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Articles

Impact of Misspecifications of the Latent Variance–Covariance and Residual Matrices on the Class Enumeration Accuracy of Growth Mixture Models

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REFERENCES

  • Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317–332. doi:10.1007/BF02294359
  • Asparouhov, T., & Muthén, B. (2014). Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling, 21, 329–341. doi:10.1080/10705511.2014.915181
  • Bakk, Z., Oberski, D., & Vermunt, J. (2014). Relating latent class assignments to external variables: Standard errors for correct inference. Political Analysis, 22, 520–540. doi:10.1093/pan/mpu003
  • Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for over-extraction of latent classes. Psychological Methods, 8, 338–363. doi:10.1037/1082-989X.8.3.338
  • Bauer, D. J., & Curran, P. J. (2004). The integration of continuous and discrete latent variable models: Potential problems and promising opportunities. Psychological Methods, 9, 3–29. doi:10.1037/1082-989X.9.1.3
  • Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., … Fox, J. (2011). OpenMx: An open source extended structural equation modeling framework. Psychometrika, 76, 306–317. doi:10.1007/s11336-010-9200-6
  • Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley.
  • Boscardin, C. K., Muthén, B., Francis, D. J., & Baker, E. L. (2008). Early identification of reading difficulties using heterogeneous developmental trajectories. Journal of Educational Psychology, 100, 192–208. doi:10.1037/0022-0663.100.1.192
  • Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52, 345–370. doi:10.1007/BF02294361
  • Buyske, S. G. (2001). MMLCR, an Splus library for mixed-mode latent class regression. New Brunswick, NJ : Statistics Department, Rutgers University.
  • Chen, F., Bollen, K. A., Paxton, P., Curran, P. J., & Kirby, J. B. (2001). Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological Methods & Research, 29, 468–508. doi:10.1177/0049124101029004003
  • Cheong, J. (2011). Accuracy of estimates and statistical power for testing mediation in latent growth curve modeling. Structural Equation Modeling, 18, 195–211. doi:10.1080/10705511.2011.557334
  • Collins, L. M., Schafer, J. L., & Kam, C.-M. (2001). A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychological Methods, 6, 330–351. doi:10.1037/1082-989X.6.4.330
  • Depaoli, S. (2014). The impact of inaccurate “informative” priors for growth parameters in Bayesian growth mixture modeling. Structural Equation Modeling, 21, 239–252. doi:10.1080/10705511.2014.882686
  • Diallo, T. M. O., & Morin, A. J. S. (2015). Power of latent growth curve models to detect piecewise linear trajectories. Structural Equation Modeling, 22, 449–460. doi:10.1080/10705511.2014.935678
  • Diallo, T. M. O., Morin, A. J. S., & Parker, P. D. (2014). Statistical power of latent growth curve models to detect quadratic growth. Behavior Research Methods, 46, 357–371. doi:10.3758/s13428-013-0395-1
  • Enders, C. K., & Tofighi, D. (2008). The impact of misspecifying class-specific residual variances in growth mixture models. Structural Equation Modeling, 15, 75–95. doi:10.1080/10705510701758281
  • Fan, X., & Fan, X. (2005). Power of latent growth modeling for detecting linear growth: Number of measurements and comparison with other analytical approaches. The Journal of Experimental Education, 73, 121–139. doi:10.3200/JEXE.73.2.121-139
  • Fanti, K. A., & Henrich, C. C. (2010). Trajectories of pure and co-occurring internalizing and externalizing problems from age 2 to age 12: Findings from the National Institute of Child Health and Human Development Study of Early Child Care. Developmental Psychology, 46, 1159–1175. doi:10.1037/a0020659
  • Ferron, J., Dailey, R., & Yi, Q. (2002). Effects of misspecifying the first-level error structure in two-level models of change. Multivariate Behavioral Research, 37, 379–403. doi:10.1207/S15327906MBR3703_4
  • Genolini, C., & Falissard, B. (2011). Kml: A package to cluster longitudinal data. Computer Methods & Programs in Biomedicine, 104, e112–e121. doi:10.1016/j.cmpb.2011.05.008
  • Heggeseth, B., & Jewell, N. (2013). The impact of covariance misspecification in multivariate Gaussian mixtures on estimation and inference: An application to longitudinal modeling. Statistics in Medicine, 32, 2790-28-3. doi:10.1002/sim.5729
