Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T21:55:41.440Z Has data issue: false hasContentIssue false
  • English
  • Français

A Monte Carlo evaluation of growth mixture modeling

Published online by Cambridge University Press:  15 March 2021

Tiffany M. Shader Open the ORCID record for Tiffany M. Shader [Opens in a new window]  and
Theodore P. Beauchaine Open the ORCID record for Theodore P. Beauchaine [Opens in a new window]
Tiffany M. Shader
Affiliation:
Department of Psychology, The Ohio State University, Columbus, OH, USA
Theodore P. Beauchaine*
Affiliation:
Department of Psychology, The Ohio State University, Columbus, OH, USA
*
Author for Correspondence: Theodore P. Beauchaine, Department of Psychology, The Ohio State University, 1835 Neil Avenue, Columbus, OH 43210; Email: beauchaine.1@osu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Growth mixture modeling (GMM) and its variants, which group individuals based on similar longitudinal growth trajectories, are quite popular in developmental and clinical science. However, research addressing the validity of GMM-identified latent subgroupings is limited. This Monte Carlo simulation tests the efficiency of GMM in identifying known subgroups (k = 1–4) across various combinations of distributional characteristics, including skew, kurtosis, sample size, intercept effect size, patterns of growth (none, linear, quadratic, exponential), and proportions of observations within each group. In total, 1,955 combinations of distributional parameters were examined, each with 1,000 replications (1,955,000 simulations). Using standard fit indices, GMM often identified the wrong number of groups. When one group was simulated with varying skew and kurtosis, GMM often identified multiple groups. When two groups were simulated, GMM performed well only when one group had steep growth (whether linear, quadratic, or exponential). When three to four groups were simulated, GMM was effective primarily when intercept effect sizes and sample sizes were large, an uncommon state of affairs in real-world applications. When conditions were less ideal, GMM often underestimated the correct number of groups when the true number was between two and four. Results suggest caution in interpreting GMM results, which sometimes get reified in the literature.

Keywords

growth mixture modelinglongitudinalMonte Carlosimulationlatent classes
Type
Regular Article
Information
Development and Psychopathology , Volume 34 , Issue 4 , October 2022 , pp. 1604 - 1617
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317–332. doi:10.1007/BF02294359CrossRefGoogle Scholar
Allan, N. P., Gros, D. F., Myers, U. S., Korte, K. J., & Acierno, R. (2017). Predictors and outcomes of growth mixture modeled trajectories across an exposure-based PTSD intervention with veterans. Journal of Clinical Psychology, 73, 1048–1063. doi:10.1002/jclp.22408CrossRefGoogle ScholarPubMed
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Arlington, VA: Author.Google Scholar
Arnold, L. E., Ganocy, S. J., Mount, K., Youngstrom, E. A., Frazier, T., Fristad, M., … Marsh, L. (2014). Three-year latent class trajectories of attention-deficit/hyperactivity disorder (ADHD) symptoms in a clinical sample not selected for ADHD. Journal of the American Academy of Child and Adolescent Psychiatry, 53, 745–760. doi:10.1016/j.jaac.2014.03.007CrossRefGoogle Scholar
Bauer, D. J., & Curran, P. J. (2003a). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338–363. doi:10.1037/1082-989X.8.3.338CrossRefGoogle Scholar
