A Systematic Review of Factor Mixture Model Applications

Abstract

In this study, a systematic review was conducted on peer-reviewed articles of factor mixture model (FMM) applications. A total of 304 studies were included with 334 applications published from 2003–2022. FMM was mostly used in these studies to detect latent classes and model heterogeneity. Most of the studies were conducted in the U.S. with samples including students, adults, and the general population. The average sample size was 3,562, and the average number of items was 17.34. Measurement tools containing mostly Likert type items and measuring structures in the field of psychology were used in these FMM analyses. Most FMM studies that were reviewed were applied with maximum likelihood estimation methods as implemented in Mplus software. Multiple fit indices were used, the most common of which were AIC, BIC, and entropy. The mean numbers of classes and factors across the 334 applications were 2.96 and 2.17, respectively. Psychological and behavioral disorders, gender, and age variables were mostly the focus of these studies and included use of covariates in these analyses. As a result of this systematic review, the trends in FMM analyses were better understood.

Keywords

• mixture models
• factor mixture model
• systematic review

References

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723. https://doi.org/10.1109/TAC.1974.1100705
2. Baron, E., Bass, J., Murray, S. M., Schneider, M., & Lund, C. (2017). A systematic review of growth curve mixture modelling literature investigating trajectories of perinatal depressive symptoms and associated risk factors. Journal of Affective Disorders, 223, 194–208. https://doi.org/10.1016/j.jad.2017.07.046
3. Berlin, K. S., Williams, N. A., & Parra, G. R. (2014). An introduction to latent variable mixture modeling (part 1): Overview and cross-sectional latent class and latent profile analyses. Journal of Pediatric Psychology, 39(2), 174–187. https://doi.org/10.1093/jpepsy/jst084
4. Brown, T. A. (2013). Latent variable measurement models. In T. D. Little (Ed.), The Oxford handbook of quantitative methods (Vol. 2, pp. 257–280). Oxford University Press.
5. Cho, S. J., Cohen, A. S., & Kim, S. H. (2014). A mixture group bifactor model for binary responses. Structural Equation Modeling: A Multidisciplinary Journal, 21(3), 375–395. https://doi.org/10.1080/10705511.2014.915371 Clark, S. L., Muthén, B. O., Kaprio, J., D’Onofrio, B. M., Viken, R., & Rose, R. J. (2013). Models and strategies for factor mixture analysis: An example concerning the structural underlying psychological disorders. Structural Equation Modeling, 20, 681–703. https://doi.org/10.1080%2F10705511.2013.824786
6. Enders, C. K. (2022). Applied missing data analysis. Guilford Publications.
7. Gagné, P. E. (2004). Generalized confirmatory factor mixture models: A tool for assessing factorial invariance across unspecified populations [Unpublished doctoral dissertation]. University of Maryland, College Park.
8. Grove, R., Baillie, A., Allison, C., Baron-Cohen, S., & Hoekstra, R. A. (2015). Exploring the quantitative nature of empathy, systemising and autistic traits using factor mixture modelling. The British Journal of Psychiatry, 207(5), 400–406. https://doi.org/10.1192/bjp.bp.114.155101

