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Effects of distance and shape on the estimation of the piecewise growth mixture model. (English) Zbl 1436.62274

J. Classif. 36, No. 3, 659-677 (2019); erratum ibid. 36, No. 3, 678 (2019).
Summary: The piecewise growth mixture model is used in longitudinal studies to tackle non-continuous trajectories and unobserved heterogeneity in a compound way. This study investigated how factors such as latent distance and shape influence the model. Two simulation studies were used exploring the 2- and 3-class situation with sample size, latent distance (Mahalanobis distance), and shape being considered as the influencing factor. The results of two simulations showed that a non-parallel shape led to a slightly better overall model fit. Parameter estimation is affected by the shape, mainly through the parameter differences between latent classes.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H11 Directional data; spatial statistics
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[1] Bauer, Dj; Curran, Pj, Distributional assumptions of growth mixture models: implications for overextraction of latent trajectory classes, Psychological Methods, 8, 3, 338-363 (2003)
[2] Bauer, Dj; Curran, Pj, Overextraction of latent trajectory classes: much ado about nothing? Reply to Rindskopf (2003), Muthén (2003), and Cudeck and Henly (2003), Psychological Methods, 8, 3, 384-393 (2003)
[3] Depaoli, S., Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation, Psychological Methods, 18, 2, 186-219 (2013)
[4] Duncan, Sc; Duncan, Te, Modeling incomplete longitudinal substance use data using latent variable growth curve methodology, Multivariate Behavioral Research, 29, 4, 313-338 (1994)
[5] Duncan, Te; Duncan, Sc, Modeling the processes of development via latent variable growth curve methodology, Structural Equation Modeling: A Multidisciplinary Journal, 2, 3, 187-213 (1995)
[6] Duncan, Te; Duncan, Sc; Alpert, A.; Hops, H.; Stoolmiller, M.; Muthen, B., Latent variable modeling of longitudinal and multilevel substance use data, Multivariate Behavioral Research, 32, 3, 275-318 (1997)
[7] Dziak, Jj; Lanza, St; Tan, X., Effect size, statistical power and sample size requirements for the bootstrap likelihood ratio test in latent class analysis, Structural Equation Modeling: A Multidisciplinary Journal, 21, 4, 534-552 (2014)
[8] Gudicha, Dw; Schmittmann, Vd; Tekle, Fb; Vermunt, Jk, Power analysis for the likelihood-ratio test in latent Markov models: shortcutting the bootstrap p-value-based method, Multivariate Behavioral Research, 51, 5, 649-660 (2016)
[9] Guerra-Peña, K.; Steinley, D., Extracting spurious latent classes in growth mixture modeling with nonnormal errors, Educational and Psychological Measurement, 76, 6, 933-953 (2016)
[10] Henson, Jm; Reise, Sp; Kim, Kh, Detecting mixtures from structural model differences using latent variable mixture modeling: a comparison of relative model fit statistics, Structural Equation Modeling: A Multidisciplinary Journal, 14, 2, 202-226 (2007)
[11] Jung, T.; Wickrama, Kas, An introduction to latent class growth analysis and growth mixture modeling, Social and Personality Psychology Compass, 2, 1, 302-317 (2008)
[12] Kainz, K.; Vernon-Feagans, L., The ecology of early reading development for children in poverty, Elementary School Journal, 107, 5, 407-427 (2007)
[13] Kamata, A.; Nese, Jf; Patarapichayatham, C.; Lai, C-F, Modeling nonlinear growth with three data points: illustration with benchmarking data, Assessment for Effective Intervention, 1534508412457872, 105-116 (2012)
[14] Kim, Sy, Determining the number of latent classes in single- and multi-phase growth mixture models, Structural Equation Modeling: A Multidisciplinary Journal, 21, 2, 263-279 (2014)
[15] Kohli, N.; Harring, Jr, Modeling growth in latent variables using a piecewise function, Multivariate Behavioral Research, 48, 3, 370-397 (2013)
[16] Kohli, N.; Hughes, Jr; Wang, C.; Zopluoglu, C.; Davison, Ml, Fitting a linear-linear piecewise growth mixture model with unknown knots: a comparison of two common approaches to inference, Psychological Methods, 20, 2, 259-275 (2015)
[17] Kohli, N.; Hughes, Jr; Zopluoglu, C., A finite mixture of nonlinear random coefficient models for continuous repeated measures data, Psychometrika, 81, 3, 851-880 (2016) · Zbl 1345.62153
[18] Li, F.; Duncan, Te; Duncan, Sc; Hops, H., Piecewise growth mixture modeling of adolescent alcohol use data, Structural Equation Modeling: A Multidisciplinary Journal, 8, 2, 175-204 (2001)
[19] Liu, Y.; Liu, H.; Li, H.; Zhao, Q., The effects of individually varying times of observations on growth parameter estimations in piecewise growth model, Journal of Applied Statistics, 42, 9, 1843-1860 (2015)
[20] Liu, Y.; Liu, H.; Hau, K-T, Reading ability development from kindergarten to junior secondary: latent transition analyses with growth mixture modeling, Frontiers in Psychology, 7, 1659 (2016)
[21] Liu, Y., Zhao, Q., & Liu, H. (2013). Methods comparison of piecewise growth modeling. Psychological Exploration, 33(5), 415-422. 10.3969/j.issn.1003-5184.2013.05.006.