Bauer, D. J., & Curran, P. J. (2003b). Overextraction of latent trajectories: Reply to Rindskopf (2003), Muthén (2003), and Cudeck and Henly (2003). Psychological Methods, 8, 384–393. doi:10.1037/1082-989X.8.3.384CrossRefGoogle Scholar
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.9.1.3Google ScholarPubMed
Bauer, D. J., & Reyes, H. L. (2010). Modeling variability in individual development: Differences of degree or kind? Child Development Perspectives, 4, 114–122. doi:10.1111/j.1750-8606.2010.00129.xCrossRefGoogle ScholarPubMed
Beauchaine, T. P. (2007). A brief taxometrics primer. Journal of Clinical Child and Adolescent Psychology, 36, 654–676. doi:10.1080/15374410701662840CrossRefGoogle ScholarPubMed
Beauchaine, T. P. (2013). Taxometrics. In Little, T. D. (Ed.), The Oxford handbook of quantitative methods (Vol. 2, pp. 612–634). New York, NY: Oxford University Press.Google Scholar
Beauchaine, T. P., & Beauchaine, R. J. (2002). A comparison of maximum covariance and k-means cluster analysis in classifying cases into known taxon groups. Psychological Methods, 7, 245–261. doi:10.1037/1082-989x.7.2.245CrossRefGoogle ScholarPubMed
Beauchaine, T. P., & Constantino, J. N. (2017). Redefining the endophenotype concept to accommodate transdiagnostic vulnerabilities and etiological complexity. Biomarkers in Medicine, 11, 769–780. doi:10.221/bmm-2017-0002CrossRefGoogle ScholarPubMed
Beauchaine, T. P., & Hinshaw, S. P. (2020). RDoc and psychopathology among youth: Misplaced assumptions and an agenda for future research. Journal of Clinical Child and Adolescent Psychology, 49, 322–340. doi:10.1080/15374416.2020.1750022CrossRefGoogle Scholar
Beauchaine, T. P., Lenzenweger, M. F., & Waller, N. (2008). Schizotypy, taxometrics, and disconfirming theories in soft science. Personality and Individual Differences, 44, 1652–1662. doi:10.1016/j.paid.2007.11.015CrossRefGoogle Scholar
Beauchaine, T. P., & Marsh, P. (2006). Taxometric methods: Enhancing early detection and prevention of psychopathology by identifying latent vulnerability traits. In Cicchetti, D. & Cohen, D. (Eds.), Developmental psychopathology: Vol 1: Theory and method (2nd ed., pp. 931–967). Hoboken, NJ: Wiley.Google Scholar
Beauchaine, T. P., & Tackett, J. L. (2020). Irritability as a transdiagnostic vulnerability trait: Current issues and future directions. Behavior Therapy, 51, 350–364. doi:10.1016/j.beth.2019.10.009CrossRefGoogle ScholarPubMed
Beauchaine, T. P., & Waters, E. (2003). Pseudotaxonicity in MAMBAC and MAXCOV analyses of rating scale data: Turning continua into classes by manipulating observer's expectations. Psychological Methods, 8, 3–15. doi:10.1037/1082-989X.8.1.3CrossRefGoogle ScholarPubMed
Beauchaine, T. P., Zisner, A., & Sauder, C. L. (2017). Trait impulsivity and the externalizing spectrum. Annual Review of Clinical Psychology, 13, 343–368. doi:10.1146/annurev-clinpsy-021815-093253CrossRefGoogle ScholarPubMed
Bergmann, C., Tsuji, S., Piccinini, P. E., Lewis, M. L., Braginsky, M., Frank, M. C., & Cristia, A. (2018). Promoting replicability in developmental research through meta-analyses: Insights from language acquisition research. Child Development, 89, 1996–2009. doi:10.1111/cdev.13079CrossRefGoogle ScholarPubMed
Biernacki, C., Celeux, G., & Govaert, G. (2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 719–725. doi:10.1109/34.865189CrossRefGoogle Scholar
Biernacki, C., & Govaert, G. (1999). Choosing models in model-based clustering and discriminant analysis. Journal of Statistical Computation and Simulation, 64, 49–71. doi:10.1080/00949659908811966CrossRefGoogle Scholar
