IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v93y2016icp146-161.html
   My bibliography  Save this article

Latent profile analysis with nonnormal mixtures: A Monte Carlo examination of model selection using fit indices

Author

Listed:
  • Morgan, Grant B.
  • Hodge, Kari J.
  • Baggett, Aaron R.

Abstract

The performances of fit indices used for model selection in cross-sectional mixture modeling with nonnormally distributed indicators were examined in two studies using Monte Carlo methods. Simulation conditions were selected to mirror conditions found in educational and psychological research. The design factors under investigation were: indicator distribution, number of indicators, sample size, and profile prevalence. All models contained five, ten, or 15 continuous indicators with varying departures from normality. The fit indices examined were Akaike’s information criterion (AIC), corrected Akaike’s information criterion (AICc), consistent Akaike’s information criterion (CAIC), Bayesian information criterion (BIC), sample size-adjusted Bayesian information criterion (SSBIC), Draper’s information criterion (DIC), integrated classification likelihood criterion with Bayesian-type approximation (ICL), entropy, and the adjusted Lo–Mendell–Rubin likelihood ratio test (LMR). In the first study, nonnormally distributed data were used to estimate the mixture models. No fit index uniformly identified the simulated number of profiles using nonnormal indicators. The fit indices that tended to identify the simulated number of profiles more frequently than others were BIC, SSBIC, CAIC, and LMR although the condition(s) in which this was observed varied. In the second study, the raw data were transformed using van der Waerden quantile normal scores. Despite deflating the indicator variances, the use of normal scores increased the frequency with which fit indices identified the simulated number of profiles across most conditions.

