2,650
Views
16
CrossRef citations to date
0
Altmetric
Tutorial

Bayesian Latent Class Analysis Tutorial

, , &

References

  • Albert, J. (2007). Bayesian computation with R. New York: Springer. doi: 10.1007/978-0-387-92298-0.
  • Andrieu, C., De Freitas, N., Doucet, A., & Jordan, M. I. (2003). An introduction to MCMC for machine learning. Machine Learning, 50, 5–43. doi: 10.1023/A:1020281327116.
  • Berry, D. A. (1995). Statistics: A Bayesian perspective. Belmont, CA: Duxbury Press.
  • Celeux, G., Hurn, M., & Robert, C. P. (2000). Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association, 95(451), 957–970. doi: 10.1080/00031305.1992.10475878.
  • Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis. Hoboken, NJ: John Wiley & Sons, Ltd. doi: 10.1002/9780470567333.
  • Elliott, M. R., Gallo, J. J., Ten Have, T. R., Bogner, H. R., & Katz, I. R. (2005). Using a Bayesian latent growth curve model to identify trajectories of positive affect and negative events following myocardial infarction. Biostatistics, 6(1), 119–143. doi: 10.1093/biostatistics/kxh022.
  • Garrett, E., & Zeger, S. L. (2000). Latent class model diagnosis. Biometrics, 56, 1055–1067. doi: 10.1111/j.0006-341X.2000.01055.x.
  • Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003). Bayesian data analysis. New York: Chapman & Hall.
  • Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. New York: Cambridge University Press.
  • Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24(6), 997–1016.
  • Gershman, S. J., & Blei, D. M. (2012). A tutorial on Bayesian nonparametric models. Journal of Mathematical Psychology, 56(1), 1–12. doi: 10.1016/j.jmp.2011.08.004.
  • Harris, K., Halpern, C., Whitsel, E., Hussey, J., Tabor, J., Entzel, P., & Udry, J. (2009). The national longitudinal study of adolescent to adult health: Research design [www document]. Retrieved from http://www.cpc.unc.edu/projects/addhealth/design.
  • Jackman, S. (2009). Bayesian analysis for the social sciences. Chichester, United Kingdom: John Wiley & Sons, Ltd..
  • Jara, A., Hanson, T., Quintana, F., Müller, P., & Rosner, G. (2011). DPpackage: Bayesian semi- and nonparametric modeling in R. Journal of Statistical Software, 40(5), 1–30. Retrieved from http://www.jstatsoft.org/v40/i05/.
  • Jasra, A., Holmes, C. C., & Stephens, D. A. (2005). Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statistical Science, 20(1), 50–67. doi: 10.1214/088342305000000016.
  • Kaplan, D. (2014). Bayesian statistics for the social sciences (Methodology in the social sciences). New York, NY: Guilford Publications.
  • Karabatsos, G. (2006). Bayesian nonparametric model selection and model testing. Journal of Mathematical Psychology, 50(2), 123–148. doi: 10.1016/j.jmp.2005.07.003.
  • Karabatsos, G., Talbott, E., & Walker, S. G. (2015). A Bayesian nonparametric meta-analysis model. Research Synthesis Methods, 6(1), 28–44. doi: 10.1002/jrsm.1117.
  • Karabatsos, G., & Walker, S. G. (2009a). A Bayesian nonparametric approach to test equating. Psychometrika, 74(2), 211–232. doi: 10.1007/s11336–008–9096–6.
  • Karabatsos, G., & Walker, S. G. (2009b). Coherent psychometric modelling with Bayesian nonparametrics. British Journal of Mathematical and Statistical Psychology, 62(1), 1–20. doi: 10.1348/000711007X246237.
  • Lanza, S. T., Collins, L. M., Schafer, J. L., & Flaherty, B. P. (2005). Using data augmentation to obtain standard errors and conduct hypothesis tests in latent class and latent transition analysis. Psychological Methods, 10(1), 84–100. doi: 10.1037/1082–989X.10.1.84.
  • Lee, M. D., & Wagenmakers, E.-J. (2013). Bayesian cognitive modeling: A practical course. Cambridge, United Kingdom: Cambridge University Press. Retrieved from www.cambridge.org/9781107603578.
  • Lee, P. M. (2012). Bayesian statistics: An introduction (4th ed.). West Sussex, United Kingdom: John Wiley & Sons, Ltd.
  • Li, Y., & Baser, R. (2012). Using R and WinBUGS to fit a generalized partial credit model for developing and evaluating patient-reported outcomes assessments. Statistics in Medicine, 31, 2010–2026. doi: 10.1002/sim.4475.
  • Lindley, D. V. (1980). Introduction to probability & statistics from a Bayesian viewpoint. New York: Cambridge University Press.
  • Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The BUGS project: Evolution, critique, and future directions. Statistics in Medicine, 28, 3049–3067. Retrieved from www.openbugs.net.