Blashfield, R. K., & Aldenderfer, M. S. (1978). The literature on cluster analysis. Multivariate Behavioral Research, 13, 271–295. doi:10.1207/s15327906mbr1303_2CrossRefGoogle ScholarPubMed
Blashfield, R. K., & Aldenderfer, M. S. (1988). The methods and problems of cluster analysis. In Nesselroade, J. R. & Cattell, R. B. (Eds.), Handbook of multivariate experimental psychology (2nd ed., pp. 447–473). New York, NY: Plenum Press.CrossRefGoogle Scholar
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:10.1037/0022-0663.100.1.192CrossRefGoogle Scholar
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/BF02294361CrossRefGoogle Scholar
Brendgen, M., Girard, A., Vitaro, F., Dionne, G., & Boivin, M. (2016). Personal and familial predictors of peer victimization trajectories from primary to secondary school. Developmental Psychology, 52, 1103–1114. doi:10.1037/dev0000107CrossRefGoogle ScholarPubMed
Brooks-Russell, A., Foshee, V. A., & Ennett, S. T. (2013). Predictors of latent trajectory classes of physical dating violence victimization. Journal of Youth and Adolescence, 42, 566–580. doi:10.1007/s10964-012-9876-2CrossRefGoogle ScholarPubMed
Celeux, G., & Soromenho, G. (1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classification, 13, 195–212. doi:10.1007/BF01246098CrossRefGoogle Scholar
Chen, Q., Kwok, O., Luo, W., & Willson, V. L. (2010). The impact of ignoring a level of nesting structure in multilevel growth mixture models: A Monte Carlo study. Structural Equation Modeling, 17, 570–589. doi:10.1080/10705511.2010.510046CrossRefGoogle Scholar
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Earlbaum.Google Scholar
Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis: With application in the social, behavioral, and health sciences. Hoboken, NJ: Wiley.Google Scholar
Connell, A. M., & Frye, A. A. (2006). Growth mixture modelling in developmental psychology: Overview and demonstration of heterogeneity in developmental trajectories of adolescent antisocial behaviour. Infant and Child Development, 15, 609–621. doi:10.1002/icd.481CrossRefGoogle Scholar
Depaoli, S. (2013). Mixture class recovery in GMM under varying degrees of class separation: Frequentist versus Bayesian estimation. Psychological Methods, 18, 186–219. doi:10.1037/a0031609CrossRefGoogle ScholarPubMed
Depaoli, S., Winter, S. D., Lai, K., & Guerra-Peña, K. (2019). Implementing continuous non-normal skewed distributions in latent growth mixture modeling: An assessment of specification errors and class enumeration. Multivariate Behavioral Research, 54, 795–821. doi:10.1080/00273171.2019.1593813CrossRefGoogle ScholarPubMed
Depaoli, S., Yang, Y., & Felt, J. (2017). Using Bayesian statistics to model uncertainty in mixture models: A sensitivity analysis of priors. Structural Equation Modeling, 24, 198–215. doi:10.1080/10705511.2016.1250640CrossRefGoogle Scholar
Dolan, C. V., Schmittmann, V. D., Lubke, G. H., & Neale, M. C. (2005). Regime switching in the latent growth curve mixture model. Structural Equation Modeling, 12, 94–119. doi:10.1207/s15328007sem1201_5CrossRefGoogle Scholar
D'Unger, A., Land, K., McCall, P., & Nagin, D. (1998). How many latent classes of delinquent/criminal careers? Results from mixed Poisson regression analyses of the London, Philadelphia, and Racine cohorts studies. American Journal of Sociology, 103, 1593–1630. doi:10.1086/231402CrossRefGoogle Scholar
Everitt, B. S., & Howell, D. C. (2005). Cluster analysis: Overview. In Everitt, B. S., & Howell, D. (Eds.), Encyclopedia of statistics in behavioral science (Vol. 1, pp. 305–315). Hoboken, NJ: Wiley.CrossRefGoogle Scholar
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/a0020659CrossRefGoogle ScholarPubMed
