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Measurement, Statistics, and Research Design

Small-Variance Priors in Bayesian Factor Analysis with Ordinal Data

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References

  • Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 397–438. https://doi.org/10.1080/10705510903008204
  • Asparouhov, T., & Muthén, B. (2010). Bayesian analysis using Mplus: Technical implementation (Mplus Technical Report, Issue). http://statmodel2.com/download/Bayes3.pdf
  • Asparouhov, T., & Muthén, B. (2021). Advances in Bayesian model fit evaluation for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 28(1), 1–14. https://doi.org/10.1080/10705511.2020.1764360
  • Asparouhov, T., Muthén, B., & Morin, A. J. (2015). Bayesian structural equation modeling with cross-loadings and residual covariances: Comments on Stromeyer. Journal of Management, 41(6), 1561–1577. https://doi.org/10.1177/0149206315591075
  • Carvalho, C. M., Polson, N. G., & Scott, J. G. (2009). Handling sparsity via the horseshoe [Paper presentation]. International Conference on Artificial Intelligence and Statistics, Clearwater Beach, FL.
  • Cudeck, R., & O’Dell, L. L. (1994). Applications of standard error estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations. Psychological Bulletin, 115(3), 475–487.
  • De Bondt, N., & Van Petegem, P. (2015). Psychometric evaluation of the overexcitability questionnaire-two applying Bayesian structural equation modeling (BSEM) and multiple-group BSEM-based alignment with approximate measurement invariance. Frontiers in Psychology, 6, 1963.
  • Depaoli, S., & van de Schoot, R. (2017). Improving transparency and replication in Bayesian statistics: The Wambs-checklist. Psychological Methods, 22(2), 240–261.
  • Feng, X.-N., Wu, H.-T., & Song, X.-Y. (2017). Bayesian adaptive lasso for ordinal regression with latent variables. Sociological Methods & Research, 46(4), 926–953. https://doi.org/10.1177/0049124115610349
  • Finney, S. J., & DiStefano, C. (2013). Non-normal and categorical data in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 439–492). IAP.
  • Friedman, J. H. (1997). On bias, variance, 0/1-loss, and the curse-of-dimensionality. Data Mining and Knowledge Discovery, 1(1), 55–77. https://doi.org/10.1023/A:1009778005914
  • Gelman, A., Meng, X. L., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6(4), 733–807.
  • Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457–472. https://doi.org/10.1214/ss/1177011136
  • Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6), 721–741. https://doi.org/10.1109/TPAMI.1984.4767596
  • Guo, J., Marsh, H. W., Parker, P. D., Dicke, T., Lüdtke, O., & Diallo, T. M. O. (2019). A systematic evaluation and comparison between exploratory structural equation modeling and Bayesian structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 26(4), 529–556. https://doi.org/10.1080/10705511.2018.1554999
  • Hayes, T., & Usami, S. (2020). Factor score regression in connected measurement models containing cross-loadings. Structural Equation Modeling: A Multidisciplinary Journal, 27(6), 942–951. https://doi.org/10.1080/10705511.2020.1729160
  • Hoijtink, H., & van de Schoot, R. (2018). Testing small variance priors using prior-posterior predictive p values. Psychological Methods, 23(3), 561–569. https://doi.org/10.1037/met0000131
  • Iwamoto, H., & Suzuki, H. (2019). An empirical study on the relationship of corporate financial performance and human capital concerning corporate social responsibility: Applying SEM and Bayesian SEM. Cogent Business & Management, 6(1), 1656443. https://doi.org/10.1080/23311975.2019.1656443
  • Jacobucci, R., Brandmaier, A. M., & Kievit, R. A. (2019). A practical guide to variable selection in structural equation modeling by using regularized multiple-indicators, multiple-causes models. Advances in Methods and Practices in Psychological Science, 2(1), 55–76. https://doi.org/10.1177/2515245919826527
  • Jacobucci, R., & Grimm, K. J. (2018). Comparison of frequentist and Bayesian regularization in structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 25(4), 639–649. https://doi.org/10.1080/10705511.2017.1410822
  • Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 555–566. https://doi.org/10.1080/10705511.2016.1154793
  • Jorgensen, T. D., Garnier-Villarreal, M., Pornprasermanit, S., & Lee, J. (2019). Small-variance priors can prevent detecting important misspecifications in Bayesian confirmatory factor [Paper presentation]. Quantitative Psychology: 83rd Annual Meeting of the Psychometric Society, New York, NY 2018.
  • Korner-Nievergelt, F., Roth, T., Von Felten, S., Guélat, J., Almasi, B., & Korner-Nievergelt, P. (2015). Bayesian data analysis in ecology using linear models with r, bugs, and stan. Academic Press.
  • Kruschke, J. (2014). Doing Bayesian data analysis: A tutorial with r, jags, and stan (2nd ed.) Academic Press.
  • Lee, S. Y. (2007). Bayesian estimation of structural equation models. In S. Y. Lee (Ed.), Structural equation modeling: A Bayesian approach (pp. 67–109). John Wiley & Sons Inc.
