Estimation of Time-Unstructured Nonlinear Mixed-Effects Mixture Models

REFERENCES

• Aydin, B., Leite, W. L., & Algina, J. (2014). The consequences of ignoring variability in measurement occasions within data collection waves in latent growth models. Multivariate Behavioral Research, 49, 149–160. doi:10.1080/00273171.2014.887901
   PubMed Web of Science ®Google Scholar
• Baltes, P. B., & Nesselroade, J. R. (1979). History and rationale of longitudinal research. In J. R. Nesselroade & P. B. Baltes (Eds.), Longitudinal research in the study of behavior and development (pp. 1–39). New York, NY: Academic Press.
   Google Scholar
• Bauer, D. J. (2007). Observations on the use of growth mixture models in psychological research. Multivariate Behavioral Research, 42, 757–786. doi:10.1080/00273170701710338
   Web of Science ®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. doi:10.1037/1082-989X.8.3.338
   PubMed Web of Science ®Google Scholar
• Blozis, S. A., & Cho, Y. I. (2008). Coding and centering of time in latent curve models in the presence of interindividual time heterogeneity. Structural Equation Modeling, 15, 413–433. doi:10.1080/10705510802154299
   Web of Science ®Google Scholar
• Browne, M. W., & du Toit, S. H. C. (1991). Models for learning data. In L. M. Collins & J. L. Horn (Eds.), Best methods for the analysis of change: Recent advances, unanswered questions, future directions (pp. 47–68). Washington, DC: American Psychological Association.
   Google Scholar
• Codd, C. L., & Cudeck, R. (2014). Nonlinear random-effects mixture models for repeated measures. Psychometrika, 79, 60–83. doi:10.1007/s11336-013-9358-9
   PubMed Web of Science ®Google Scholar
• Cudeck, R., & Harring, J. R. (2007). Analysis of nonlinear patterns of change with random coefficient models. Annual Review of Psychology, 58, 615–637. doi:10.1146/annurev.psych.58.110405.085520
   PubMed Web of Science ®Google Scholar
• Curran, P. J., & Bauer, D. J. (2011). The disaggregation of within-person and between-person effects in longitudinal models of change. Annual Review of Psychology, 62, 583–619. doi:10.1146/annurev.psych.093008.100356
   PubMed Web of Science ®Google Scholar
• Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In J. M. Bernardo, J. O. Berger, A. P. Dawiv, & A. F. M. Smith (Eds.), Bayesian statistics 4: Proceedings of the fourth Valencia International Meeting (pp. 169–194). Oxford, UK: Clarendon.
   Google Scholar
• Grimm, K. J., & Ram, N. (2009). Non-linear growth models in Mplus and SAS. Structural Equation Modeling, 16, 676–701. doi:10.1080/10705510903206055
   PubMed Web of Science ®Google Scholar
• Grimm, K. J., Ram, N., & Estabrook, R. (2010). Nonlinear structured growth mixture models in Mplus and OpenMx. Multivariate Behavioral Research, 45, 887–909. doi:10.1080/00273171.2010.531230
   PubMed Web of Science ®Google Scholar
• Grimm, K. J., Ram, N., Shiyko, M. P., & Lo, L. L. (2013). A simulation study of the ability of growth mixture models to uncover growth heterogeneity. In J. J. McArdle & G. Ritschard (Eds.), Contemporary issues in exploratory data mining (pp. 172–189). New York, NY: Routledge.
   Google Scholar
• Hallquist, M., & Wiley, J. (2014). MplusAutomation: Automating Mplus model estimation and interpretation. R package version 0.6-3. Retrieved from http://CRAN.R-project.org/package=MplusAutomation
   Google Scholar
• Harring, J. R. (2012). Finite mixtures of nonlinear mixed effects models. In J. R. Harring & G. R. Hancock (Eds.), Advances in longitudinal methods in the social and behavioral sciences (pp. 159–192). Charlotte, NC: Information Age.
   Google Scholar
• Henson, J. M., Reise, S. P., & Kim, K. H. (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
• Hoogland, J. J., & Boomsma, A. (1998). Robustness studies in covariance structure modeling: An overview and a meta-analysis. Sociological Methods & Research, 26, 329–367. doi:10.1177/0049124198026003003
   Web of Science ®Google Scholar
• Kaplan, D. (2002). Methodological advances in the analysis of individual growth with relevance to education policy. Peabody Journal of Education, 77, 189–215. doi:10.1207/S15327930PJE7704_9
   Google Scholar
• Kelley, K. (2008). Nonlinear change models in populations with unobserved heterogeneity. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 4, 97–112. doi:10.1027/1614-2241.4.3.97
   Web of Science ®Google Scholar
• Kohli, N., Harring, J. R., & Zopluoglu, C. (in press). A finite mixture of nonlinear random coefficient models for continuous repeated measures data. Psychometrika.
