Application of factor mixture models (FMMs) requires determining the correct number of latent classes. A number of studies have examined the performance of several information criterion (IC) indices, but as yet none have studied the effectiveness of the elbow plot method. In this study, therefore, the effectiveness of the elbow plot method was compared with the lowest value criterion and the difference method calculated from five commonly used IC indices. Results of a simulation study showed the elbow plot method to detect the generating model at least 90% of the time for two- and three-class FMMs. Results also showed the elbow plot method did not perform well for two-factor and four-class conditions. The performance of the elbow plot method was generally better than that of the lowest IC value criterion and difference method under two- and three-class conditions. For the four-latent class conditions, there were no meaningful differences between the results of the elbow plot method and the lowest value criterion method. On the other hand, the difference method outperformed the other two methods in conditions with two factors and four classes.
AkaikeH. (1974). A new look at the statistical model identification. In Springer series in statistics (Vol. 19, pp. 716–723). Springer. https://doi.org/10.1007/978-1-4612-1694-0_16
BozdoganH. (1987). Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345–370. https://doi.org/10.1007/BF02294361
ChenQ.LuoW.PalardyG. J.GlamanR.McEnturffA. (2017). The efficacy of common fit indices for enumerating classes in growth mixture models when nested data structure is ignored: A Monte Carlo study. Sage Open, 7(1), 2158244017700459. https://doi.org/10.1177/2158244017700459
6.
ChenX.MorinA. J.ParkerP. D.MarshH. W. (2015). Developmental investigation of the domain-specific nature of the life satisfaction construct across the post-school transition. Developmental Psychology, 51(8), 1074-1085. https://doi.org/10.1037/a0039477
7.
ClarkS. L.MuthénB.KaprioJ.D'OnofrioB. M.VikenR.RoseR. J. (2013). Models and strategies for factor mixture analysis: An example concerning the structure underlying psychological disorders. Structural Equation Modeling: A Multidisciplinary Journal, 20(4), 681–703. https://doi.org/10.1080/10705511.2013.824786
8.
CollinsL. M.LanzaS. T. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences(Vol. 718).John Wiley.
9.
GaoM.LeiteW.HuJ. (2018). The performance of model fit indices for class enumeration in multilevel factor mixture models. American Journal of Theoretical and Applied Statistics, 7(6), 222–228. https://doi.org/10.11648/j.ajtas.20180706.14
10.
GeisserS.EddyW. F. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74(365), 153–160. https://doi.org/10.2307/2286745
11.
GelmanA.CarlinJ. B.SternH. S.RubinD. B. (1996). Bayesian data analysis. Chapman & Hall.
12.
HensonJ. M.ReiseS. P.KimK. H. (2007). 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. https://doi.org/10.1080/10705510709336744
13.
HurvichC. M.TsaiC. L. (1989). Regression and time series model selection in small samples. Biometrika, 76(2), 297–307. https://doi.org/10.1093/biomet/76.2.297
14.
KassR. E.RafteryA. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773–795. https://doi.org/10.2307/2291091
15.
KimE.WangY.HsuH. Y. (2023). A systematic review of and reflection on the applications of factor mixture modeling. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000630
16.
LiF.CohenA. S.KimS. H.ChoS. J. (2009). Model selection methods for mixture dichotomous IRT models. Applied Psychological Measurement, 33(5), 353–373. https://doi.org/10.1177/0146621608326422
17.
LinesR. L.CraneM.DuckerK. J.NtoumanisN.Thøgersen‐NtoumaniC.FletcherD.GucciardiD. F. (2020). Profiles of adversity and resilience resources: A latent class analysis of two samples. British Journal of Psychology, 111(2), 174–199. https://doi.org/10.1111/bjop.12397
LubkeG.MuthénB. O. (2007). 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. https://doi.org/10.1080/10705510709336735
LubkeG.NealeM. C. (2006). Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood?Multivariate Behavioral Research, 41(4), 499–532. https://doi.org/10.1207/s15327906mbr4104_4
22.
LubkeG. H.CampbellI.McArtorD.MillerP.LuninghamJ.van den BergS. M. (2017). Assessing model selection uncertainty using a bootstrap approach: An update. Structural Equation Modeling: A Multidisciplinary Journal, 24(2), 230–245. https://doi.org/10.1080/10705511.2016.1252265
23.
LubkeG. H.MuthénB. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10(1), 21–39. https://doi.org/10.1037/1082-989x.10.1.21
24.