  • Lunn, D., Thomas, A., Best, N., & Spiegelhalter, D. (2000). WinBUGS – A Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10, 325–337.
  • Lynch, S. M. (2007). Introduction to applied Bayesian statistics and estimation for social sciences. New York, NY: Springer.
  • MacKay, D. J. C. (2003). Information theory, inference, and learning algorithms. Cambridge, UK: Cambridge University Press.
  • McElreath, R. (2016). Statistical rethinking: A Bayesian course with examples in R and Stan. Boca Raton, FL: CRC Press.
  • Merkle, E. C., & Rosseel, Y. (2016). blavaan: Bayesian structural equation models via parameter expansion. arXiv 1511.05604. Retrieved from https://arxiv.org/abs/1511.05604.
  • Muthén, L. K., & Muthén, B. O. (2011). Mplus user’s guide (6th ed.). Los Angeles, CA: Muthén & Muthén. Retrieved from http://www.statmodel.com/discussion/messages/11/8751.html?1460746088.
  • Neelon, B., O’Malley, A. J., & Normand, S. L. (2011a). A Bayesian two-part latent class model for longitudinal medical expenditure data: Assessing the impact of mental health and substance abuse parity. Biometrics, 67(1), 280–289. doi: 10.1111/j.1541–0420.2010.01439.x.
  • Neelon, B., Swamy, G. K., Burgette, L. F., & Miranda, M. L. (2011b). A Bayesian growth mixture model to examine maternal hypertension and birth outcomes. Statistics in Medicine, 30(22), 2721–2735. doi: 10.1002/sim.4291.
  • Neelon, B., Zhu, L., & Neelon, S. E. (2015). Bayesian two-part spatial models for semicontinuous data with application to emergency department expenditures. Biostatistics, 16(3), 465–479. doi: 10.1093/biostatistics/kxu062.
  • Papastamoulis, P. (2016). label.switching: An R package for dealing with the label switching problem in MCMC outputs. Journal of Statistical Software, 69(1), 1–24. Retrieved from http://www.jstatsoft.org/v61/i13.
  • Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), Vienna, Austria. Retrieved from http://mcmc-jags.sourceforge.net/.
  • Raiffa, H., & Schaifer, R. (1961). Applied statistical decision theory. Cambridge, MA: Division of Research, Graduate School of Business Administration, Harvard University.
  • Richardson, S., & Green, P. J. (1998). Corrigendum: On Bayesian analysis of mixtures with an unknown number of components (vol 59, pg 731, 1997). Journal of the Royal Statistical Society Series B, 60, U3–U3.
  • Rozanov, Y. A. (1977). Probability theory: A concise course. New York, NY: Dover Publications, Inc.
  • Seidenberg, M., Haltiner, A., Taylor, M. A., Hermann, B. B., & Wyler, A. (1994). Development and validation of a multiple ability self-report questionnaire. Journal of Clinical Experimental Neuropsychology, 16(1), 93–104. doi: 10.1080/01688639408402620.
  • Spiegelhalter, D., Best, N., Carlin, B., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of Royal Statistical Society Series B, 64(4), 583–639. Blackwell Publishers. doi: 10.1111/1467–9868.00353.
  • Stan Development Team (2016). rstanarm: Bayesian applied regression modeling via Stan. R package version 2.13.1. Retrieved from http://mc-stan.org/.
  • Stan Development Team (2017). Stan Modeling Language Users Guide and Reference Manual, Version 2.16.0. Retrieved from http://mc-stan.org/.
  • Stephens, M. (2000). Dealing with label switching in mixture models. Journal of the Royal Statistical Society Series B, 62, 795–809. doi: 10.1111/1467–9868.00265.
  • Van de Schoot, R., Winter, S., Ryan, O., Zondervan-Zwijnenburg, M., & Depaoli, S. (2017). A systematic review of Bayesian articles in psychology: The last 25 years. Psychological Methods, 22, 217–239. doi: 10.1037/met0000100.
  • Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11, 3571–3594.
  • White, A., & Murphy, T. B. (2014). BayesLCA: An R package for Bayesian latent class analysis. Journal of Statistical Software, 61(13), 1–28. Retrieved from http://www.jstatsoft.org/v61/i13.
  • Wilkinson, D. (2011, July 16). Gibbs sampler in various languages (revisited) [Blog post]. Retrieved from http://darrenjw.wordpress.com/2011/07/16/gibbs-sampler-in-various-languages-revisited/.
  • Winkler, R. L. (2003). An introduction to Bayesian inference and decision (2nd ed.). Gainesville, FL: Probabilistic Publishing.
  • Wyse, J., & Friel, N. (2012). Block clustering with collapsed latent block models. Statistics and Computing, 22(1), 415–428. doi: 10.1007/s11222–011–9233–4.

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.