Latent class analysis (LCA) is a useful statistical approach for understanding heterogeneity in a population. This article provides a pedagogical introduction to LCA modeling and provides an example of its use to understand youths’ daily coping strategies. The analytic procedures are outlined for choosing the number of classes and integration of the LCA variable within a structural equation model framework, specifically a latent class moderation model, and a detailed table provides a summary of relevant modeling steps. This applied example demonstrates the modeling context when the LCA variable is moderating the association between a covariate and two outcome variables. Results indicate that students’ coping strategies moderate the association between social stress and negative mood; however, they do not moderate the social stress-positive mood association. Online supplemental materials include R (MplusAutomation) code to automate the enumeration procedure, ML three-step auxiliary variable integration, and the generation of figures for visually depicting LCA results.
AsparouhovT.MuthénB. (2014). Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling, 21(3), 329–341. https://doi.org/10.1080/10705511.2014.915181
2.
BakkZ.KuhaJ. (2018). Two-step estimation of models between latent classes and external variables. Psychometrika, 83(4), 871–892.
3.
BakkZ.KuhaJ. (2021). Relating latent class membership to external variables: An overview. British Journal of Mathematical and Statistical Psychology, 74(2), 340–362.
4.
BellmoreA.ChenW. T.RischallE. (2013). The reasons behind early adolescents’ responses to peer victimization. Journal of Youth and Adolescence, 42(2), 275–284. https://doi.org/10.1007/s10964-012-9825-0
5.
BolckA.CroonM.HagenaarsJ. (2004). Estimating latent structure models with categorical variables: One-step versus three-step estimators. Political Analysis, 12(1), 3–27.
6.
BruscoM. J.ShiremanE.SteinleyD. (2017). A comparison of latent class, K-means, and K-median methods for clustering dichotomous data. Psychological Methods, 22(3), 563–580. https://doi.org/10.1037/met0000095
7.
CauseyD. L.DubowE. F. (1992). Development of a self-report coping measure for elementary school children. Journal of Clinical Child and Adolescent Psychology, 21(1), 47–59. https://doi.org/10.1207/s15374424jccp2101_8
8.
ClarkS. L.MuthénB. (2009). Relating latent class analysis results to variables not included in the analysis.
9.
CollierZ. K.LeiteW. L. (2017). A comparison of three-step approaches for auxiliary variables in latent class and latent profile analysis. Structural Equation Modeling, 24(6), 819–830.
10.
DwyerC. A. (1996). Cut scores and testing: Statistics, judgment, truth, and error. Psychological Assessment, 8(4), 360–362. https://doi.org/10.1037/1040-3590.8.4.360
11.
FopM.MurphyT. B. (2018). Variable selection methods for model-based clustering. Statistics Surveys, 12, 18–65. https://doi.org/10.1214/18-ss119
12.
GageN. A.ScottT.HirnR.MacSuga-GageA. S. (2018). The relationship between teachers’ implementation of classroom management practices and student behavior in elementary school. Behavioral Disorders, 43(2), 302–315. https://doi.org/10.1177/0198742917714809
HallquistM. N.WileyJ. F. (2018). MplusAutomation: An R package for facilitating large-scale latent variable analyses in Mplus. Structural Equation Modeling, 25(4), 621–638.
15.
HoltM. K.FelixE.GrimmR.Nylund-GibsonK.GreenJ. G.PoteatV. P.ZhangC. (2017). A latent class analysis of past victimization exposures as predictors of college mental health. Psychology of Violence, 7(4), 521–532. https://doi.org/0.1037/vio0000068
16.
KavčičT.AvsecA.KocjanG. Z. (2021). Coping profiles and their association with psychological functioning: A latent profile analysis of coping strategies during the COVID-19 pandemic. Personality and Individual Differences, 185, Article 111287.
17.
KingsburyM.LiuJ.CoplanR. J.ChenX.LiD. (2016). Assessment and implications of coping styles in response to a social stressor among early adolescents in China. The. Journal of Early Adolescence, 36(2), 222–250.
18.
Leon-PerezJ. M.NotelaersG.ArenasA.MunduateL.MedinaF. J. (2014). Identifying victims of workplace bullying by integrating traditional estimation approaches into a latent class cluster model. Journal of Interpersonal Violence, 29(7), 1155–1177.
19.
LittleT. D.CunninghamW. A.ShaharG.WidamanK. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling, 9(2), 151–173.
20.
LubkeG. H.MuthénB. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10(1), 21–39.
21.
MagidsonJ.VermuntJ. (2002). Latent class models for clustering: A comparison with K-means. Canadian Journal of Marketing Research, 20(1), 36–43.
22.