Suggested Citation

  • Morgan, Grant B. & Hodge, Kari J. & Baggett, Aaron R., 2016. "Latent profile analysis with nonnormal mixtures: A Monte Carlo examination of model selection using fit indices," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 146-161.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:146-161
    DOI: 10.1016/j.csda.2015.02.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315000602
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.02.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Glenn Milligan & Martha Cooper, 1988. "A study of standardization of variables in cluster analysis," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 181-204, September.
    2. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    3. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2014. "Mixtures of skew-t factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 326-335.
    4. Conor Dolan & Han Maas, 1998. "Fitting multivariage normal finite mixtures subject to structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 227-253, September.
    5. Gilles Celeux & Gilda Soromenho, 1996. "An entropy criterion for assessing the number of clusters in a mixture model," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 195-212, September.
    6. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    7. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    8. Anne B. Koehler & Emily S. Murphree, 1988. "A Comparison of the Akaike and Schwarz Criteria for Selecting Model Order," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(2), pages 187-195, June.
    9. Hunt, Lynette & Jorgensen, Murray, 2003. "Mixture model clustering for mixed data with missing information," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 429-440, January.
    10. Venkatram Ramaswamy & Wayne S. Desarbo & David J. Reibstein & William T. Robinson, 1993. "An Empirical Pooling Approach for Estimating Marketing Mix Elasticities with PIMS Data," Marketing Science, INFORMS, vol. 12(1), pages 103-124.
    11. Neal O. Jeffries, 2003. "A note on 'Testing the number of components in a normal mixture'," Biometrika, Biometrika Trust, vol. 90(4), pages 991-994, December.
    12. Yang, Chih-Chien, 2006. "Evaluating latent class analysis models in qualitative phenotype identification," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1090-1104, February.
    13. Christian Hennig & Tim F. Liao, 2013. "How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 309-369, May.
    14. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 125-145, June.
    15. Stanley Sclove, 1987. "Application of model-selection criteria to some problems in multivariate analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 333-343, September.
    16. Vrbik, Irene & McNicholas, Paul D., 2014. "Parsimonious skew mixture models for model-based clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 196-210.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel McNeish & Jeffrey R. Harring, 2017. "The Effect of Model Misspecification on Growth Mixture Model Class Enumeration," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 223-248, July.
    2. Qi Chen & Wen Luo & Gregory J. Palardy & Ryan Glaman & Amber McEnturff, 2017. "The Efficacy of Common Fit Indices for Enumerating Classes in Growth Mixture Models When Nested Data Structure Is Ignored," SAGE Open, , vol. 7(1), pages 21582440177, March.
    3. Han, Yoonsun & Kang, Hae Rin & Choe, Ji Won & Kim, Hyein, 2021. "The moderating role of parental support in the relationship between latent profiles of bullying victimization and sense of school belonging: A cross-national comparison," Children and Youth Services Review, Elsevier, vol. 122(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qi Chen & Wen Luo & Gregory J. Palardy & Ryan Glaman & Amber McEnturff, 2017. "The Efficacy of Common Fit Indices for Enumerating Classes in Growth Mixture Models When Nested Data Structure Is Ignored," SAGE Open, , vol. 7(1), pages 21582440177, March.
    2. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    3. Po-Hsien Huang, 2017. "Asymptotics of AIC, BIC, and RMSEA for Model Selection in Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 407-426, June.
    4. Roy Levy & Gregory R. Hancock, 2011. "An Extended Model Comparison Framework for Covariance and Mean Structure Models, Accommodating Multiple Groups and Latent Mixtures," Sociological Methods & Research, , vol. 40(2), pages 256-278, May.
    5. Sarah Brown & William Greene & Mark Harris, 2020. "A novel approach to latent class modelling: identifying the various types of body mass index individuals," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 983-1004, June.
    6. Marianna Virtanen & Jussi Vahtera & Jenny Head & Rosemary Dray-Spira & Annaleena Okuloff & Adam G Tabak & Marcel Goldberg & Jenni Ervasti & Markus Jokela & Archana Singh-Manoux & Jaana Pentti & Marie , 2015. "Work Disability among Employees with Diabetes: Latent Class Analysis of Risk Factors in Three Prospective Cohort Studies," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-14, November.
    7. Durand, Robert B. & Greene, William H. & Harris, Mark N. & Khoo, Joye, 2022. "Heterogeneity in speed of adjustment using finite mixture models," Economic Modelling, Elsevier, vol. 107(C).
    8. Ana Oliveira-Brochado & Francisco Vitorino Martins, 2008. "Determining the Number of Market Segments Using an Experimental Design," FEP Working Papers 263, Universidade do Porto, Faculdade de Economia do Porto.
    9. Tian, Amy Wei & Meyer, John P. & Ilic-Balas, Tatjana & Espinoza, Jose A. & Pepper, Susan, 2023. "In search of the pseudo-transformational leader: A person-centered approach," Journal of Business Research, Elsevier, vol. 158(C).
    10. Danks, Nicholas P. & Sharma, Pratyush N. & Sarstedt, Marko, 2020. "Model selection uncertainty and multimodel inference in partial least squares structural equation modeling (PLS-SEM)," Journal of Business Research, Elsevier, vol. 113(C), pages 13-24.
    11. Imami, Drini & Zhllima, Edvin & Merkaj, Elvina & Chan-Halbrendt, Catherine & Canavar, Maurizio, 2016. "Albanian consumer preferences for the use of dry milk in cheese-making: A conjoint choice experiment," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 17(1), January.
    12. Gebregziabher, Mulugeta & Shotwell, Matthew S. & Charles, Jane M. & Nicholas, Joyce S., 2012. "Comparison of methods for identifying phenotype subgroups using categorical features data with application to autism spectrum disorder," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 114-125, January.
    13. Adrian Bruhin & Ernst Fehr & Daniel Schunk, 2019. "The many Faces of Human Sociality: Uncovering the Distribution and Stability of Social Preferences," Journal of the European Economic Association, European Economic Association, vol. 17(4), pages 1025-1069.
    14. Schreier, Alayna & Stenersen, Madeline R. & Strambler, Michael J. & Marshall, Tim & Bracey, Jeana & Kaufman, Joy S., 2023. "Needs of caregivers of youth enrolled in a statewide system of care: A latent class analysis," Children and Youth Services Review, Elsevier, vol. 147(C).
    15. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "Erratum to: The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 327-355, July.
    16. Sun-Joo Cho & Allan Cohen & Brian Bottge, 2013. "Detecting Intervention Effects Using a Multilevel Latent Transition Analysis with a Mixture IRT Model," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 576-600, July.
    17. Li, Yumei & Duan, Wenjie & Chen, Zheng, 2020. "Latent profiles of the comorbidity of the symptoms for posttraumatic stress disorder and generalized anxiety disorder among children and adolescents who are susceptible to COVID-19," Children and Youth Services Review, Elsevier, vol. 116(C).
    18. repec:jss:jstsof:06:i02 is not listed on IDEAS
    19. Utkarsh J. Dang & Michael P.B. Gallaugher & Ryan P. Browne & Paul D. McNicholas, 2023. "Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 145-167, April.
    20. Tang, Yang & Browne, Ryan P. & McNicholas, Paul D., 2015. "Model based clustering of high-dimensional binary data," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 84-101.
    21. Moira Mckniff & Stephanie M. Simone & Tania Giovannetti, 2023. "Age, Loneliness, and Social Media Use in Adults during COVID-19: A Latent Profile Analysis," IJERPH, MDPI, vol. 20(11), pages 1-12, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:146-161. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.