The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models
American Journal of Theoretical and Applied Statistics
Volume 7, Issue 6, November 2018, Pages: 222-228
Received: Oct. 2, 2018;
Accepted: Oct. 16, 2018;
Published: Nov. 1, 2018
Views 544 Downloads 55
Miao Gao, College of Education, Nanjing Normal University, Nanjing, China
Walter Leite, College of Education, University of Florida, Gainesville, USA
Jinxiang Hu, School of Medicine, University of Kansas Medical Center, Kansas City, USA
Factor mixture models combine the common factor model and latent class analysis. Given that multilevel data structures are very common in educational and social research, the multilevel factor mixture model (ML FMM) is appropriate for analyzing nested measurement data when population heterogeneity is unobserved. This simulation study aims to investigate the performance of model fit indices with multilevel factor mixture models under various conditions. In data simulation, the five-items and one-factor model with between- and within-cluster was chosen. Two subgroups with the factor mean difference were simulated so two-class was the correct number of classes. To investigate the performance of information criterions, the following conditions were manipulated in this study: class separation, the intraclass correlation (ICC), sample size. For each of the generated dataset, one correct model and three mis-specified models were analyzed to fit the data. The results showed that class separation was an important factor on detecting the correct number of classes in multilevel factor mixture models. The proportion correct increases as the class separation gets larger. Although no single criterion is always best, AIC yield a more accurate model selection than aBIC and BIC overall. Only when class separation is large, aBIC is more trustworthy for model selection. The results of this study can provide the information for educational researchers interested in analyzing multilevel data when the heterogeneity of the population is unknown.
The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models, American Journal of Theoretical and Applied Statistics.
Vol. 7, No. 6,
2018, pp. 222-228.
Lubke, G. H., & Muthén, B. O. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10, 21-39.
Varriale, R. & Vermunt, J. K. (2012). Multilevel Mixture Factor Models. Multivariate Behavioral Research, 47(2), 247-275.
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.
Asparouhov, T. & Muthén, B. (2008). Multilevel Mixture Models. In Hancock, G. R. & Samuelsen, K. M. (Eds.), Advances in Latent Variable Mixture Models, 27-52. Charlotte, NC: Information Age Publishing, Inc.
Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317-332.
Miloslavsky, M. & van der Laan, M. J. (2003). Fitting of mixtures with unspecified number of components using cross validation distance estimate. Computational Statistics &Data Analysis, 41, 413-428.
Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist., 6, 461-464.
Yang, C. (2006). Evaluating latent class analyses in qualitative phenotype identification. Computational Statistics & Data Analysis, 50, 1090-1104.
Sclove, L. S. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333-343.
Keribin, C. (2000). Consistent estimation of the order of mixture models. Sankhya Ser, A62, 49-66.
Lubke, G. H., & 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(1), 26-47.
Lukociene, O., Varriale, R. & Vermunt, J. K. (2010). The simultaneous decision(s) about the number of lower- and higher-level classes in multilevel latent classes analysis. Sociological Methodology, 40(1), 247-283.
Nylund, K. L., Asparouhov, T., & Muthén, B. (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.
Kim, E. S., Joo, S. H., Lee, P., Wang, Y., & Stark, S. (2016). Measurement invariance testing across between-level latent classes using multilevel factor mixture modeling. Structural Equation Modeling A Multidisciplinary Journal, 23(6), 1-18.
Allua, S., Stapleton, L. M., Beretvas, S. N. (2008). Testing Latent Mean Difference Between Observed and Unobserved Grouping Using Multilevel Factor Mixture Models. Educational and Psychological Measurement, 68(3), 357-378.
Chen, Q., Luo, W., Palardy, G. J., Glaman, R., & Mcenturff, A. (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).
Preacher, K. J., Zyphur, M. J., & Zhang. Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological Methods, 15(3), 209-233.
Hox, J. J., & Maas, C. J. M. (2001). The accuracy of multilevel structural equation modeling with psuedobalanced groups and small samples. Structural Equation Modeling, 8, 157-174.
Ludtke, O., Marsh, H. W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: a new, more reliable approach to group-level effects in contextual studies. Psychol Methods, 13(3), 203-229.
Tofighi, D. & Enders, C. K. (2007). Identifying the Correct Number of Classes in Growth Mixture Models. Advances in Latent Variable Mixture Models, 317-341.
Asparouhov, T. & Muthén, B. (2012). Using Mplus TECH 11 and TECH 14 to test the number of latent classes. Mplus Web Notes: No.14, May 22, 2012.