The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models

Miao Gao; Walter Leite; Jinxiang Hu

doi:doi:10.11648/j.ajtas.20180706.14

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The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models

Miao Gao, Walter Leite, Jinxiang Hu

Received: 2 October 2018 Accepted: 16 October 2018 Published: 1 November 2018

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Abstract

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.

DOI	10.11648/j.ajtas.20180706.14
Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 6, November 2018)
Page(s)	222-228
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Class Enumeration, Multilevel Factor Mixture Models, Information Indices, Likelihood Ratio Tests

References

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APA Style

Miao Gao, Walter Leite, Jinxiang Hu. (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

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ACS Style

Miao Gao; Walter Leite; Jinxiang Hu. The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models. Am. J. Theor. Appl. Stat. 2018, 7(6), 222-228. doi: 10.11648/j.ajtas.20180706.14

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AMA Style

Miao Gao, Walter Leite, Jinxiang Hu. The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models. Am J Theor Appl Stat. 2018;7(6):222-228. doi: 10.11648/j.ajtas.20180706.14

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@article{10.11648/j.ajtas.20180706.14,
  author = {Miao Gao and Walter Leite and Jinxiang Hu},
  title = {The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {6},
  pages = {222-228},
  doi = {10.11648/j.ajtas.20180706.14},
  url = {https://doi.org/10.11648/j.ajtas.20180706.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180706.14},
  abstract = {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.},
 year = {2018}
}

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TY  - JOUR
T1  - The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models
AU  - Miao Gao
AU  - Walter Leite
AU  - Jinxiang Hu
Y1  - 2018/11/01
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180706.14
DO  - 10.11648/j.ajtas.20180706.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 222
EP  - 228
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180706.14
AB  - 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.
VL  - 7
IS  - 6
ER  -

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Author Information

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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Plain Text BibTeX RIS

APA Style

Miao Gao, Walter Leite, Jinxiang Hu. (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

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ACS Style

Miao Gao; Walter Leite; Jinxiang Hu. The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models. Am. J. Theor. Appl. Stat. 2018, 7(6), 222-228. doi: 10.11648/j.ajtas.20180706.14

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AMA Style

Miao Gao, Walter Leite, Jinxiang Hu. The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models. Am J Theor Appl Stat. 2018;7(6):222-228. doi: 10.11648/j.ajtas.20180706.14

Copy | Download

@article{10.11648/j.ajtas.20180706.14,
  author = {Miao Gao and Walter Leite and Jinxiang Hu},
  title = {The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {6},
  pages = {222-228},
  doi = {10.11648/j.ajtas.20180706.14},
  url = {https://doi.org/10.11648/j.ajtas.20180706.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180706.14},
  abstract = {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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - The Performance of Model Fit Indices for Class Enumeration in Multilevel Factor Mixture Models
AU  - Miao Gao
AU  - Walter Leite
AU  - Jinxiang Hu
Y1  - 2018/11/01
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180706.14
DO  - 10.11648/j.ajtas.20180706.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 222
EP  - 228
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180706.14
AB  - 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.
VL  - 7
IS  - 6
ER  -

Copy | Download