[22] Lo, Y.; Mendell, Nr; Rubin, Db, Testing the number of components in a normal mixture, Biometrika, 88, 3, 767-778 (2001) · Zbl 0985.62019
[23] Lubke, G.; Muthén, Bo, Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters, Structural Equation Modeling: A Multidisciplinary Journal, 14, 1, 26-47 (2007)
[24] Lubke, G.; Neale, Mc, Distinguishing between latent classes and continuous factors: resolution by maximum likelihood?, Multivariate Behavioral Research, 41, 4, 499-532 (2006)
[25] Lubke, G.; Neale, Mc, Distinguishing between latent classes and continuous factors with categorical outcomes: class invariance of parameters of factor mixture models, Multivariate Behavioral Research, 43, 4, 592-620 (2008)
[26] Lubke, G.; Tueller, S., Latent class detection and class assignment: a comparison of the MAXEIG taxometric procedure and factor mixture modeling approaches, Structural Equation Modeling: A Multidisciplinary Journal, 17, 4, 605-628 (2010)
[27] Mcardle, Jj; Epstein, D., Latent growth curves within developmental structural equation models, Child Development, 58, 110-133 (1987)
[28] Mcauley, E.; Mailey, El; Mullen, Sp; Szabo, An; Wójcicki, Tr; White, Sm, Growth trajectories of exercise self-efficacy in older adults: Influence of measures and initial status, Health Psychology, 30, 1, 75-83 (2011)
[29] Mclachlan, Gj, On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture, Journal of the Royal Statistical Society, 36, 3, 318-324 (1987)
[30] Muthén, Bo, Beyond SEM: general latent variable modeling, Behaviormetrika, 29, 1, 81-117 (2002) · Zbl 1017.62125
[31] Muthén, Bo; Kaplan, D., Latent variable analysis: growth mixture modeling and related techniques for longitudinal data, The SAGE handbook of quantitative methodology for the social sciences, 346-370 (2004), Thousand Oaks, CA: SAGE Publications, Inc., Thousand Oaks, CA
[32] Muthén, Bo; Brown, Hc, Estimating drug effects in the presence of placebo response: causal inference using growth mixture modeling, Statistics in Medicine, 28, 27, 3363-3385 (2009)
[33] Muthén, Bo; Shedden, K., Finite mixture modeling with mixture outcomes using the EM algorithm, Biometrics, 55, 2, 463-469 (1999) · Zbl 1059.62599
[34] Nylund, Kl; Asparouhov, T.; Muthén, Bo, Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study, Structural Equation Modeling: A Multidisciplinary Journal, 14, 4, 535-569 (2007)
[35] Peugh, J.; Fan, X., How well does growth mixture modeling identify heterogeneous growth trajectories? A simulation study examining GMM’s performance characteristics, Structural Equation Modeling: A Multidisciplinary Journal, 19, 2, 204-226 (2012)
[36] Preacher, Kj; Merkle, Ec, The problem of model selection uncertainty in structural equation modeling, Psychological Methods, 17, 1, 1-14 (2012)
[37] Raudenbush, Sw; Bryk, As, Hierarchical linear models: applications and data analysis methods (2002), Thousand Oaks: Sage, Thousand Oaks
[38] Snijders, T.; Bosker, R., Multilevel modeling: an introduction to basic and advanced multilevel modeling (1999), Newbury Park: Sage, Newbury Park · Zbl 0953.62127
[39] Tekle, Fb; Gudicha, Dw; Vermunt, Jk, Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models, Advances in Data Analysis and Classification, 10, 2, 209-224 (2016) · Zbl 1414.62061
[40] 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: Information Age Publishing.
[41] Tolvanen, A. (2007). Latent growth mixture modeling: a simulation study. (Doctoral dissertation), University of Jyväskylä, Finland. · Zbl 1153.65012
[42] Tourangeau, K.; Nord, C.; Lê, T.; Sorongon, A.; Najarian, M.; Hausken, E., Early childhood longitudinal study, kindergarten class of 1998-99 (ECLS-K), combined user’s manual for the ECLS-K eighth-grade and K-8 full sample data files and electronic codebooks (NCES 2009-004) (2009), Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education, Washington, DC
[43] Tueller, S.; Lubke, G., Evaluation of structural equation mixture models: parameter estimates and correct class assignment, Structural Equation Modeling: A Multidisciplinary Journal, 17, 2, 165-192 (2010)
[44] Wang, L.; Mcardle, Jj, A simulation study comparison of Bayesian estimation with conventional methods for estimating unknown change points, Structural Equation Modeling: A Multidisciplinary Journal, 15, 1, 52-74 (2008)
[45] Yang, C-C, Evaluating latent class analysis models in qualitative phenotype identification, Computational Statistics & Data Analysis, 50, 4, 1090-1104 (2006) · Zbl 1431.62516
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