Feldman, B. J., Masyn, K. E., & Conger, R. D. (2009). New approaches to studying problem behaviors: A comparison of methods for modeling longitudinal, categorical adolescent drinking data. Developmental Psychology, 45, 652–676. doi:10.1037/a0014851CrossRefGoogle ScholarPubMed
Fialkowski, A. C. (2018). SimMultiCorrData: Simulation of Correlated Data with Multiple Variable Types. R package version 0.2.2. https://CRAN.R-project.org/package=SimMultiCorrDataGoogle Scholar
Fleishman, A. I. (1978). A method for simulating nonnormal distribution. Psychometrika, 43, 521–532. doi:10.1007/BF02293811CrossRefGoogle Scholar
Fontaine, N. G., McCrory, E. P., Boivin, M., Moffitt, T. E., & Viding, E. (2011). Predictors and outcomes of joint trajectories of callous–unemotional traits and conduct problems in childhood. Journal of Abnormal Psychology, 120, 730–742. doi:10.1037/a0022620CrossRefGoogle ScholarPubMed
Fredriksen, E., von Soest, T., Smith, L., & Moe, V. (2017). Patterns of pregnancy and postpartum depressive symptoms: Latent class trajectories and predictors. Journal of Abnormal Psychology, 126, 173–183. doi:10.1037/abn0000246CrossRefGoogle ScholarPubMed
Garg, R. K. (1996). The influence of positive and negative wording and issue involvement on responses to Likert scales in marketing research. Journal of the Market Research Society, 38, 235–246. doi:10.1177/147078539603800304CrossRefGoogle Scholar
Grimm, K. J., Ram, N., Shiyko, M. P., & Lo, L. L. (2014). Simulation study of the ability of growth mixture models to uncover growth heterogeneity. In McArdle, J. J. & Ritschard, G. (Eds.), Quantitative methodology series. Contemporary issues in exploratory data mining in the behavioral sciences (pp. 172–189). New York, NY: Routledge/Taylor and Francis Group.Google Scholar
Guerra-Peña, K., García-Batista, Z. E., Depaoli, S., & Garrido, L. E. (2020). Class enumeration false positive in skew-t family of continuous growth mixture models. PLoS One, 15, e0231525. doi:10.1371/journal.pone.0231525CrossRefGoogle ScholarPubMed
Hallquist, M. N., & Lenzenweger, M. F. (2013). Identifying latent trajectories of personality disorder symptom change: Growth mixture modeling in the longitudinal study of personality disorders. Journal of Abnormal Psychology, 122, 138–155. doi:10.1037/a0030060CrossRefGoogle ScholarPubMed
Hallquist, M. N., & Wiley, J. F. (2018). MplusAutomation: An R package for facilitating large-scale latent variable analyses in Mplus. Structural Equation Modeling, 25, 621–638. doi:10.1080/10705511.2017.140233CrossRefGoogle Scholar
Harring, J. R., & Hodis, F. A. (2016). Mixture modeling: Applications in educational psychology. Educational Psychologist, 51, 354–367. doi:10.1080/00461520.2016.1207176Google Scholar
Haslam, N. (2019). Unicorns, snarks, and personality types: A review of the first 102 taxometric studies of personality. Australian Journal of Psychology, 71, 39–49. doi:10.1111/ajpy.12228CrossRefGoogle Scholar
Haslam, N., & Kim, H. C. (2002). Categories and continua: A review of taxometric research. Genetic, Social, and General Psychology Monographs, 128, 271–320.Google ScholarPubMed
Hipp, J. R., & Bauer, D. J. (2006). Local solutions in the estimation of growth mixture models. Psychological Methods, 11, 36–53. doi:10.1037/1082-989X.11.1.36CrossRefGoogle ScholarPubMed
Hoeksma, J. B., & Kelderman, H. (2006). On growth curves and mixture models. Infant and Child Development, 15, 627–634. doi:10.1002/icd.483CrossRefGoogle Scholar
Hoyt, W. T., & Kerns, M. D. (1999). Magnitude and moderators of bias in observer ratings: A meta-analysis. Psychological Methods, 4, 403–424. doi:10.1037/1082-989X.4.4.403CrossRefGoogle Scholar
