Methods and measures: growth mixture modeling: a method for identifying differences in longitudinal change among unobserved groups
Open accessAbstract
Growth mixture modeling (GMM) is a method for identifying multiple unobserved sub-populations, describing longitudinal change within each unobserved sub-population, and examining differences in change among unobserved sub-populations. We provide a practical primer that may be useful for researchers beginning to incorporate GMM analysis into their research. We briefly review basic elements of the standard latent basis growth curve model, introduce GMM as an extension of multiple-group growth modeling, and describe a four-step approach to conducting a GMM analysis. Example data from a cortisol stress-response paradigm are used to illustrate the suggested procedures.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Growth mixture modeling is a statistical method designed to identify classes of individuals who are homogeneous in terms of their longitudinal change in a set of variables of interest.
“Growth mixture modeling (GMM) is a statistical method designed to identify classes of 90 individuals who are homogeneous in terms of their longitudinal change in a set of 91 variables of interest (Muthén, 2006; Ram and Grimm, 2009).”
From Time in treatment: Examining mental illness trajectories across inpatient psychiatric treatment (2020) · cites this paper as Ram and Grimm, 2009
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705510701575396 · Cited by 11,415 · see citing works
Testing the number of components in a normal mixture
Lo, Y. (2001) · Biometrika · doi:10.1093/biomet/88.3.767 · Cited by 4,640 · see citing works
Group-Based Modeling of Development
NAGIN, D. (2005) · doi:10.4159/9780674041318 · Cited by 4,164 · see citing works
Miller, G. E., Chen, E., & Zhou, E. S. (2007) · Psychological Bulletin · doi:10.1037/0033-2909.133.1.25 · Cited by 2,467 · see citing works
Analyzing developmental trajectories: A semiparametric, group-based approach.
Nagin, D. S. (1999) · Psychological Methods · doi:10.1037/1082-989x.4.2.139 · Cited by 2,346 · cited 2× · see citing works
“We also highlight another subset of GMMs, often called latent class growth analysis (LCGA; cf. Nagin, 1999, 2005).”
BackgroundMethodLatent Variable Modeling of Differences and Changes with Longitudinal Data
McArdle, J. J. (2009) · Annual Review of Psychology · doi:10.1146/annurev.psych.60.110707.163612 · Cited by 1,952 · see citing works
Flagged first, then by citations
Research works printed but not linked: 30
- Bauer DJ Curran PJ 2003a Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes Psychological Methods 8 338 363 14596495
- Bauer DJ Curran PJ 2003b Overextraction of latent trajectory classes: Much ado about nothing? Reply to Risdskopf (2003), Muthen (2003), and Cudeck and Henly (2003) Psychological Methods 8 384 393 14596495
- Bauer DJ Curran PJ 2004 The integration of continuous and discrete latent variable models: Potential problems and promising opportunities Psychological Methods 9 3 29 15053717
- Bollen KA Curran PJ 2006 Latent curve models: A structural equation perspective New York Wiley
- Bryk AS Raudenbush SW 1987 Application of hierarchical linear models to assessing change Psychological Bulletin 101 147 158
- Bryk AS Raudenbush SW 1992 Hierarchical Linear Models: Applications and Data Analysis Newbury Park CA Sage Publications
- Greenbaum PE Del Boca FK Darkes J Wang C Goldman MS 2005 Variation in the drinking trajectories of freshmen college students Journal of Consulting and Clinical Psychology 73 229 238 15796630
- Grimm KJ Ram N (in press) Non-linear growth models in Mplus and SAS Structural Equation Modeling: A Multidisciplinary Journal PMC3717396 23882134
- Grimm KJ Ram N (in press) A second order growth mixture model for developmental research Research in Human Development
- Harring J 2005 Nonlinear mixed effects mixture model: A model for clustering nonlinear longitudinal profile Unpublished doctoral dissertation University of Minnesota
