Label Switching in Latent Class Analysis: Accuracy of Classification, Parameter Estimates, and Confidence Intervals

References

• Ahlquist, J. S., & Breunig, C. (2012). Model-based clustering and typologies in the social sciences. Political Analysis, 20, 92–112. https://doi.org/10.1093/pan/mpr039
   Web of Science ®Google Scholar
• Aitkin, M., & Rubin, D. B. (1985). Estimation and hypothesis testing in finite mixture models. Journal of the Royal Statistical Society Series B, 47, 67–75. https://doi.org/10.1111/j.2517-6161.1985.tb01331.x
   Google Scholar
• Berlin, K. S., Williams, N. A., & Parra, G. R. (2014). An introduction to latent variable mixture modeling (part 1): Overview and cross-sectional latent class and latent profile analyses. Journal of Pediatric Psychology, 39, 174–187. https://doi.org/10.1093/jpepsy/jst084c
   PubMed Web of Science ®Google Scholar
• Clark, S. L., Muthén, B., Kaprio, J., D'Onofrio, B. M., Viken, R., & Rose, R. J. (2013). Models and strategies for factor mixture analysis: An example concerning the structure underlying psychological disorders. Structural Equation Modeling A, 20, 681–703. https://doi.org/10.1080/10705511.2013.824786
   Web of Science ®Google Scholar
• Clogg, C. C., & Goodman, L. A. (1985). Simultaneous latent structure analysis in several groups. Sociological Methodology, 15, 81–110. https://doi.org/10.2307/270847
   Google Scholar
• Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis: with applications in the social behavioral, and health sciences. Wiley.
   Google Scholar
• Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society B, 39, 1–22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
   Google Scholar
• Depaoli, S. (2013). Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation. Psychological Methods, 18, 186–219. https://doi.org/10.1037/a0031609
   PubMed Web of Science ®Google Scholar
• Dziak, J. J., Lanza, S. T., & Tan, X. (2014). Effect size, statistical power, and sample size requirements for the bootstrap likelihood ratio test in latent class analysis. Structural Equation Modeling, 21, 534–552. https://doi.org/10.1080/10705511.2014.919819
   PubMed Web of Science ®Google Scholar
• Efron, B. (1979). Bootstrap methods: Another look at the Jackknife. The Annals of Statistics, 7, 1–26. https://doi.org/10.1214/aos/1176344552
   Web of Science ®Google Scholar
• Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. CRC press.
   Google Scholar
• Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231. https://doi.org/10.2307/2334349
   Web of Science ®Google Scholar
• Gudicha, D. W., Schmittmann, V. D., & Vermunt, J. K. (2017). Statistical power of likelihood ratio and wald tests in latent class models with covariates. Behavior Research Methods, 49, 1824–1837. https://doi.org/10.3758/s13428-016-0825-y
   PubMed Web of Science ®Google Scholar
• Hancock, G. R., Harring, J. R., & Macready, G. B. (2019). Advances in latent class analysis: A festschrift in honor of c. mitchell dayton. IAP.
   Google Scholar
• Jaki, T., Kim, M., Lamont, A., George, M., Chang, C., Feaster, D., & Van Horn, M. L. (2019). The effects of sample size on the estimation of regression mixture models. Educational and Psychological Measurement, 79, 358–384. https://doi.org/10.1177/0013164418791673
   PubMed Web of Science ®Google Scholar
• Kankaraš, M., Moors, G., & Vermunt, J. K. (2018). Testing for measurement invariance with latent class analysis. In E. Davidov, P. Schmidt, & J. Billiet (Eds.), Cross-cultural analysis (pp. 393–419). Routledge.
   Google Scholar
• Killian, M. O., Cimino, A. N., Weller, B. E., & Hyun Seo, C. (2019). A systematic review of latent variable mixture modeling research in social work journals. Journal of Evidence-Based Social Work, 16, 192–210. https://doi.org/10.1080/23761407.2019.1577783
   Google Scholar
• Lazarsfeld, P. F. (1950). The logical and mathematical foundation of latent structure analysis. In Studies in Social Psychology in World War II Vol. IV: Measurement and Prediction (p. 362–412). Princeton University Press.
   Google Scholar
• Lazarsfeld, P. F. (1954). Conceptual introduction to latent structure analysis. Producteur Inconnu.
   Google Scholar
• Linzer, D. A., & Lewis, J. B. (2011). polca: An r package for polytomous variable latent class analysis. Journal of Statistical Software, 42, 1–29. https://doi.org/10.18637/jss.v042.i10
   Web of Science ®Google Scholar
• Lubke, G., & Muthén, B. O. (2007). Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters. Structural Equation Modeling A, 14, 26–47. https://doi.org/10.1207/s15328007sem1401_2
   Web of Science ®Google Scholar
• Lubke, G., & Neale, M. C. (2006). Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood? Multivariate Behavioral Research, 41, 499–532. https://doi.org/10.1207/s15327906mbr4104_4
   PubMed Web of Science ®Google Scholar
• McLachlan, G. J. (2000). Finite mixture models. Wiley.
