1,461
Views
61
CrossRef citations to date
0
Altmetric
Original Articles

Fit for a Bayesian: An Evaluation of PPP and DIC for Structural Equation Modeling

&

References

  • Ando, T. (2011). Predictive Bayesian model selection. American Journal of Mathematical and Management Sciences, 31(1–2), 13–38. doi:10.1080/01966324.2011.10737798
  • Asparouhov, T., & Muthén, B. (2010a). Bayesian analysis of latent variable models using Mplus. Retrieved June, 17, 2014, from http://www.statmodel2.com/download/BayesAdvantages18.pdf
  • Asparouhov, T., & Muthén, B. O. (2010b). Bayesian analysis using Mplus: Technical implementation. Manuscript Submitted for Publication. Retrieved from https://www.statmodel.com/download/Bayes3.pdf
  • Asparouhov, T., Muthén, B. O., & Morin, A. J. (2015). Bayesian structural equation modeling with cross-loadings and residual covariances: Comments on Stromeyer et al. Los Angeles, CA: Sage Publications Sage CA.
  • Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238–246. doi:10.1037/0033-2909.107.2.238
  • Berger, J. (2006). The case for objective Bayesian analysis. Bayesian Analysis, 1(3), 385–402. doi:10.1214/06-BA115
  • Bollen, K. A., Harden, J. J., Ray, S., & Zavisca, J. (2014). BIC and alternative Bayesian information criteria in the selection of structural equation models. Structural Equation Modeling, 21(1), 1–19. doi:10.1080/10705511.2014.856691
  • Chen, F., Curran, P. J., Bollen, K. A., Kirby, J., & Paxton, P. (2008). An empirical evaluation of the use of fixed cutoff points in RMSEA test statistic in structural equation models. Sociological Methods & Research, 36(4), 462–494. doi:10.1177/0049124108314720
  • De la Horra, J., & Teresa Rodriguez-Bernal, M. (2003). Bayesian robustness of the posterior predictive p-value. Communications in Statistics-Theory and Methods, 32(8), 1493–1503. doi:10.1081/STA-120022241
  • Ellison, A. M. (2004). Bayesian inference in ecology. Ecology Letters, 7(6), 509–520. doi:10.1111/ele.2004.7.issue-6
  • Fan, X., & Sivo, S. A. (2007). Sensitivity of fit indices to model misspecification and model types. Multivariate Behavioral Research, 42(3), 509–529. doi:10.1080/00273170701382864
  • Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1(3), 515–534. doi:10.1214/06-BA117A
  • Gelman, A., Meng, X.-L., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6(4), 733–760.
  • Gelman, A., & Shalizi, C. R. (2013). Philosophy and the practice of Bayesian statistics. British Journal of Mathematical and Statistical Psychology, 66(1), 8–38. doi:10.1111/j.2044-8317.2011.02037.x
  • Hjort, N. L., Dahl, F. A., & Steinbakk, G. H. (2006). Post-processing posterior predictive p values. Journal of the American Statistical Association, 101(475), 1157–1174. doi:10.1198/016214505000001393
  • Hu, L., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3(4), 424–453. doi:10.1037/1082-989X.3.4.424
  • Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. doi:10.1080/10705519909540118
  • Jeon, M., & De Boeck, P. (2017). Decision qualities of Bayes factor and p value-based hypothesis testing. Psychological Methods, 22(2), 340–360. doi:10.1037/met0000140
  • Johnson, V. E. (2013). Uniformly most powerful Bayesian tests. Annals of Statistics, 41(4), 1716–1741. doi:10.1214/13-AOS1123
  • Jordan, M. (2011). What are the open problems in Bayesian statistics. The ISBA Bulletin, 18, 1–4.
  • Jöreskog, K. G. (1967). A general approach to confirmatory maximum likelihood factor analysis. ETS Research Bulletin Series, (1967(2), 183–202. doi:10.1002/j.2333-8504.1967.tb00991.x
  • Kaplan, D., & Depaoli, S. (2012). Bayesian structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 650–673). New York, NY, US: Guilford Press.
  • Kenny, D. A., & McCoach, B. D. (2003). Effect of the number of variables on measures of fit in structural equation modeling. Structural Equation Modeling, 10(3), 333–351. doi:10.1207/S15328007SEM1003_1
  • Lee, S.-Y. (2007). Structural equation modeling: A Bayesian approach. Chichester, England: John Wiley & Sons.
  • Lee, S.-Y., & Song, X.-Y. (2012). Basic and advanced Bayesian structural equation modeling: With applications in the medical and behavioral sciences. Chichester, England: John Wiley & Sons.
  • Li, Y., Bolt, D. M., & Fu, J. (2006). A comparison of alternative models for testlets. Applied Psychological Measurement, 30(1), 3–21. doi:10.1177/0146621605275414