  • 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
  • Jones, B. L., Nagin, D. S., & Roeder, K. (2001). A SAS procedure based on mixture models for estimating developmental trajectories. Sociological Methods & Research, 29, 374–393. doi:10.1177/0049124101029003005
  • Kwok, O., Luo, W., & West, S. G. (2010). Using modification indexes to detect turning points in longitudinal data: A Monte Carlo study. Structural Equation Modeling, 17, 216–240. doi:10.1080/10705511003659359
  • Kwok, O.-M., West, S. G., & Green, S. B. (2007). The impact of misspecifying the within-subject covariance structure in multiwave longitudinal multilevel models: A Monte Carlo study. Multivariate Behavioral Research, 42, 557–592. doi:10.1080/00273170701540537
  • Li, L., & Hser, Y.-I. (2011). On inclusion of covariates for class enumeration of growth mixture models. Multivariate Behavioral Research, 46, 266–302. doi:10.1080/00273171.2011.556549
  • Lo, Y., Mendell, N., & Rubin, D. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767–778. doi:10.1093/biomet/88.3.767
  • Liu, M., & Hancock, G.R. (2014). Unrestricted mixture models for class identification in growth mixture modeling. Educational and Psychological Measurement, 74, 557–584. doi: 10.1177/0013164413519798
  • Lu, Z. L., Zhang, Z., & Lubke, G. (2011). Bayesian inference for growth mixture models with latent class dependent missing data. Multivariate Behavioral Research, 46, 567–597. doi:10.1080/00273171.2011.589261
  • Lubke, G., & Muthén, B. (2007). Performance of factor mixture models as a function of model size, criterion measure effects, and class-specific parameters. Structural Equation Modeling, 14, 26–47. doi:10.1080/10705510709336735
  • Lubke, G., & Neale, M. (2006). Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood? Multivariate Behavioral Research, 41, 499–532. doi:10.1207/s15327906mbr4104_4
  • Lubke, G., & Neale, M. (2008). Distinguishing between latent classes and continuous factors with categorical outcomes: Class invariance of parameters of factor mixture models? Multivariate Behavioral Research, 43, 592–620. doi:10.1080/00273170802490673
  • Magidson, J., & Vermunt, J. K. (2004). Latent class models. In D. Kaplan (Ed.), Handbook of quantitative methodology for the social sciences (pp. 175–198). Newbury Park, CA: Sage.
  • Marsh, H. W., Lüdtke, O., Trautwein, U., & Morin, A. J. S. (2009). Latent profile analysis of academic self-concept dimensions: Synergy of person- and variable-centered approaches to the internal/external frame of reference model. Structural Equation Modeling, 16, 1–35.
  • Martin, D. P., & Von Oertzen, T. (2015). Growth mixture models outperform simpler clustering algorithms when detecting longitudinal heterogeneity, even with small sample sizes. Structural Equation Modeling, 22, 264–275. doi:10.1080/10705511.2014.936340
  • McLachlan, G., & Peel, D. (2000). Finite mixture models. New York, NY: Wiley.
  • Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122. doi:10.1007/BF02294746
  • Morin, A. J. S., Maïano, C., Marsh, H. W., Nagengast, B., & Janosz, M. (2013). School life and adolescents’ self-esteem trajectories. Child Development, 84, 1967–1988. doi:10.1111/cdev.12089
  • Morin, A. J. S., Maïano, C., Nagengast, B., Marsh, H. W., Morizot, J., & Janosz, M. (2011). Growth mixture modeling of adolescents trajectories of anxiety across adolescence: The impact of untested invariance assumptions on substantive interpretations. Structural Equation Modeling, 18, 613–648. doi:10.1080/10705511.2011.607714
  • Morin, A. J. S., Rodriguez, D., Fallu, J.-S., Maïano, C., & Janosz, M. (2012). Academic achievement and adolescent smoking: A general growth mixture model. Addiction, 107, 819–828. doi:10.1111/j.1360-0443.2011.03725.x
  • 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.
  • Muthén, B., Brown, C. H., Masyn, K., Jo, B., Khoo, S. T., Yang, C. C., … Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3, 459–475. doi:10.1093/biostatistics/3.4.459
  • Muthén, B. O., & Muthén, L. (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/j.1530-0277.2000.tb02070.x
  • Muthén, B. O., & 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
  • Muthén, L. K., & Muthén, B. O. (1998-2014). Mplus user’s guide. Los Angeles, CA: Muthén & Muthén.
