An Evaluation of Non-Iterative Estimators in the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM)

References

• Albert, A. A. (1944). The minimum rank of a correlation matrix. Proceedings of the National Academy of Sciences of the United States of America, 30, 144–146. https://doi.org/10.1073/pnas.30.6.144
   PubMedGoogle Scholar
• Anderson, T. W. (1984). An introduction to multivariate statistical analysis.
   Google Scholar
• Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49, 155–173. https://doi.org/10.1007/BF02294170
   Web of Science ®Google Scholar
• Arbuckle, J. (1997). Amos users’ guide. version 3.6.
   Google Scholar
• Bakk, Z., & Kuha, J. (2018). Two-step estimation of models between latent classes and external variables. Psychometrika, 83, 871–892. https://doi.org/10.1007/s11336-017-9592-7
   PubMed Web of Science ®Google Scholar
• Bartlett, M. S. (1937). The statistical conception of mental factors. British Journal of Psychology. General Section, 28, 97–104. https://doi.org/10.1111/j.2044-8295.1937.tb00863.x
   Google Scholar
• Bartlett, M. S. (1938). Methods of estimating mental factors. Nature, 141, 609–610.
   Google Scholar
• Bentler, P. M. (1982). Confirmatory factor analysis via noniterative estimation: A fast, inexpensive method. Journal of Marketing Research, 19, 417–424. https://doi.org/10.1177/002224378201900403
   Web of Science ®Google Scholar
• Bentler, P. M. (1985). Theory and implementation of eqs: A structural equations program. BMDP Statistical Software.
   Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. John Wiley & Sons.
   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., Gates, K. M., & Fisher, Z. (2018). Robustness conditions for miiv-2sls when the latent variable or measurement model is structurally misspecified. Structural Equation Modeling : a Multidisciplinary Journal, 25, 848–859. https://doi.org/10.1080/10705511.2018.1456341
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., Kirby, J. B., Curran, P. J., Paxton, P. M., & Chen, F. (2007). Latent variable models under misspecification: Two-stage least squares (2sls) and maximum likelihood (ml) estimators. Sociological Methods & Research, 36, 48–86. https://doi.org/10.1177/0049124107301947
   Web of Science ®Google Scholar
• Boomsma, A. (1985). Nonconvergence, improper solutions, and starting values in lisrel maximum likelihood estimation. Psychometrika, 50, 229–242. https://doi.org/10.1007/BF02294248
   Web of Science ®Google Scholar
• Burghgraeve, E. (2021). Alternative estimation procedures for structural equation models. [Unpublished doctoral dissertation]. Ghent University.
   Google Scholar
• Burghgraeve, E., De Neve, J., & Rosseel, Y. (2021). Estimating structural equation models using james–stein type shrinkage estimators. Psychometrika, 86, 96–130. https://doi.org/10.1007/s11336-021-09749-2
   PubMed Web of Science ®Google Scholar
• Burt, R. S. (1973). Confirmatory factor-analytic structures and the theory construction process. Sociological Methods & Research, 2, 131–190. https://doi.org/10.1177/004912417300200201
   Web of Science ®Google Scholar
• Burt, R. S. (1976). Interpretational confounding of unobserved variables in structural equation models. Sociological Methods & Research, 5, 3–52. https://doi.org/10.1177/004912417600500101
   Web of Science ®Google Scholar
• Costa, P., & McCrae, R. R. (2008). The revised neo personality inventory (neo-pi-r). Sage Publications, Inc.
   Google Scholar
• Croon, M. (2002). Using predicted latent scores in general latent structure models. In G. Marcoulides & I. Moustaki (Eds.), Latent variable and latent structure models (pp. 195–224). Lawrence Erlbaum.
