Assessing Model Selection Uncertainty Using a Bootstrap Approach: An Update

REFERENCES

• Bollen, K., & Stine, R. (1992). Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods & Research, 21, 205–229. doi:10.1177/0049124192021002004
   Web of Science ®Google Scholar
• Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52, 345–370. doi:10.1007/BF02294361
   Web of Science ®Google Scholar
• Burnham, K., & Anderson, D. (2002). Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). New York, NY: Springer.
   Google Scholar
• Burnham, K., & Anderson, D. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods and Research, 33, 261–304. doi:10.1177/0049124104268644
   Web of Science ®Google Scholar
• Cudeck, R., & Henly, S. J. (1991). Model selection in covariance structures analysis and the “problem” of sample size: A clarification. Psychological Bulletin, 109, 512–519. doi:10.1037/0033-2909.109.3.512
   PubMed Web of Science ®Google Scholar
• Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26. doi:10.1214/aos/1176344552
   Web of Science ®Google Scholar
• Efron, B. (2014). Estimation and accuracy after model selection. Journal of the American Statistical Association, 109, 991–1007. doi:10.1080/01621459.2013.823775
   PubMed Web of Science ®Google Scholar
• Gershman, S. J., & Blei, D. M. (2012). A tutorial on Bayesian nonparametric models. Journal of Mathematical Psychology, 56, 1–12. doi:10.1016/j.jmp.2011.08.004
   Web of Science ®Google Scholar
• Griffiths, T. L., & Ghahramani, Z. (2005). Infinite latent feature models and the Indian buffet process ( Tech. Rep. No. 2005-001). London, UK: Gatsby Computational Neuroscience Unit.
   Google Scholar
• Henson, J., Reise, S., & Kim, K. (2007). Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics. Structural Equation Modeling, 14, 202–226. doi:10.1080/10705510709336744
   Web of Science ®Google Scholar
• Hjort, N. L., Holmes, C., Müller, P., & Walker, S. (2010). Bayesian nonparametrics. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Holzinger, K. J., & Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution. Chicago, IL: The University of Chicago.
   Google Scholar
• Jeffreys, H. (1961). Theory of probability (3rd ed.). Oxford, UK: Oxford University Press.
   Google Scholar
• Kass, R., & Raftery, A. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795. doi:10.1080/01621459.1995.10476572
   Web of Science ®Google Scholar
• Kass, R., & Wasserman, L. (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association, 90, 928–934. doi:10.1080/01621459.1995.10476592
   Web of Science ®Google Scholar
• Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22(1), 79–86. doi:10.1214/aoms/1177729694
   Google Scholar
• Li, F., Cohen, A. S., Kim, S.-H., & Cho, S.-J. (2009). Model selection methods for mixture dichotomous IRT models. Applied Psychological Measurement, 33, 353–373. doi:10.1177/0146621608326422
   Web of Science ®Google Scholar
• Linhart, H., & Zucchini, W. (1986). Model selection. New York, NY: Wiley.
   Google Scholar
• Lubke, G., & Campbell, I. (2016). Inference based on the best-fitting model can contribute to the replication crisis: Assessing model selection uncertainty using a bootstrap approach. Structural Equation Modeling, 23, 479–490. doi:10.1080/10705511.2016.1141355
   PubMed Web of Science ®Google Scholar
• Lubke, G., & Neale, M. (2006). Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood? Multivariate Behavioral Research, 41, 499–532. doi:10.1207/s15327906mbr4104_4
   PubMed Web of Science ®Google Scholar
• Lubke, G., & Neale, M. (2008). Distinguishing between latent classes and continuous factors with categorical outcomes: Class invariance of parameters of factor mixture models. Multivariate Behavioral Research, 43, 592–620. doi:10.1080/00273170802490673
   PubMed Web of Science ®Google Scholar
• Lubke, G., & Tueller, S. (2010). Latent class detection and class assignment: A comparison of the MAXEIG taxometric procedure and factor mixture modeling approaches. Structural Equation Modeling, 17, 605–628. doi:10.1080/10705511.2010.510050
   PubMed Web of Science ®Google Scholar
• Nylund, K., Asparouhov, T., & Muthén, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14, 535–569. doi:10.1080/10705510701575396
   Web of Science ®Google Scholar
• Preacher, K. J., & Merkle, E. C. (2012). The problem of model selection uncertainty in structural equation modeling. Psychological Methods, 17, 1–14. doi:10.1037/a0026804
   PubMed Web of Science ®Google Scholar
• Preacher, K., Zhang, G., Kim, C., & Mels, G. (2013). Choosing the optimal number of factors in exploratory factor analysis: A model selection perspective. Multivariate Behavioral Research, 48, 28–56. doi:10.1080/00273171.2012.710386
   PubMed Web of Science ®Google Scholar
• Rousseliere, D., & Rousseliere, S. (2016). Decomposing the effects of time on the social acceptability of biotechnology using age-period-cohort-country models. Public Understanding of Science. Advance online publication. doi:10.1177/0963662515622394
   PubMed Web of Science ®Google Scholar
• Satorra, A., & Saris, W. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50, 83–90. doi:10.1007/BF02294150
   Web of Science ®Google Scholar
• Song, X.-Y., & Lee, S.-Y. (2002). A Bayesian approach for multigroup nonlinear factor analysis. Structural Equation Modeling, 9, 523–553. doi:10.1207/S15328007SEM0904_4
   Web of Science ®Google Scholar
• Vrieze, S. I. (2012). Model selection and psychological theory: A discussion of the differences between the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Psychological Methods, 17, 228–243. doi:10.1037/a0027127
   PubMed Web of Science ®Google Scholar
• Wasserman, L. (2000). Bayesian model selection and model averaging. Journal of Mathematical Psychology, 44, 92–107. doi:10.1006/jmps.1999.1278
   PubMed Web of Science ®Google Scholar
• Yang, C.-C., & Yang, C.-C. (2007). Separating latent classes by information criteria. Journal of Classification, 24, 183–203. doi:10.1007/s00357-007-0010-1
   Web of Science ®Google Scholar
• Yuan, K.-H., Hayashi, K., & Yanagihara, H. (2007). A class of population covariance matrices in the bootstrap approach to covariance structure analysis. Multivariate Behavioral Research, 42, 261–281. doi:10.1080/00273170701360662
   PubMed Web of Science ®Google Scholar