  • Nagin, D. S. (1999). Analyzing developmental trajectories: A semiparametric, group-based approach. Psychological Methods, 4, 139–157. doi:10.1037/1082-989X.4.2.139
  • Nagin, D. S. (2010). Group-based trajectory modeling: An overview. In A. R. Piquero & D. Weisburd (Eds.), Handbook of quantitative criminology (pp. 53–67). New York, NY: Springer.
  • 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, 14, 535–569. doi:10.1080/10705510701575396
  • Nagin, D.S., & Tremblay, R.E. (2005). Developmental trajectory groups: Fact or useful fiction? Criminology, 43, 873–904. doi: 10.1111/j.1745-9125.2005.00026.x
  • Pastor, D. A., & Gagné, P. (2013). Mean and covariance structure mixture models. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 343–393). Charlotte, NC: Information Age.
  • Peugh, J., & Fan, X. (2012). How well does growth mixture modeling identify heterogenous growth trajectories? A simulation study examining GMM’s performance characteristics. Structural Equation Modeling, 19, 204–226. doi:10.1080/10705511.2012.659618
  • Peugh, J., & Fan, X. (2013). Modeling unobserved heterogeneity using latent profile analysis: A Monte Carlo simulation. Structural Equation Modeling, 20, 616–639. doi:10.1080/10705511.2013.824780
  • Prince, M. A., & Maisto, S. A. (2013). The clinical course of alcohol use disorders: Using joinpoint analyses to aid in the interpretation of growth mixture models. Drug & Alcohol Dependence, 133, 433–439. doi:10.1016/j.drugalcdep.2013.06.033
  • Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). GLLAMM manual (U.C. Berkeley Division of Biostatistics Working Paper 160). University of California, Berkeley.
  • Raudenbush, S. W., & Liu, X. (2001). Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological Methods, 6, 387–401. doi:10.1037/1082-989X.6.4.387
  • Sampson, R. J. & Laub. J.H. (2005). Seductions of method: Rejoinder to Nagin and Tremblay's “Developmental trajectory groups: Fact or useful fiction?” Criminology, 43, 905–913. doi: 10.1111/j.1745-9125.2005.00027.x
  • Schaeffer, C. M., Petras, H., Ialongo, N., Poduska, J., & Kellam, S. (2003). Modeling growth in boys’ aggressive behaviour across elementary school: Links to later criminal involvement, conduct disorder, and antisocial personality disorder. Developmental Psychology, 39, 1020–1035. doi:10.1037/0012-1649.39.6.1020
  • Schwartz, G. (1978). Estimating the dimensions of a model. Annals of Statistics, 6, 461–464. doi:10.1214/aos/1176344136
  • Sclove, L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333–343. doi:10.1007/BF02294360
  • Sterba, S. K., Prinstein, M. J., & Cox, M. J. (2007). Trajectories of internalizing problems across childhood: Heterogeneity, external validity, and gender differences. Development and Psychopathology, 19, 345–366. doi:10.1017/S0954579407070174
  • Tein, J.-Y., Coxe, S., & Cham, H. (2013). Statistical power to detect the correct number of classes in latent profile analysis. Structural Equation Modeling, 20, 640–657. doi:10.1080/10705511.2013.824781
  • Tofighi, D., & Enders, C. K. (2007). 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.
  • Tolvanen, A. (2007). Latent growth mixture modeling: A simulation study ( Unpublished doctoral dissertation). Department of Mathematics, University of Jyvaskyla, Jyvaskyla, Finland.
  • Vermunt, J. K. (2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18, 450–469. doi:10.1093/pan/mpq025
  • Vermunt, J. K., & Magidson, J. (2005). Latent Gold 4.0 user’s guide. Belmont, MA: Statistical Innovations.
  • Vuong, Q. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57, 307–333. doi:10.2307/1912557
  • Wagmiller, R. L., Lennon, M. C., Kuang, L., Alberti, P. M., & Aber, J. L. (2006). The dynamics of economic disadvantage and children’s life chances. American Sociological Review, 71, 847–866. doi:10.1177/000312240607100507
  • Yang, C. (2006). Evaluating latent class analyses in qualitative phenotype identification. Computational Statistics & Data Analysis, 50, 1090–1104. doi:10.1016/j.csda.2004.11.004
  • Yu, C.Y. (2002). Evaluating cutoff criteria of model fit indices for latent variable models with binary and continuous outcomes. Doctoral dissertation, University of California, Los Angeles.

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