   Google Scholar
• Cudeck, R. (1991). Noniterative factor analysis estimators, with algorithms for subset and instrumental variable selection. Journal of Educational Statistics, 16, 35–52. https://doi.org/10.3102/10769986016001035
   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, 412–427. https://doi.org/10.1080/10705511.2021.1982716
   Web of Science ®Google Scholar
• Devlieger, I., Talloen, W., & Rosseel, Y. (2019). New developments in factor score regression: Fit indices and a model comparison test. Educational and Psychological Measurement, 79, 1017–1037. https://doi.org/10.1177/0013164419844552
   PubMed Web of Science ®Google Scholar
• Dhaene, S., & Rosseel, Y. (2023). An evaluation of non-iterative estimators in confirmatory factor analysis. Structural Equation Modeling: A Multidisciplinary Journal. Advance online publication. https://doi.org/10.1080/10705511.2023.2187285
   Web of Science ®Google Scholar
• Dolan, C. V., Oort, F. J., Stoel, R. D., & Wicherts, J. M. (2009). Testing measurement invariance in the target rotated multigroup exploratory factor model. Structural Equation Modeling: A Multidisciplinary Journal, 16, 295–314. https://doi.org/10.1080/10705510902751416
   Web of Science ®Google Scholar
• Epskamp, S., Cramer, A. O., Waldorp, L. J., Schmittmann, V. D., & Borsboom, D. (2012). qgraph: Network visualizations of relationships in psychometric data. Journal of Statistical Software, 48, 1–18. https://doi.org/10.18637/jss.v048.i04
   Web of Science ®Google Scholar
• Fisher, Z., Bollen, K., Gates, K., Rönkkö, M. (2021). Miivsem: Model implied instrumental variable (miiv) estimation of structural equation models. [Computer software manual]. (R package version 0.5.8). https://CRAN.R-project.org/package=MIIVsem
   Google Scholar
• Grønneberg, S., Foldnes, N., & Marcoulides, K. M. (2022). covsim: An r package for simulating non-normal data for structural equation models using copulas. Journal of Statistical Software, 102, 1–45. https://doi.org/10.18637/jss.v102.i03
   Web of Science ®Google Scholar
• Guttman, L. (1944). General theory and methods for matric factoring. Psychometrika, 9, 1–16. https://doi.org/10.1007/BF02288709
   Google Scholar
• Guttman, L. (1952). Multiple group methods for common-factor analysis: Their basis, computation, and interpretation. Psychometrika, 17, 209–222. https://doi.org/10.1007/BF02288783
   Google Scholar
• Hägglund, G. (1982). Factor analysis by instrumental variables methods. Psychometrika, 47, 209–222. https://doi.org/10.1007/BF02296276
   Web of Science ®Google Scholar
• Harman, H. H. (1976). Modern factor analysis (3rd ed.). University of Chicago press.
   Google Scholar
• Holzinger, K. J. (1944). A simple method of factor analysis. Psychometrika, 9, 257–262. https://doi.org/10.1007/BF02288737
   Google Scholar
• Hunter, J. E., & Gerbing, D. W. (1982). Unidimensional measurement, second-order factor analysis, and causal models. Research in Organizational Behavior, 4, 267–320.
   Web of Science ®Google Scholar
• Ihara, M., & Kano, Y. (1986). A new estimator of the uniqueness in factor analysis. Psychometrika, 51, 563–566. https://doi.org/10.1007/BF02295595
   Web of Science ®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., Gruvaeus, G. T., & Van Thillo, M. (1970). Acovs a general computer program for analysis of covariance structures. ETS Research Bulletin Series, 1970, i–54. https://doi.org/10.1002/j.2333-8504.1970.tb01009.x
   Google Scholar
• Kano, Y. (1990). Noniterative estimation and the choice of the number of factors in exploratory factor analysis. Psychometrika, 55, 277–291. https://doi.org/10.1007/BF02295288
   Web of Science ®Google Scholar
• Kaplan, D. (1988). The impact of specification error on the estimation, testing, and improvement of structural equation models. Multivariate Behavioral Research, 23, 69–86. https://doi.org/10.1207/s15327906mbr2301_4
   PubMed Web of Science ®Google Scholar
• Kochenderfer, M. J., & Wheeler, T. A. (2019). Algorithms for optimization. Mit Press.
   Google Scholar
• Kuha, J., & Bakk, Z. (2023). Two-step estimation of latent trait models. arXiv preprint arXiv:2303.16101.
   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
• Levy, R. (2023). Precluding interpretational confounding in factor analysis with a covariate or outcome via measurement and uncertainty preserving parametric modeling. Structural Equation Modeling: A Multidisciplinary Journal. Advance online publication. https://doi.org/10.1080/10705511.2022.2154214
   Web of Science ®Google Scholar
• McCrae, R. R., Zonderman, A. B., Costa, P. T., Jr, Bond, M. H., & Paunonen, S. V. (1996). Evaluating replicability of factors in the revised neo personality inventory: Confirmatory factor analysis versus procrustes rotation. Journal of Personality and Social Psychology, 70, 552–566. https://doi.org/10.1037/0022-3514.70.3.552
   Web of Science ®Google Scholar
• R Core Team (2023). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. https://www.R-project.org/
   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). A structural after measurement approach to structural equation modeling. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000503
   PubMed Web of Science ®Google Scholar
• Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures. Methods of Psychological Research Online, 8, 23–74.
   Google Scholar
• Stuive, I. (2007). A comparison of confirmatory factor analysis methods: Oblique multiple group method versus confirmatory common factor method.
   Google Scholar
• Thurstone, L. L. (1945). A multiple group method of factoring the correlation matrix. Psychometrika, 10, 73–78. https://doi.org/10.1007/BF02288876
   Google Scholar
• Van Driel, O. P. (1978). On various causes of improper solutions in maximum likelihood factor analysis. Psychometrika, 43, 225–243. https://doi.org/10.1007/BF02293865
   Web of Science ®Google Scholar