   Google Scholar
• Morgan, G. B. (2015). Mixed mode latent class analysis: An examination of fit index performance for classification. Structural Equation Modeling A, 22, 76–86. https://doi.org/10.1080/10705511.2014.935751
   Web of Science ®Google Scholar
• Morgan, G. B., Hodge, K. J., & Baggett, A. R. (2016). Latent profile analysis with nonnormal mixtures: A monte carlo examination of model selection using fit indices. Computational Statistics & Data Analysis, 93, 146–161. https://doi.org/10.1016/j.csda.2015.02.019
   Web of Science ®Google Scholar
• Muthén, B., Kaplan, D., & Hollis, M. (1987). On structural equation modeling with data that are not missing completely at random. Psychometrika, 52, 431–462. https://doi.org/10.1007/BF02294365
   Web of Science ®Google Scholar
• Muthén, B., & Muthén, L. K. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism, Clinical and Experimental Research, 24, 882–891. https://doi.org/10.1111/j.1530-0277.2000.tb02070.x
   PubMed Web of Science ®Google Scholar
• Nevitt, J., & Hancock, G. R. (2001). Performance of bootstrapping approaches to model test statistics and parameter standard error estimation in structural equation modeling. Structural Equation Modeling A, 8, 353–377. https://doi.org/10.1207/S15328007SEM0803_2
   Web of Science ®Google Scholar
• Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A monte carlo simulation study. Structural Equation Modeling A, 14, 535–569. https://doi.org/10.1080/10705510701575396
   Web of Science ®Google Scholar
• Papastamoulis, P. (2016). label.switching: An r package for dealing with the label switching problem in MCMC outputs. Journal of Statistical Software, 69, 1–24. https://www.jstatsoft.org/index.php/jss/article/view/v069c01 https://doi.org/10.18637/jss.v069.c01
   Web of Science ®Google Scholar
• Patterson, B. H., Dayton, C. M., & Graubard, B. I. (2002). Latent class analysis of complex sample survey data: application to dietary data. Journal of the American Statistical Association, 97, 721–741. https://doi.org/10.1198/016214502388618465
   Web of Science ®Google Scholar
• Peugh, J., & Fan, X. (2013). Modeling unobserved heterogeneity using latent profile analysis: A Monte Carlo simulation. Structural Equation Modeling A, 20, 616–639. https://doi.org/10.1080/10705511.2013.824780
   Web of Science ®Google Scholar
• R Core Team. (2013). R: A language and environment for statistical computing. R Foundation for statistical Computing.
   Google Scholar
• Redner, R. A., & Walker, H. F. (1984). Mixture densities, maximum likelihood and the EM algorithm. SIAM Review, 26, 195–239. https://doi.org/10.1137/1026034
   Web of Science ®Google Scholar
• Rodríguez, C. E., & Walker, S. G. (2014). Label switching in Bayesian mixture models: Deterministic relabeling strategies. Journal of Computational and Graphical Statistics, 23, 25–45. https://doi.org/10.1080/10618600.2012.735624
   Web of Science ®Google Scholar
• Stephens, M. (2000). Dealing with label switching in mixture models. Journal of the Royal Statistical Society Series B, 62, 795–809. https://doi.org/10.1111/1467-9868.00265
   Google Scholar
• Tekle, F. B., Gudicha, D. W., & Vermunt, J. K. (2016). Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models. Advances in Data Analysis and Classification, 10, 209–224. https://doi.org/10.1007/s11634-016-0251-0
   Web of Science ®Google Scholar
• Tueller, S. J., Drotar, S., & Lubke, G. H. (2011). Addressing the problem of switched class labels in latent variable mixture model simulation studies. Structural Equation Modeling A, 18, 110–131. https://doi.org/10.1080/10705511.2011.534695
   Web of Science ®Google Scholar
• Velicer, W. F., Martin, R. A., & Collins, L. M. (1996). Latent transition analysis for longitudinal data. Addiction, 91, S197–S209. https://doi.org/10.1111/j.1360-0443.1996.tb02339.x
   PubMed Web of Science ®Google Scholar
• Vermunt, J. K. (2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18, 450–469. https://doi.org/10.1093/pan/mpq025
   Web of Science ®Google Scholar
• Vermunt, J. K. (2011). K-means may perform as well as mixture model clustering but may also be much worse: comment on steinley and brusco (2011), Psychol Methods, 16, 82–92. https://doi.org/10.1037/a0020144
   PubMed Web of Science ®Google Scholar
• Vermunt, J. K., Van Ginkel, J. R., Van der Ark, L. A., & Sijtsma, K. (2008). 9. multiple imputation of incomplete categorical data using latent class analysis. Sociological Methodology, 38, 369–397. https://doi.org/10.1111/j.1467-9531.2008.00202.x
   Web of Science ®Google Scholar
• Whittaker, T. A., & Miller, J. (2021). Exploring the enumeration accuracy of cross-validation indices in latent class analysis. Structural Equation Modeling A, 28, 376–390. https://doi.org/10.1080/10705511.2020.1802280
   Web of Science ®Google Scholar
• Woo, S. E., Jebb, A. T., Tay, L., & Parrigon, S. (2018). Putting the “person” in the center: Review and synthesis of person-centered approaches and methods in organizational science. Organizational Research Methods, 21, 814–845. https://doi.org/10.1177/1094428117752467
   Web of Science ®Google Scholar
• Wurpts, I. C., & Geiser, C. (2014). Is adding more indicators to a latent class analysis beneficial or detrimental? results of a Monte-Carlo study. Frontiers in Psychology, 5, 920. https://doi.org/10.3389/fpsyg.2014.00920
   PubMed Web of Science ®Google Scholar
• Yao, W. (2015). Label switching and its solutions for frequentist mixture models. Journal of Statistical Computation and Simulation, 85, 1000–1012. https://doi.org/10.1080/00949655.2013.859259
   Web of Science ®Google Scholar
• Yuan, K.-H., Tong, X., & Zhang, Z. (2015). Bias and efficiency for SEM with missing data and auxiliary variables: Two-stage robust method versus two-stage ML. Structural Equation Modeling A, 22, 178–192. https://doi.org/10.1080/10705511.2014.935750
   Web of Science ®Google Scholar