Insel, T., Cuthbert, B., Garvey, M., Heinssen, R., Pine, D. S., Quinn, K., … Wang, P. (2010). Research domain criteria (RDoc): Toward a new classification framework for research on mental disorders. American Journal of Psychiatry, 167, 748–751. doi:10.1176/appi.ajp.2010.09091379CrossRefGoogle Scholar
Jinnin, R., Okamoto, Y., Takagaki, K., Nishiyama, Y., Yamamura, T., Okamoto, Y., … Yamawaki, S. (2016). Detailed course of depressive symptoms and risk for developing depression in late adolescents with subthreshold depression: A cohort study. Neuropsychiatric Disease and Treatment, 13, 25–33. doi:10.2147/NDT.S117846CrossRefGoogle ScholarPubMed
Jung, T., & Wickrama, K. S. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2, 302–317. doi:10.1111/j.1751-9004.2007.00054.xCrossRefGoogle Scholar
Kim, S. (2012). Sample size requirements in single- and multiphase growth mixture models: A Monte Carlo simulation study. Structural Equation Modeling, 19, 457–476. doi:10.1080/10705511.2012.687672CrossRefGoogle Scholar
Kotov, R., Krueger, R. F., Watson, D., Achenbach, T. M., Althoff, R. R., Bagby, R. M., … Wright, A. G. C. (2017). The hierarchical taxonomy of psychopathology (HiTOP): A dimensional alternative to traditional nosologies. Journal of Abnormal Psychology, 126, 454–477. doi:10.1037/abn0000258CrossRefGoogle ScholarPubMed
Krueger, R. F., Kotov, R., Watson, D., Forbes, M. K., Eaton, N. R., Ruggero, C. J., … Zimmerman, J. (2018). Progress in achieving quantitative classification of psychopathology. World Psychiatry, 17, 282–293. doi:10.1002/wps.20566CrossRefGoogle ScholarPubMed
Krueger, R. F., & Piasecki, T. M. (2002). Toward a dimensional and psychometrically-informed approach to conceptualizing psychopathology. Behavior Research and Therapy, 40, 485–499. doi:10.1016/s0005-7967(02)00016-5CrossRefGoogle Scholar
Kwon, S., Janz, K. F., Letuchy, E. M., Burns, T. L., & Levy, S. M. (2015). Developmental trajectories of physical activity, sports, and television viewing during childhood to young adulthood. JAMA Pediatrics, 169, 666–672. doi:10.1001/jamapediatrics.2015.0327CrossRefGoogle ScholarPubMed
Lanza, S. T., & Collins, L. M. (2006). A mixture model of discontinuous development in heavy drinking from ages 18 to 30: The role of college enrollment. Journal of Studies on Alcohol, 67, 552–561. doi:10.15288/jsa.2006.67.552CrossRefGoogle ScholarPubMed
Lazarsfeld, P. F. (1950). The logical and mathematical foundation of latent structure analysis. In Stouffer, S. A., Guttman, L., Suchman, E. A., Lazarsfeld, P. F., Star, S. A. & Clausen, J. A. (Eds.), Measurement and prediction (pp. 362–412). Princeton, NJ: Princeton University Press.Google Scholar
Lazarsfeld, P. F. (1955). Recent developments in latent structure analysis. Sociometry, 18, 391–403. doi:10.2307/2785875CrossRefGoogle Scholar
Lee, T. K., Wickrama, K. S., O'Neal, C. W., & Lorenz, F. O. (2017). Social stratification of general psychopathology trajectories and young adult social outcomes: A second-order growth mixture analysis over the early life course. Journal of Affective Disorders, 208, 375–383. doi:10.1016/j.jad.2016.08.037CrossRefGoogle Scholar
Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767–778. doi:10.1093/biomet/88.3.767CrossRefGoogle Scholar
MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19–40. doi:10.1037/1082-989X.7.1.19CrossRefGoogle ScholarPubMed
Macmillan, N. A., & Creelman, C. D. (1990). Response bias: Characteristics of detection theory, threshold theory and “nonparametric” indices. Psychological Bulletin, 107, 401–413. doi:10.1037/0033-2909.107.3.401CrossRefGoogle Scholar