MarshH. W.LüdtkeO.TrautweinU.MorinA. J. (2009). Classical latent profile analysis of academic self-concept dimensions: Synergy of person-and variable-centered approaches to theoretical models of self-concept. Structural Equation Modeling: A Multidisciplinary Journal, 16(2), 191–225. https://doi.org/10.1080/10705510902751010
MorganG. B. (2015). Mixed mode latent class analysis: An examination of fit index performance for classification. Structural Equation Modeling: A Multidisciplinary Journal, 2(1), 76–86. https://doi.org/10.1080/10705511.2014.935751
27.
MorinA. J.BoudriasJ. S.MarshH. W.McInerneyD. M.Dagenais-DesmaraisV.MadoreI.LitalienD. (2017). Complementary variable-and person-centered approaches to the dimensionality of psychometric constructs: Application to psychological wellbeing at work. Journal of Business and Psychology, 32(4), 395–419. https://psycnet.apa.org/doi/10.1007/s10869-016-9448-7
28.
MorinA. J.MaianoC.NagengastB.MarshH. W.MorizotJ.JanoszM. (2011). General growth mixture analysis of adolescents’ developmental trajectories of anxiety: The impact of untested invariance assumptions on substantive interpretations. Structural Equation Modeling: A Multidisciplinary Journal, 18(4), 613–648. https://doi.org/10.1080/10705511.2011.607714
29.
MorinA. J.MarshH. W. (2015). Disentangling shape from level effects in person-centered analyses: An illustration based on university teachers’ multidimensional profiles of effectiveness. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 39–59. https://doi.org/10.1080/10705511.2014.919825
30.
MorinA. J.MeyerJ. P.CreusierJ.BiétryF. (2016). Multiple-group analysis of similarity in latent profile solutions. Organizational Research Methods, 19(2), 231–254. https://doi.org/10.1177/1094428115621148
NylundK. L.AsparouhovT.Muthe´nB. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14(4), 535–569. https://doi.org/10.1080/10705510701575396
34.
PetrasH.MasynK. (2010). General growth mixture analysis with antecedents and consequences of change. In PiqueroA. R.WeisburdD. (Eds.), Handbook of quantitative criminology (pp. 69–100). Springer.
35.
PreinerstorferD.FormanA. K. (2012). Parameter recovery and model selection in mixed Rasch model. British Journal of Mathematical and Statistical Psychology, 65, 252–262. https://doi.org/10.1111/j.2044-8317.2011.02020.x
36.
RafteryA. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–163. https://doi.org/10.2307/271063
37.
SchubertE. (2023). Stop using the elbow criterion for k-means and how to choose the number of clusters instead. ACM SIGKDD Explorations Newsletter, 25(1), 36–42. https://doi.org/10.1145/3606274.3606278
ScloveS. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52(3), 333–343. https://doi.org/10.1007/BF02294360
40.
ŞenS.CohenA. (2024). A systematic review of factor mixture model applications. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 15(2), 79–93. https://doi.org/10.21031/epod.1423427
41.
SenS.CohenA. S. (2020). The impact of test and sample characteristics on model selection and classification accuracy in the multilevel mixture IRT model. Frontiers in Psychology, 11, 197. https://doi.org/10.3389/fpsyg.2020.00197
42.
SenS.CohenA. S. (2023). An evaluation of fit indices used in model selection of dichotomous mixture IRT models. Educational and Psychological Measurement, 84(3), 1–29. https://doi.org/10.1177/00131644231180529
43.
SinhaP.CalfeeC. S.DelucchiK. L. (2021). Practitioner’s guide to latent class analysis: Methodological considerations and common pitfalls. Critical Care Medicine, 49(1), e63–e79. https://doi.org/10.1097/ccm.0000000000004710
44.
SpiegelhalterD. J.BestN. G.CarlinB. P. (1998). Bayesian deviance, the effective number of parameters, and the comparison of arbitrarily complex models. Technical Report. MRC Biostatistics Unit.
45.
TeinJ. Y.CoxeS.ChamH. (2013). Statistical power to detect the correct number of classes in latent profile analysis. Structural Equation Modeling: A Multidisciplinary Journal, 20(4), 640–657. https://doi.org/10.1080/10705511.2013.824781
46.
TofighiD.EndersC. K. (2008). Identifying the correct number of classes in growth mixture models. In HancockG. R.SamuelsenK. M. (Eds.), Advances in latent variable mixture models (pp. 317–341). Charlotte, NC: Information Age Publishing.
47.
YangC. C. (2006). Evaluating latent class analysis models in qualitative phenotype identification. Computational Statistics & Data Analysis, 50(4), 1090–1104. https://doi.org/10.1016/j.csda.2004.11.004
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