- Heim C Elhert U Hellhammer D 2000 The potential role of hypocortisolism in the pathophysiology of stress-related bodily disorders Psychoneuroendricinology 25 1 35 10633533
- Hipp JR Bauer DJ 2006 Local solutions in the estimation of growth mixture models Psychological Methods 11 36 53 16594766
- Kelley K 2005 Estimating nonlinear change models in heterogeneous populations when class membership is unknown: Defining and developing the latent classification differential change model Unpublished Doctoral Dissertation University of Notre Dame
- Little RJA Rubin DB 1987 Statistical Analysis with Missing Data J. Wiley & Sons New York
- Masyn K (in press) Discrete-time survival factor mixture analysis for low-frequency recurrent event histories Research in Human Development 4 ???-??? PMC3905990 24489519
- McArdle JJ Epstein DB 1987 Latent growth curves within developmental within developmental structural equation models Child Development 58 110 133 3816341
- McArdle JJ Nesselroade JR Shinka J Velicer W 2003 Growth curve analysis in contemporary psychological research Comprehensive handbook of psychology, Volume two: Research methods in psychology 447 480 New York Wiley
- McLachlan GJ Peel D 2000 Finite Mixture Models New York John Wiley & Sons
- Muthén B 2003 Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran (2003) Psychological Methods 8 369 377 14596497
- Muthén B Kaplan D 2004 Latent variable analysis. Growth mixture modeling and related techniques for longitudinal data The Sage handbook of quantitative methodology for the social sciences 345 368 Thousand Oaks Sage Publications
- Muthén BO Shedden K 1999 Finite mixture modeling with mixture outcomes using the EM algorithm Biometrics 55 463 469 11318201
- Muthén BO Masyn K 2005 Discrete-time survival mixture analysis Journal of Educational and Behavioral Statistics 30 27 58
- Muthén BO Muthén LK 2000 Integrating person-centered and variable-centered analysis: Growth mixture modeling with latent trajectory classes Alcoholism: Clinical and Experimental Research 24 882 891 10888079
- Preacher KJ Wichman AL MacCallum RC Briggs NE 2008 Latent growth curve modeling Thousand Oaks, CA Sage Publications
- Ram N Grimm K 2007 Using simple and complex growth models to articulate developmental change: Matching theory to method International Journal of Behavioral Development 31 303 316
- Rindskopf D 2003 Mixture or homogeneous? Comment on Bauer and Curran (2003) Psychological Methods 8 364 368 14596496
- Seeman TE Berkman LF Gulanski B Robbins R Greenspan S Charpentier P Rowe J 1995 Self-esteem and neuroendocrine response to challenge: MacArthur Successful Aging Studies Psychosomatic Research 39 69 84 7760305
- Seeman TE Singer B Charpentier P 1995 Gender differences in pattern of HPA axis response to challenge: MacArthur Studies of Successful Aging Psychoneuroendicrinology 20 711 725 8848517
- Singer JD Willet JB 2003 Applied longitudinal data analysis: Modeling change and event occurrence NY Oxford University Press
- Wohlwill JF 1973 The study of behavioral development San Diego, CA Academic Press
Cited by
Sorted by citations
Spurk, D., Hirschi, A., Wang, M., Valero, D., & Kauffeld, S. (2020) · Journal of Vocational Behavior · doi:10.1016/j.jvb.2020.103445 · Cited by 2,119 · see citing works
The GRoLTS-Checklist: Guidelines for Reporting on Latent Trajectory Studies
van de Schoot, R., Sijbrandij, M., Winter, S. D., Depaoli, S., & Vermunt, J. K. (2017) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705511.2016.1247646 · Cited by 721 · see citing works
Marceau, K., Ram, N., Houts, R. M., Grimm, K. J., & Susman, E. J. (2011) · Developmental Psychology · doi:10.1037/a0023838 · Cited by 389 · see citing works
Baron, E., Bass, J., Murray, S. M., Schneider, M., & Lund, C. (2017) · Journal of Affective Disorders · doi:10.1016/j.jad.2017.07.046 · Cited by 146 · see citing works
“Given the exploratory nature of GCMM, Ram and Grimm (2009) also suggest basing the identification of the optimal model on past research and theory as much as possible.”
