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
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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
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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.
Class Enumeration, Multilevel Factor Mixture Models, Information Indices, Likelihood Ratio Tests
To cite this article
Miao Gao, Walter Leite, Jinxiang Hu, 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. doi: 10.11648/j.ajtas.20180706.14
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