  • Li, C.-H. (2016). The performance of ML, DWLS, and ULS estimation with robust corrections in structural equation models with ordinal variables. Psychological Methods, 21(3), 369–387.
  • Liang, X. (2020). Prior sensitivity in Bayesian structural equation modeling for sparse factor loading structures. Educational and Psychological Measurement, 80(6), 1025–1058. https://doi.org/10.1177/0013164420906449
  • Liang, X., & Jacobucci, R. (2020). Regularized structural equation modeling to detect measurement bias: Evaluation of lasso, adaptive lasso, and elastic net. Structural Equation Modeling: A Multidisciplinary Journal, 27(5), 722–734. https://doi.org/10.1080/10705511.2019.1693273
  • Liang, X., Yang, Y., & Cao, C. (2020). The performance of ESEM and BSEM in structural equation models with ordinal indicators. Structural Equation Modeling: A Multidisciplinary Journal, 27(6), 874–887. https://doi.org/10.1080/10705511.2020.1716770
  • Liang, X., Yang, Y., & Huang, J. (2018). Evaluation of structural relationships in autoregressive cross-lagged models under longitudinal approximate invariance: A Bayesian analysis. Structural Equation Modeling: A Multidisciplinary Journal, 25(4), 558–572. https://doi.org/10.1080/10705511.2017.1410706
  • Lopes, V. P., Barnett, L. M., Saraiva, L., Gonçalves, C., Bowe, S. J., Abbott, G., & Rodrigues, L. P. (2016). Validity and reliability of a pictorial instrument for assessing perceived motor competence in Portuguese children. Child: Care, Health and Development, 42(5), 666–674.
  • Lu, Z. H., Chow, S. M., & Loken, E. (2016). Bayesian factor analysis as a variable-selection problem: Alternative priors and consequences. Multivariate Behavioral Research, 51(4), 519–539.
  • Marsh, H. W., Muthén, B. O., Asparouhov, T., Lüdtke, O., Robitzsch, A., Morin, A. J. S., & Trautwein, U. (2009). Exploratory structural equation modeling, integrating CFA and EFA: Application to students' evaluations of university teaching. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 439–476. https://doi.org/10.1080/10705510903008220
  • McDonald, R. P. (1985). Factor analysis and related methods. Hillsdale, NJ: Lawrence Erlbaum.
  • Meng, X. L. (1994). Posterior predictive p-values. The Annals of Statistics, 22(3), 1142–1160. https://doi.org/10.1214/aos/1176325622
  • Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105(1), 156–166. https://doi.org/10.1037/0033-2909.105.1.156
  • Mitchell, T. J., & Beauchamp, J. J. (1988). Bayesian variable selection in linear regression. Journal of the American Statistical Association, 83(404), 1023–1032. https://doi.org/10.1080/01621459.1988.10478694
  • Muthén, B., Asparouhov, T. (2002). Latent variable analysis with categorical outcomes: Multiple-group and growth modeling in Mplus (Mplus Web Notes 4, Issue). https://www.statmodel.com/download/webnotes/CatMGLong.pdf
  • Muthén, B. O., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313–335. https://doi.org/10.1037/a0026802
  • Muthén, B. O., & Asparouhov, T. (2013). BSEM measurement invariance analysis. https://www.statmodel.com/examples/webnotes/webnote17.pdf
  • Muthén, L. K., & Muthén, B. O. (1998–2017). Mplus user's guide (8th ed.) Muthén & Muthén. https://www.statmodel.com/HTML_UG/introV8.htm
  • Park, T., & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association, 103(482), 681–686. https://doi.org/10.1198/016214508000000337
  • Plummer, M. (2003). Jags: A program for analysis of Bayesian graphical models using Gibbs sampling. Proceedings of the 3rd International Workshop on Distributed Statistical Computing. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.3406
  • Reis, D. (2019). Further insights into the German version of the multidimensional assessment of interoceptive awareness (MAIA): Exploratory and Bayesian structural equation modeling approaches. European Journal of Psychological Assessment, 35(3), 317–325. https://doi.org/10.1027/1015-5759/a000404
  • Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373.
  • SAS Institute Inc. (2002–2020). Version 9.4.
  • Scharf, F., & Nestler, S. (2019). Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeling: A Multidisciplinary Journal, 26(4), 576–590. https://doi.org/10.1080/10705511.2018.1558060
  • Sörbom, D. (1989). Model modification. Psychometrika, 54(3), 371–384. https://doi.org/10.1007/BF02294623
  • Stan Development Team. (2021). Rstan: The r interface to stan. In R package version 2.27. http://mc-stan.org
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
  • van Erp, S., Mulder, J., & Oberski, D. L. (2018). Prior sensitivity analysis in default Bayesian structural equation modeling. Psychological Methods, 23(2), 363–388.
  • Xiao, Y., Liu, H., & Hau, K.-T. (2019). A comparison of CFA, ESEM, and BSEM in test structure analysis. Structural Equation Modeling: A Multidisciplinary Journal, 26(5), 665–677. https://doi.org/10.1080/10705511.2018.1562928

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