Masyn, K. E. (2013). Latent class analysis and finite mixture modeling. In Little, T. D. (Ed.), The Oxford handbook of quantitative methods (Vol. 2, pp. 551–611). New York, NY: Oxford University Press.Google Scholar
McLachlan, G., & Peel, D. (2000). Finite mixture models. New York, NY: Wiley.CrossRefGoogle Scholar
Meehl, P. E. (1992). Factors and taxa, traits and types, differences of degree and differences in kind. Journal of Personality, 60, 117–174. doi:10.1111/j.1467-6494.1992.tb00269.xCrossRefGoogle Scholar
Meehl, P. E. (1995). Bootstraps taxometrics: Solving the classification problem in psychopathology. American Psychologist, 50, 266–275. doi:10.1037/0003-066X.50.4.266CrossRefGoogle ScholarPubMed
Milligan, G. W. (1980). An examination of the effects of six types of error perturbation on fifteen clustering algorithms. Psychometrika, 45, 325–342. doi:10.1007/BF02293907CrossRefGoogle Scholar
Montroy, J. J., Bowles, R. P., Skibbe, L. E., McClelland, M. M., & Morrison, F. J. (2016). The development of self-regulation across early childhood. Developmental Psychology, 52, 1744–1762. doi:10.1037/dev0000159CrossRefGoogle ScholarPubMed
Munson, J., Dawson, G., Sterling, L., Beauchaine, T., Zhou, A., Koehler, E., … Abbott, R. (2008). Evidence for latent classes of IQ in young children with autism spectrum disorder. American Journal on Mental Retardation, 113, 439–452. doi:10.1352/2008.113:439-452CrossRefGoogle ScholarPubMed
Muthén, B. (2004). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In Kaplan, D. (Ed.), Handbook of quantitative methodology for the social sciences (pp. 345–368). Newbury Park, CA: Sage.Google Scholar
Muthén, B. (2006). The potential of growth mixture modelling. Infant and Child Development, 15, 623–625. doi:10.1002/icd.482CrossRefGoogle Scholar
Muthén, B., & Asparouhov, T. (2015). Growth mixture modeling with non-normal distributions. Statistics in Medicine, 34, 1041–1058. doi:10.1002/sim.6388CrossRefGoogle ScholarPubMed
Muthén, B. O., & Khoo, S. (1998). Longitudinal studies of achievement growth using latent variable modeling. Learning and Individual Differences, 10, 73–101. doi:10.1016/S1041-6080(99)80135-6CrossRefGoogle 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/j.1530-0277.2000.tb02070.xCrossRefGoogle ScholarPubMed
Muthén, L. K., & Muthén, B. O. (2015). Mplus user's guide (7th ed.). Los Angeles, CA: Muthén & Muthén.Google Scholar
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.xCrossRefGoogle ScholarPubMed
Nagin, D. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4, 139–157. doi:10.1037/1082-989X.4.2.139CrossRefGoogle Scholar
Nagin, D. S. (2005). Group-based modeling of development. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Nagin, D. S., & Tremblay, R. E. (2001). Analyzing developmental trajectories of distinct but related behaviors: A group-based method. Psychological Methods, 6, 18–34. doi:10.1037/1082-989X.6.1.18CrossRefGoogle ScholarPubMed
National Institute of Mental Health. (2019). RDoC Matrix. retrieved from https://www.nimh.nih.gov/research/research-funded-by-nimh/rdoc/constructs/rdoc-matrix.shtml on 9/20/2019.Google Scholar
Nkansah-Amankra, S. (2013). Adolescent suicidal trajectories through young adulthood: Prospective assessment of religiosity and psychosocial factors among a population-based sample in the United States. Suicide and Life-Threatening Behavior, 43, 439–459. doi:10.1111/sltb.12029CrossRefGoogle ScholarPubMed
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:10.1080/10705510701575396CrossRefGoogle Scholar