BackgroundMethodInfluentialSchool Life and Adolescents' Self-Esteem Trajectories
Morin, A. J. S., Maïano, C., Marsh, H. W., Nagengast, B., & Janosz, M. (2013) · Child Development · doi:10.1111/cdev.12089 · Cited by 112 · see citing works
Lee, C. S., Vellone, E., Lyons, K. S., Cocchieri, A., Bidwell, J. T., D’Agostino, F., Hiatt, S. O., Alvaro, R., Buck, H. G., & Riegel, B. (2015) · International Journal of Nursing Studies · doi:10.1016/j.ijnurstu.2014.11.005 · Cited by 109 · see citing works
Hair cortisol concentrations in war-affected adolescents: A prospective intervention trial
Dajani, R., Hadfield, K., van Uum, S., Greff, M., & Panter-Brick, C. (2018) · Psychoneuroendocrinology · doi:10.1016/j.psyneuen.2017.12.012 · Cited by 108 · see citing works
Han, L. K. M., Verhoeven, J. E., Tyrka, A. R., Penninx, B. W. J. H., Wolkowitz, O. M., Månsson, K. N. T., Lindqvist, D., Boks, M. P., Révész, D., Mellon, S. H., et al. (2019) · Psychoneuroendocrinology · doi:10.1016/j.psyneuen.2019.04.004 · Cited by 104 · see citing works
Pagé, M. G., Katz, J., Romero Escobar, E. M., Lutzky-Cohen, N., Curtis, K., Fuss, S., & Clarke, H. A. (2015) · Pain · doi:10.1097/01.j.pain.0000460327.10515.2d · Cited by 91 · see citing works
Gueorguieva, R., Chekroud, A. M., & Krystal, J. H. (2017) · The Lancet Psychiatry · doi:10.1016/s2215-0366(17)30038-x · Cited by 67 · see citing works
Ocay, D. D., Li, M. M. J., Ingelmo, P., Ouellet, J. A., Pagé, M. G., & Ferland, C. E. (2020) · Pain Research and Management · doi:10.1155/2020/9874739 · Cited by 45 · see citing works
Vowles, K. E., Witkiewitz, K., Levell, J., Sowden, G., & Ashworth, J. (2017) · Journal of Consulting and Clinical Psychology · doi:10.1037/ccp0000159 · Cited by 41 · see citing works
Coa, K. I., Wiseman, K. P., Higgins, B., & Augustson, E. (2019) · Nicotine & Tobacco Research · doi:10.1093/ntr/nty073 · Cited by 31 · see citing works
Yoon, S. (2018) · Journal of Child and Family Studies · doi:10.1007/s10826-017-0904-4 · Cited by 31 · see citing works
Hill, T. D., Burdette, A. M., Taylor, J., & Angel, J. L. (2016) · Journal of Health and Social Behavior · doi:10.1177/0022146515627850 · Cited by 31 · see citing works
Vowles, K. E., Sowden, G., Hickman, J., & Ashworth, J. (2019) · Behaviour Research and Therapy · doi:10.1016/j.brat.2018.10.012 · Cited by 24 · see citing works
Time in treatment: Examining mental illness trajectories across inpatient psychiatric treatment
Oh, H., Lee, J., Kim, S., Rufino, K. A., Fonagy, P., Oldham, J. M., Schanzer, B., & Patriquin, M. A. (2020) · Journal of Psychiatric Research · doi:10.1016/j.jpsychires.2020.07.001 · Cited by 15 · see citing works
Childhood emotional dysregulation paths for suicide-related behaviour engagement in adolescence
de la Torre-Luque, A., Essau, C. A., Lara, E., Leal-Leturia, I., & Borges, G. (2023) · European Child & Adolescent Psychiatry · doi:10.1007/s00787-022-02111-6 · Cited by 11 · see citing works
Proteomic clusters underlie heterogeneity in preclinical Alzheimer’s disease progression
Wisch, J. K., Butt, O. H., Gordon, B. A., Schindler, S. E., Fagan, A. M., Henson, R. L., Yang, C., Boerwinkle, A. H., Benzinger, T. L. S., Holtzman, D. M., et al. (2023) · Brain · doi:10.1093/brain/awac484 · Cited by 11 · see citing works
- Authors
- Ram, N., & Grimm, K. J.
- Affiliations
- The Pennsylvania State University, USA, and Max Planck Institute for Human Development, Germany,
- Max Planck Institute for Human Development (DE)
- ORCID
- Grimm, Kevin J.
- Venue
- International Journal of Behavioral Development
- Publisher
- SAGE Publications
- Published
- 2009-10-26
- Volume
- 33
- Issue
- 6
- Pages
- 565-576
- ISSN
- 0165-0254 (ISSN-L)
- 1464-0651
- PMC
- PMC3718544
- OpenAlex
- W2121236536
- Cited by
- 1,143
- References
- 6
- Citations by year
- 2026: 126 · 2025: 116 · 2024: 109 · 2023: 111 · 2022: 105 · 2021: 106 · 2020: 89 · 2019: 80 · 2018: 87 · 2017: 59 · 2016: 54 · 2015: 35 · 2014: 17 · 2013: 19 · 2012: 14
- FWCI
- 13.55
- Type
- journal article
- Language
- en
- Open access
- green
- europepmc.org
- Locations
- International Journal of Behavioral Development (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Funders
- National Institute on Aging (T32AG020500)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Keywords
- growth mixture modeling, longitudinal change, cortisol stress response
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review