Determining the Number of Latent Classes in Single- and Multiphase Growth Mixture Models

References

• Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & B. F. Csaki (Eds.), Second international symposium on information theory (pp. 267–281). Budapest, Hungary: Academiai Kiado.
   Google Scholar
• Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338–363.
   PubMed Web of Science ®Google Scholar
• Beauchaine, T. P., & Beauchaine, R. J., III (2002). A comparison of maximum covariance and k-means cluster analysis in classifying cases into known taxon groups. Psychological Methods, 7, 245–261.
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation modeling perspective. Hoboken, NJ: Wiley.
   Google Scholar
• Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): The general theory and its analytic extensions. Psychometrika, 52, 345–370.
   Web of Science ®Google Scholar
• Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33, 261–304.
   Web of Science ®Google Scholar
• Collins, L. M., Fidler, P. L., Wugalter, S. E., & Long, J. D. (1993). Goodness-of-fit testing for latent class models. Multivariate Behavioral Research, 28, 375–389.
   PubMed Web of Science ®Google Scholar
• Duncan, T. E., Duncan, S. C., Strycker, L. A., Okut, H., & Li, F. (2002). Growth mixture modeling of adolescent alcohol use data. Retrieved from http://people.oregonstate.edu/ãcock/growth-curves/mixture1-30-02.pdf
   Google Scholar
• Entink, K., & Herman, R. (2009). Statistical models for responses and response times. Retrieved from http://doc.utwente.nl/60452/1/thesis_R_Klein_Entink.pdf
   Google Scholar
• Everitt, B. S. (1981). A Monte Carlo investigation of the likelihood ratio test for the number of components in a mixture of normal distribution. Multivariate Behavioral Research, 16, 171–180.
   PubMed Web of Science ®Google Scholar
• Formann, A. K. (2003). Latent class model diagnostics—A review and some proposals. Computational Statistics & Data Analysis, 41, 549–559.
   Web of Science ®Google Scholar
• Hagenaars, J. A., & McCutcheon, A. L. (2002). Applied latent class analysis. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Hix-Small, H., Duncan, T. E., Duncan, S. C., & Okut, H. (2004). A multivariate associative finite growth mixture modeling approach examining adolescent alcohol and marijuana use. Journal of Psychopathology and Behavioral Assessment, 26, 255–270.
   Web of Science ®Google Scholar
• Kim, S.-Y. (2012). Sample size requirements in single- and multi-phase growth mixture models: A Monte Carlo simulation study. Structural Equation Modeling.
   Web of Science ®Google Scholar
• Kim, S.-Y., & Kim, J.-S. (2012). Investigating stage-sequential growth mixture models with multiphase longitudinal data. Structural Equation Modeling.
   Web of Science ®Google Scholar
• Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22, 79–86.
   Google Scholar
• Li, F., Duncan, T. E., Duncan, S. C., & Hops, H. (2001). Piecewise growth mixture modeling of adolescent alcohol use data. Structural Equation Modeling, 8, 175–204.
   Web of Science ®Google Scholar
• Lo, Y., Mendell, N., & Rubin, D. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767–778.
   Web of Science ®Google Scholar
• Magidson, J., & Vermunt, J. K. (2004). Latent class models. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 175–198). Newbury Park, CA: Sage.
   Google Scholar
• McLachlan, G., & Peel, D. (2000). Finite mixture models. New York, NY: Wiley.
   Google Scholar
• Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.
   Web of Science ®Google Scholar
• Muthén, B. O. (2001a). Latent variable mixture modeling. In G. Marcoulides & R. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 1–33). Mahwah, NJ: Erlbaum.
   Google Scholar
• Muthén, B. (2001b). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 291–322). Washington, DC: American Psychological Association.
   Google Scholar
• Muthén, B. (2001c). Two-part growth mixture modeling. Retrieved from http://gseis.ucla.edu/faculty/muthen/articles/Article_094.pdf
   Google Scholar
• Muthén, B. (2003). Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran (2003). Psychological Methods, 8, 369–377.
   PubMed Web of Science ®Google Scholar
• Muthén, B. (2004). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data, In D. Kaplan (Ed.), Handbook of quantitative methodology for the social sciences (pp. 345–368). Newbury Park, CA: Sage.
   Google Scholar
• Muthén, B., Khoo, S.-T., Francis, D. J., & Boscardin, C. K. (2003). Analysis of reading skills development from kindergarten through first grade: An application of growth mixture modeling to sequential processes. In S. R. Reise & N. Duan (Eds.), Multilevel modeling: Methodological advances, issues, and applications (pp. 71–89). Mahwah, NJ: Erlbaum.
   Google Scholar
• Muthén, B., & Muthén, L. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research,24, 882.
   PubMed Web of Science ®Google Scholar
• Muthén, B. O., & Muthén, L. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599–620.
   Web of Science ®Google Scholar
• Muthén, L., & Muthén, B. (1998–2013). Mplus: Statistical analysis with latent variables user’s guide 6.0. Los Angeles, CA: Muthén & Muthén.
   Google Scholar
• Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463–469.
   PubMed Web of Science ®Google Scholar
• Nagin, D. S. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4,139–157.
   Web of Science ®Google Scholar
• Nylund, K. L., 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.
   Web of Science ®Google Scholar
• Ramaswamy, V., DeSarbo, W. S., Reibstein, D. J., & Robinson, W. T. (1993). An empirical pooling approach for estimating marketing mix elasticities with PIMS data. Marketing Science, 12, 103–124.
   Web of Science ®Google Scholar
• Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Newbury Park, CA: Sage.
   Google Scholar
• Reiser, M., & Lin, Y. (1999). A goodness-of-fit test for the latent class model when expected frequencies are small. In M. E. Sobel, & M. P. Becker (Eds.), Sociological methodology (pp. 81–111). Oxford, UK: Blackwell.
   Google Scholar
• Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464.
   Web of Science ®Google Scholar
• Sclove, L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333–343.
   Web of Science ®Google Scholar
• Stone, A. A., & Shiffman, S. (1994). Ecological momentary assessment (EMA) in behavorial medicine. Annals of Behavioral Medicine, 16, 199–202.
   Google Scholar
• Tofighi, D., & Enders, C. K. (2008). Indentifying the correct number of classes in growth mixture models. In G. R. Hancock & K. M. Samuelsen, (Eds.), Advances in latent variable mixture models (pp. 317–341). Greenwich, CT: Information Age.
   Google Scholar
• Walls, T. A., & Schafer, J. L. (2006). Models for intensive longitudinal data. New York, NY: Oxford University Press.
   Google Scholar
• Yang, C.-C. (2006). Evaluating latent class analysis models in qualitative phenotype indentification. Computational Statistics & Data Analysis, 50, 1090–1104.
   Web of Science ®Google Scholar