standard error of measurement. Britannica. https://www.britannica.com/science/standard-error-of-measurement
   Google Scholar
• Lu, I. R. R., Kwan, E., Thomas, D. R., & Cedzynski, M. (2011). Two new methods for estimating structural equation models: An illustration and a comparison with two established methods. International Journal of Research in Marketing, 28, 258–268. https://doi.org/10.1016/j.ijresmar.2011.03.006
   Web of Science ®Google Scholar
• Marsh, H. W., Wen, Z., Hau, K.-T., & Nagengast, B. (2013). Structural equation models of latent interaction and quadratic effects. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course, 2nd ed. (pp. 267–308). IAP Information Age Publishing.
   Google Scholar
• Mattson, S. (1997). How to generate non-normal data for simulation of structural equation models. Multivariate Behavioral Research, 32, 355–373. https://doi.org/10.1207/s15327906mbr3204_3
   PubMed Web of Science ®Google Scholar
• Maydeu-Olivares, A., & Coffman, D. L. (2006). Random intercept item factor analysis. Psychological Methods, 11, 344–362. https://doi.org/10.1037/1082-989X.11.4.344
   PubMed Web of Science ®Google Scholar
• McDonald, R. P. (2004). Respecifying improper structures. Structural Equation Modeling: A Multidisciplinary Journal, 11, 194–209. https://doi.org/10.1207/s15328007sem1102_3
   Web of Science ®Google Scholar
• Mulaik, S. A. (2009). Foundations of factor analysis (2nd ed.). Chapman and Hall/CRC Press. https://doi.org/10.1201/b15851
   Google Scholar
• Newsom, J. T. (2014). Improper solutions in SEM. https://web.pdx.edu/∼newsomj/semclass/ho_improper.pdf
   Google Scholar
• Oldenburg, G. (2020). Structural equation modeling. The Mathematica Journal, 22, 1–17. https://doi.org/10.3888/tmj.22-5
   Google Scholar
• Podsakoff, P. M., MacKenzie, S. B., Lee, J.-Y., & Podsakoff, N. P. (2003). Common method biases in behavioral research: A critical review of the literature and recommended remedies. The Journal of Applied Psychology, 88, 879–903. https://doi.org/10.1037/0021-9010.88.5.879.
   PubMed Web of Science ®Google Scholar
• Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36. https://doi.org/10.18637/jss.v048.i02
   Web of Science ®Google Scholar
• Rosseel, Y., & Loh, W. W. (2022). The Structural-After-Measurement (SAM) approach to SEM. Manuscript under review. Retrieved from https://osf.io/w9bmf
   Google Scholar
• Skrondal, A., & Laake, P. (2001). Regression among factor scores. Psychometrika, 66, 563–575. https://doi.org/10.1007/BF02296196
   Web of Science ®Google Scholar
• Sočan, G. (2003). The incremental value of minimum rank factor analysis. University of Groningen.
   Google Scholar
• Sörbom, D. (1989). Model modification. Psychometrika, 54, 371–384. https://doi.org/10.1007/BF02294623
   Web of Science ®Google Scholar
• Steiger, J. H. (1979). Factor indeterminacy in the 1930’s and the 1970’s some interesting parallels. Psychometrika, 44, 157–167. https://doi.org/10.1007/BF02293967
   Web of Science ®Google Scholar
• Steiger, J. H. (2016). Notes on the Steiger–Lind (1980) handout. Structural Equation Modeling: A Multidisciplinary Journal, 23, 777–781. https://doi.org/10.1080/10705511.2016.1217487
   Web of Science ®Google Scholar
• Thurstone, L. L. (1934). The vectors of mind. Psychological Review, 41, 1–32. https://doi.org/10.1037/h0075959
   Google Scholar
• Unkel, S., & Trendafilov, N. T. (2010). Simultaneous parameter estimation in exploratory factor analysis: An expository review. International Statistical Review, 78, 363–382. https://doi.org/10.1111/j.1751-5823.2010.00120.x
   Web of Science ®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, 76, 913–934. https://doi.org/10.1177/0013164413495237.
   PubMed Web of Science ®Google Scholar
• Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data (2nd ed.). The MIT Press.
   Google Scholar