9. Hofmans, J., Wille, B., & Schreurs, B. (2020). Person-centered methods in vocational research. Journal of Vocational Behavior, 118, 103398. https://doi.org/10.1016/j.jvb.2020.103398
10. Killian, M. O., Cimino, A. N., Weller, B. E., & Hyun Seo, C. (2019). A systematic review of latent variable mixture modeling research in social work journals. Journal of Evidence-Based Social Work, 16(2), 192–210. https://doi.org/10.1080/23761407.2019.1577783
11. Kim, E., Wang, Y., & Hsu, H. 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
12. Krawietz, C. E., & Pett, R. C. (2023). A systematic literature review of latent variable mixture modeling in communication scholarship. Communication Methods and Measures, 17(2), 83–110. https://doi.org/10.1080/19312458.2023.2179612
13. Lazarsfeld, P., & Henry, N. (1968). Latent structure analysis. Houghton Mifflin.
14. Lin, Y., & Mâsse, L. C. (2021). A look at engagement profiles and behavior change: A profile analysis examining engagement with the Aim2Be lifestyle behavior modification app for teens and their families. Preventive Medicine Reports, 24, 101565. https://doi.org/10.1016/j.pmedr.2021.101565
15. Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767–778. https://www.jstor.org/stable/2673445
16. Lubke, G. (2019). Latent variable mixture models. In G. R., Hancock, L. M., Stapleton, & R. O. Mueller (Eds.), The reviewer’s guide to quantitative methods in the social sciences (pp. 202–213). Routledge.
17. Lubke, G., & Muthén, B. O. (2007). Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters. Structural Equation Modeling, 14, 26–47. https://doi.org/10.1080/10705510709336735
18. Lubke, G. H., & Muthén, B. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10, 21–39. https://doi.org/10.1037/1082-989X.10.1.21
19. Ma, X., Wang, M., Ma, J., Zhang, Z., Hao, Y., & Yan, N. (2022). The association between lifestyles and health conditions and the choice of traditional Chinese medical treatment in China: A latent class analysis. Medicine, 101(51), e32422. https://doi.org/10.1097/md.0000000000032422
20. Magidson, J., & Vermunt, J. K. (2001). Latent class factor and cluster models, bi‐plots, and related graphical displays. Sociological Methodology, 31(1), 223–264. http://dx.doi.org/10.1111/0081-1750.00096
21. Masyn, K. E., Henderson, C. E., & Greenbaum, P. E. (2010). Exploring the latent structures of psychological constructs in social development using the dimensional–categorical spectrum. Social Development, 19(3), 470–493. https://doi.org/10.1111/j.1467-9507.2009.00573.x
22. McDonald, R. P. (2003). A review of multivariate taxometric procedures: Distinguishing types from continua. Journal of Educational and Behavioral Statistics, 28, 77–81. http://dx.doi.org/10.3102/10769986028001077
23. McLachlan, G., & Peel, D. (2000). Finite mixture models. Wiley.
24. Mislevy, R.J., & Verhelst, N. (1990). Modeling item responses when different subjects employ different solution strategies. Psychometrika, 55(2), 195–215. https://psycnet.apa.org/doi/10.1007/BF02295283
25. Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & Prisma Group. (2009). Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement. PLoS Medicine, 6, e1000097. https://doi.org/10.1136/bmj.b2535
26. Moors, G., Kieruj, N. D., & Vermunt, J. K. (2014). The effect of labeling and numbering of response scales on the likelihood of response bias. Sociological Methodology, 44(1), 369–399. https://doi.org/10.1177/0081175013516114
27. Morin, A. J., & Marsh, H. 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
28. Muthén, B. (2006). Should substance use disorders be considered as categorical or dimensional?. Addiction, 101, 6–16. https://doi.org/10.1111/j.1360-0443.2006.01583.x
29. Muthén, L. K., & Muthén, B. O. (1998/2017). Mplus user’s guide (Eight ed.). Muthén & Muthén.
30. Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55(2), 463–469. https://doi.org/10.1111/j.0006-341x.1999.00463.x Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H., (2006). Mx: Statistical Modeling, 7th ed. Medical College of Virginia, Richmond.
31. 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. https://doi.org/10.1080/10705510701575396
32. Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271–282. https://doi.org/10.1177/014662169001400305
33. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. https://www.jstor.org/stable/2958889
34. Scrucca, L., Fop, M., Murphy, T. B., & Raftery, A. E. (2016). mclust 5: clustering, classification and density estimation using Gaussian finite mixture models. The R journal, 8(1), 289–317.
35. Sen, S., & Cohen, A. S. (2019). Applications of mixture IRT models: A literature review. Measurement: Interdisciplinary Research and Perspectives, 17(4), 177–191. https://doi.org/10.1080/15366367.2019.1583506
36. Spearman, C. (1904). ‘General intelligence’ objectively determined and measured. American Journal of Psychology, 5, 201–293.
37. Spiegelhalter, D., Thomas, A., & Best, N. (2003). WinBUGS (Version 1.4) [Computer software]. Cambridge, UK: Biostatistics Unit, Institute of Public Health.
38. Spurk, D., Hirschi, A., Wang, M., Valero, D., & Kauffeld, S. (2020). Latent profile analysis: A review and “how to” guide of its application within vocational behavior research. Journal of Vocational Behavior, 120, 103445. https://doi.org/10.1016/j.jvb.2020.103445
39. Ulbricht, C. M., Chrysanthopoulou, S. A., Levin, L., & Lapane, K. L. (2018). The use of latent class analysis for identifying subtypes of depression: A systematic review. Psychiatry Research, 266, 228–246. https://doi.org/10.1016/j.psychres.2018.03.003
40. Vermunt, J. K., & Magidson, J. (2003). Latent Gold 3.0. Belmont, MA. URL http://www. statisticalinnovations.com.
41. Viroli, C. (2011). FactMixtAnalysis: Factor Mixture Analysis with covariates.
42. von Davier, M. (2006). Multidimensional Latent Trait Modelling (MDLTM) [Computer Software]. Educational Testing Service.
43. Wang, Y., Cao, C., & Kim, E. (2022). Covariate inclusion in factor mixture modeling: Evaluating one-step and three-step approaches under model misspecification and overfitting. Behavior Research Methods, 1–16. https://doi.org/10.3758/s13428-022-01964-8
44. Yung, Y. F. (1997). Finite mixtures in confirmatory factor-analysis models. Psychometrika, 62, 297–330. https://doi.org/10.1007/BF02294554