  • Lunn, D., Thomas, A., Best, N., & Spiegelhalter, D. (2000). WinBUGS — A Bayesian modelling framework: Concepts, structure, and extensibility. Statistics and Computing, 10, 325–337. doi:10.1023/A:1008929526011
  • Marsh, H. W., Hau, K.-T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Structural Equation Modeling: A Multidisciplinary Journal, 11(3), 320–341. doi:10.1207/s15328007sem1103_2
  • Maxwell, S., & Delaney, H. (2004). A brief primer of principles of formulating and comparing models. In Designing experiments and analyzing data: A model comparison perspective (2nd ed., pp. B-26–B-36). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Meng, X.-L. (1994). Posterior predictive p-values. The Annals of Statistics, 22, 1142–1160. doi:10.1214/aos/1176325622
  • Muthén, B. O., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313–335. doi:10.1037/a0026802
  • Muthén, L. K., & Muthén, B. O. (2012). Mplus User’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
  • Palomo, J., Dunson, D. B., & Bollen, K. (2007). Bayesian structural equation modeling. Handbook of Latent Variable and Related Models, 1, 163–188.
  • Paxton, P., Curran, P. J., Bollen, K. A., Kirby, J., & Chen, F. (2001). Monte Carlo experiments: Design and implementation. Structural Equation Modeling: A Multidisciplinary Journal, 8(2), 287–312. doi:10.1207/S15328007SEM0802_7
  • Plummer, M. (2006). Comment on article by Celeux et al. Bayesian Analysis, 1(4), 681–686. doi:10.1214/06-BA122C
  • Plummer, M. (2008). Penalized loss functions for Bayesian model comparison. Biostatistics, 9(3), 523–539. doi:10.1093/biostatistics/kxm049
  • Raftery, A. E. (1993). Bayesian model selection in structural equation models. In K. A. Bollen and J. S. Long (Eds.), Testing Structural Equation Models (pp. 163–180),  Beverly Hills, CA: Sage..
  • R Core Team. (2016). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.R-project.org/
  • Rupp, A. A., Dey, D. K., & Zumbo, B. D. (2004). To Bayes or Not to Bayes, from whether to when: Applications of Bayesian methodology to modeling. Structural Equation Modeling, 11(3), 424–451. doi:10.1207/s15328007sem1103_7
  • Satorra, A., & Saris, W. E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50(1), 83–90. doi:10.1007/BF02294150
  • Scheines, R., Hoijtink, H., & Boomsma, A. (1999). Bayesian estimation and testing of structural equation models. Psychometrika, 64(1), 37–52. doi:10.1007/BF02294318
  • Seaman, J. W., III, Seaman, J. W., Jr, & Stamey, J. D. (2012). Hidden dangers of specifying noninformative priors. The American Statistician, 66(2), 77–84. doi:10.1080/00031305.2012.695938
  • Sinharay, S. (2006). Bayesian item fit analysis for unidimensional item response theory models. British Journal of Mathematical and Statistical Psychology, 59(2), 429–449. doi:10.1348/000711005X66888
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Linde, A. (2014). The deviance information criterion: 12 years on. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(3), 485–493. doi:10.1111/rssb.2014.76.issue-3
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583–639. doi:10.1111/rssb.2002.64.issue-4
  • Steiger, J. H., & Lind, J. C. (1980). Statistically based tests for the number of common factors. In Annual meeting of the Psychometric Society, Iowa City, IA (Vol.758, pp. 424–453).
  • van de Schoot, R., & Depaoli, S. (2014). Bayesian analyses: Where to start and what to report. Marta Marques & Kyra Hamilton, 36, 75
  • Van Der Linde, A. (2005). DIC in variable selection. Statistica Neerlandica, 59(1), 45–56. doi:10.1111/stan.2005.59.issue-1
  • Van Der Linde, A. (2012). A Bayesian view of model complexity. Statistica Neerlandica, 66(3), 253–271. doi:10.1111/j.1467-9574.2011.00518.x
  • Ward, E. J. (2008). A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools. Ecological Modelling, 211(1–2), 1–10. doi:10.1016/j.ecolmodel.2007.10.030
  • Zhang, Z., Lai, K., Lu, Z., & Tong, X. (2013). Bayesian inference and application of Robust growth curve models using student’s t distribution. Structural Equation Modeling, 20(1), 47–78. doi:10.1080/10705511.2013.742382
  • Zhu, X., & Stone, C. A. (2012). Bayesian comparison of alternative graded response models for performance assessment applications. Educational and Psychological Measurement, 72(5), 774–799. doi:10.1177/0013164411434638

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.