MasynK. E. (2013). Latent class analysis and finite mixture modeling. In LittleT. D. (Ed.), The Oxford handbook of quantitative methods (Vol. 2: Statistical analysis, pp. 551–611). Oxford University Press.
23.
MasynK. E. (2017). Measurement invariance and differential item functioning in latent class analysis with stepwise multiple indicator multiple cause modeling. Structural Equation Modeling, 24(2), 180–197.
24.
McLarnonM. J.O’NeillT. A. (2018). Extensions of auxiliary variable approaches for the investigation of mediation, moderation, and conditional effects in mixture models. Organizational Research Methods, 21(4), 955–982.
25.
ModeckiK. L.Zimmer-GembeckM. J.GuerraN. (2017). Emotion regulation, coping, and decision making: Three linked skills for preventing externalizing problems in adolescence. Child Development, 88(2), 417–426. https://doi.org/10.1111/cdev.12734
26.
MorovatiD. (2014). The intersection of sample size, number of indicators, and class enumeration in LCA: A Monte Carlo study [Doctoral dissertation, UC Santa Barbara].
27.
MuthénB. O. (2003). Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran (2003). Psychological Methods, 8(3), 369–377.
28.
MuthénB. O.SheddenK.SpisicD. (1999). General latent variable mixture modelling (Technical report). Santa Monica, CA: Muthén & Muthén.
29.
MuthénL. K.MuthénB. O. (1998–2017). Mplus user’s guide (8th ed.).
30.
NaginD. S. (2005). Group-based modeling of development. Harvard University Press.
31.
NylundK.BellmoreA.NishinaA.GrahamS. (2007). Subtypes, severity, and structural stability of peer victimization: What does latent class analysis say?Child Development, 78, 1706–1722. https://doi.org/10.1111/j.1467-8624.2007.01097.x
32.
NylundK. L.AsparouhovT.MuthénB. 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(4), 535–569.
33.
Nylund-GibsonK.ChoiA. Y. (2018). Ten frequently asked questions about latent class analysis. Translational Issues in Psychological Science, 4(4), 440–461.
34.
Nylund-GibsonK.GrimmR.QuirkM.FurlongM. (2014). A latent transition mixture model using the three-step specification. Structural Equation Modeling, 21(3), 439–454. https://doi.org/10.1080/10705511.2014.915375
35.
Nylund-GibsonK.GrimmR. P.MasynK. E. (2019). Prediction from latent classes: A demonstration of different approaches to include distal outcomes in mixture models. Structural Equation Modeling, 26(6), 967–985.
36.
O’NeillT. A.McLarnonM. J.XiuL.LawS. J. (2016). Core self-evaluations, perceptions of group potency, and job performance: The moderating role of individualism and collectivism cultural profiles. Journal of Occupational and Organizational Psychology, 89(3), 447–473. https://doi.org/10.1111/joop.12135
37.
RamN.GrimmK. J. (2009). Methods and measures: Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. International Journal of Behavioral Development, 33(6), 565–576.
38.
SchmiegeS. J.MasynK. E.BryanA. D. (2018). Confirmatory latent class analysis: Illustrations of empirically driven and theoretically driven model constraints. Organizational Research Methods, 21(4), 983–1001.
39.
ThibodeauE. L.MasynK. E.RogoschF. A.CicchettiD. (2019). Child maltreatment, adaptive functioning, and polygenic risk: A structural equation mixture model. Development and Psychopathology, 31(2), 443–456.
40.
TofighiD.EndersC. K. (2008). The impact of misspecifying class-specific residual variances in growth mixture models. Structural Equation Modeling, 15(1), 75–95.
41.
TsiantisA. C. J.BeratisI. N.SyngelakiE. M.StefanakouA.AsimopoulosC.SideridisG. D.TsiantisJ. (2013). The effects of a clinical prevention program on bullying, victimization, and attitudes toward school of elementary school students. Behavioral Disorders, 38(4), 243–257. https://doi.org/10.1177/019874291303800406
42.
TuellerS.LubkeG. (2010). Evaluation of structural equation mixture models: Parameter estimates and correct class assignment. Structural Equation Modeling, 17(2), 165–192.
43.
VermuntJ. K. (2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 450–469. https://doi.org/10.1093/pan/mpq025
44.
VermuntJ. K. (2011). K-means may perform as well as mixture model clustering but may also be much worse: Comment. https://doi.org/10.1037/a0020144
45.
WaasdorpT. E.BradshawC. P. (2011). Examining student responses to frequent bullying: A latent class approach. Journal of Educational Psychology, 103(2), 336–352.
WhittakerT. A.MillerJ. E. (2021). Exploring the enumeration accuracy of cross-validation indices in latent class analysis. Structural Equation Modeling: A Multidisciplinary Journal, 28(3), 376–390.
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