Odgers, C. L., Moffitt, T. E., Broadbent, J. M., Dickson, N., Hancox, R. J., Harrington, H., … Caspi, A. (2008). Female and male antisocial trajectories: From childhood origins to adult outcomes. Development and Psychopathology, 20, 673–716. doi:10.1017/S0954579408000333CrossRefGoogle ScholarPubMed
Oshri, A., Carlson, M. W., Kwon, J. A., Zeichner, A., & Wickrama, K. S. (2017). Developmental growth trajectories of self-esteem in adolescence: Associations with child neglect and drug use and abuse in young adulthood. Journal of Youth and Adolescence, 46, 151–164. doi:10.1007/s10964-016-0483-5CrossRefGoogle ScholarPubMed
Papalia, N. L., Luebbers, S., Ogloff, J. R., Cutajar, M., & Mullen, P. E. (2017). Exploring the longitudinal offending pathways of child sexual abuse victims: A preliminary analysis using latent variable modeling. Child Abuse and Neglect, 66, 84–100. doi:10.1016/j.chiabu.2017.01.005CrossRefGoogle ScholarPubMed
Passarotti, A. M., Crane, N. A., Hedeker, D., & Mermelstein, R. J. (2015). Longitudinal trajectories of marijuana use from adolescence to young adulthood. Addictive Behaviors, 45, 301–308. doi:10.1016/j.addbeh.2015.02.008CrossRefGoogle ScholarPubMed
Pepe, M. S., & Janes, H. (2006). Insights into latent class analysis of diagnostic test performance. Biostatistics, 8, 474–484. doi:10.1093/biostatistics/kxl038CrossRefGoogle ScholarPubMed
Peugh, J., & Fan, X. (2012). How well does growth mixture modeling identify heterogeneous growth trajectories? A simulation study examining GMM's performance characteristics. Structural Equation Modeling, 19, 204–226. doi:10.1080/10705511.2012.659618CrossRefGoogle Scholar
Ram, N., & Grimm, K. J. (2009). Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. International Journal of Behavioral Development, 33, 565–576. doi:10.1177/0165025409343765CrossRefGoogle ScholarPubMed
R Core Team. (2013). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org/.Google Scholar
Ruscio, J., & Ruscio, A. M. (2004). Clarifying boundary issues in psychopathology: The role of taxometrics in a comprehensive program of structural research. Journal of Abnormal Psychology, 113, 24–38. doi:10.1037/0021-843X.113.1.24CrossRefGoogle Scholar
Schwartz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464. doi:10.1214/aos/1176344136Google 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:10.1080/10705511.2014.937322CrossRefGoogle Scholar
Sokal, R. R., & Sneath, P. H. (1963). Principles of numerical taxonomy. San Francisco, CA: Freeman.Google Scholar
Spinhoven, P., Batelaan, N., Rhebergen, D., van Balkom, A., Schoevers, R., & Penninx, B. W. (2016). Prediction of 6-yr symptom course trajectories of anxiety disorders by diagnostic, clinical and psychological variables. Journal of Anxiety Disorders, 44, 92–101. doi:10.1016/j.janxdis.2016.10.011CrossRefGoogle ScholarPubMed
Tueller, S., & Lubke, G. (2010). Evaluation of structural equation mixture models: Parameter estimates and correct class assignment. Structural Equation Modeling, 17, 165–192. doi:10.1080/10705511003659318CrossRefGoogle ScholarPubMed
Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293–315. doi:10.1.1.304.6549CrossRefGoogle Scholar
Westland, C. J. (2010). Lower bounds on sample size in structural equation modeling. Electronic Commerce Research and Applications, 9, 476–487. doi:10.1016/j.elerap.2010.07.003CrossRefGoogle Scholar
Supplementary material: File

Shader and Beauchaine supplementary material

Appendix B

Download Shader and Beauchaine supplementary material(File)
File 58 KB
Supplementary material: File

Shader and Beauchaine supplementary material

Appendix A

Download Shader and Beauchaine supplementary material(File)
File 2.1 MB