   PubMed Web of Science ®Google Scholar
• Lu, X., & Huang, Y. (2014). Bayesian analysis of nonlinear mixed-effects mixture models for longitudinal data with heterogeneity and skewness. Statistics in Medicine, 33, 2830–2849. doi:10.1002/sim.6136
   PubMed Web of Science ®Google Scholar
• Lu, Z., & Zhang, Z. (2014). Robust growth mixture models with non-ignorable missingness: Models, estimation, selection, and application. Computational Statistics & Data Analysis, 71, 220–240. doi:10.1016/j.csda.2013.07.036
   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, 14, 26–47. doi:10.1080/10705510709336735
   Web of Science ®Google Scholar
• Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The BUGS project: Evolution, critique, and future directions. Statistics in Medicine, 28, 3049–3067. doi:10.1002/sim.3680
   PubMed Web of Science ®Google Scholar
• Lunn, D. J., 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
   Web of Science ®Google Scholar
• McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In J. R. Nesselroade & R. B. Cattell (Eds.), Handbook of multivariate experimental psychology (Vol. 2, pp. 561–614). New York, NY: Plenum.
   Google Scholar
• McArdle, J. J., & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110–133. doi:10.2307/1130295
   PubMed Web of Science ®Google Scholar
• McLachlan, G., & Peel, D. (2000). Finite mixture models. New York, NY: Wiley.
   Google Scholar
• Mehta, P. D., & Neale, M. C. (2005). People are variables too: Multilevel structural equations modeling. Psychological Methods, 10, 259–284. doi:10.1037/1082-989X.10.3.259
   PubMed Web of Science ®Google Scholar
• Mehta, P. D., & West, S. G. (2000). Putting the individual back into individual growth curves. Psychological Methods, 5, 23–43. doi:10.1037/1082-989X.5.1.23
   PubMed Web of Science ®Google Scholar
• Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122. doi:10.1007/BF02294746
   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. doi:10.1111/acer.2000.24.issue-6
   PubMed Web of Science ®Google Scholar
• Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463–469. doi:10.1111/j.0006-341X.1999.00463.x
   PubMed Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998–2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
   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. doi:10.1080/10705510701575396
   Web of Science ®Google Scholar
• Pianta, R. C., Belsky, J., Vandergrift, N., Houts, R., & Morrison, F. J. (2008). Classroom effects on children’s achievement trajectories in elementary school. American Educational Research Journal, 45, 365–397. doi:10.3102/0002831207308230
   Web of Science ®Google Scholar
• R Core Team. (2014). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333–343. doi:10.1007/BF02294360
   Web of Science ®Google Scholar
• Serang, S., Zhang, Z., Helm, J., Steele, J. S., & Grimm, K. J. (2015). Evaluation of a Bayesian approach to estimating nonlinear mixed-effects mixture models. Structural Equation Modeling, 22, 202–215. doi:10.1080/10705511.2014.937322
   Web of Science ®Google Scholar
• Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York, NY: Oxford University Press.
   Google Scholar
• 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, 583–639. doi:10.1111/rssb.2002.64.issue-4
   Web of Science ®Google Scholar
• Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van Der Linde, A. (2014). The deviance information criterion: 12 years on. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76, 485–493. doi:10.1111/rssb.2014.76.issue-3
   Web of Science ®Google Scholar
• Sterba, S. K. (2014). Fitting nonlinear latent growth curve models with individually varying time points. Structural Equation Modeling, 21, 630–647. doi:10.1080/10705511.2014.919828
   Web of Science ®Google Scholar
• Sturtz, S., Ligges, U., & Gelman, A. (2005). R2WinBUGS: A package for running WinBUGS from R. Journal of Statistical Software, 12, 1–16. doi:10.18637/jss.v012.i03
   Web of Science ®Google Scholar
• Timmons, A. C., & Preacher, K. J. (2015). The importance of temporal design: How do measurement intervals affect the accuracy and efficiency of parameter estimates in longitudinal research? Multivariate Behavioral Research, 50, 41–55. doi:10.1080/00273171.2014.961056
   PubMed Web of Science ®Google Scholar
• Tofighi, D., & Enders, C. K. (2008). Identifying 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). Charlotte, NC: Information Age.
   Google Scholar
• Usami, S. (2014). Performance of information criteria for model selection in a latent growth curve mixture model. Journal of the Japanese Society of Computational Statistics, 27, 17–48. doi:10.5183/jjscs.1309001_207
   Google Scholar