IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v71y2014icp220-240.html
   My bibliography  Save this article

Robust growth mixture models with non-ignorable missingness: Models, estimation, selection, and application

Author

Listed:
  • Lu, Zhenqiu (Laura)
  • Zhang, Zhiyong

Abstract

Challenges in the analyses of growth mixture models include missing data, outliers, estimation, and model selection. Four non-ignorable missingness models to recover the information due to missing data, and three robust models to reduce the effect of non-normality are proposed. A full Bayesian method is implemented by means of data augmentation algorithm and Gibbs sampling procedure. Model selection criteria are also proposed in the Bayesian context. Simulation studies are then conducted to evaluate the performances of the models, the Bayesian estimation method, and selection criteria under different situations. The application of the models is demonstrated through the analysis of education data on children’s mathematical ability development. The models can be widely applied to longitudinal analyses in medical, psychological, educational, and social research.

Suggested Citation

  • Lu, Zhenqiu (Laura) & Zhang, Zhiyong, 2014. "Robust growth mixture models with non-ignorable missingness: Models, estimation, selection, and application," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 220-240.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:220-240
    DOI: 10.1016/j.csda.2013.07.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313002818
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.07.036?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. D. B. Dunson, 2000. "Bayesian latent variable models for clustered mixed outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 355-366.
    2. Bengt Muthén & Kerby Shedden, 1999. "Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm," Biometrics, The International Biometric Society, vol. 55(2), pages 463-469, June.
    3. Bohning, Dankmar & Seidel, Wilfried, 2003. "Editorial: recent developments in mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 349-357, January.
    4. Bohning, Dankmar & Seidel, Wilfried & Alfo, Macro & Garel, Bernard & Patilea, Valentin & Walther, Gunther, 2007. "Advances in Mixture Models," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5205-5210, July.
    5. 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.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Song, Weixing & Yao, Weixin & Xing, Yanru, 2014. "Robust mixture regression model fitting by Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 128-137.
    8. William Meredith & John Tisak, 1990. "Latent curve analysis," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 107-122, March.
    9. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 803-826, October.
    10. 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.
    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. Dingjing Shi & Xin Tong, 2017. "The Impact of Prior Information on Bayesian Latent Basis Growth Model Estimation," SAGE Open, , vol. 7(3), pages 21582440177, August.
    2. Özgür Asar & David Bolin & Peter J. Diggle & Jonas Wallin, 2020. "Linear mixed effects models for non‐Gaussian continuous repeated measurement data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1015-1065, November.

    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. Terry Elrod & Gerald Häubl & Steven Tipps, 2012. "Parsimonious Structural Equation Models for Repeated Measures Data, with Application to the Study of Consumer Preferences," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 358-387, April.
    2. 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).
    3. Dingjing Shi & Xin Tong, 2017. "The Impact of Prior Information on Bayesian Latent Basis Growth Model Estimation," SAGE Open, , vol. 7(3), pages 21582440177, August.
    4. 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.
    5. Daniel M. McNeish, 2016. "Using Data-Dependent Priors to Mitigate Small Sample Bias in Latent Growth Models," Journal of Educational and Behavioral Statistics, , vol. 41(1), pages 27-56, February.
    6. Marco Guerra & Francesca Bassi & José G. Dias, 2020. "A Multiple-Indicator Latent Growth Mixture Model to Track Courses with Low-Quality Teaching," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 147(2), pages 361-381, January.
    7. Rufo, M.J. & Pérez, C.J. & Martín, J., 2009. "Local parametric sensitivity for mixture models of lifetime distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1238-1244.
    8. Aline Riboli Marasca & Maurício Scopel Hoffmann & Anelise Reis Gaya & Denise Ruschel Bandeira, 2021. "Subjective Well-Being and Psychopathology Symptoms: Mental Health Profiles and their Relations with Academic Achievement in Brazilian Children," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 14(3), pages 1121-1137, June.
    9. Cai, Jing-Heng & Song, Xin-Yuan & Lam, Kwok-Hap & Ip, Edward Hak-Sing, 2011. "A mixture of generalized latent variable models for mixed mode and heterogeneous data," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2889-2907, November.
    10. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    11. Fernández, D. & Arnold, R. & Pledger, S., 2016. "Mixture-based clustering for the ordered stereotype model," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 46-75.
    12. Chun Wang & Steven W. Nydick, 2020. "On Longitudinal Item Response Theory Models: A Didactic," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 339-368, June.
    13. Isabelle Archambault & Véronique Dupéré, 2017. "Joint trajectories of behavioral, affective, and cognitive engagement in elementary school," The Journal of Educational Research, Taylor & Francis Journals, vol. 110(2), pages 188-198, March.
    14. Meng Li & Sijia Xiang & Weixin Yao, 2016. "Robust estimation of the number of components for mixtures of linear regression models," Computational Statistics, Springer, vol. 31(4), pages 1539-1555, December.
    15. Pietro Lovaglio & Mario Mezzanzanica, 2013. "Classification of longitudinal career paths," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(2), pages 989-1008, February.
    16. Leila Amiri & Mojtaba Khazaei & Mojtaba Ganjali, 2018. "A mixture latent variable model for modeling mixed data in heterogeneous populations and its applications," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 95-115, January.
    17. dos Santos, Fabio Luis Marques & Duboz, Amandine & Grosso, Monica & Raposo, María Alonso & Krause, Jette & Mourtzouchou, Andromachi & Balahur, Alexandra & Ciuffo, Biagio, 2022. "An acceptance divergence? Media, citizens and policy perspectives on autonomous cars in the European Union," Transportation Research Part A: Policy and Practice, Elsevier, vol. 158(C), pages 224-238.
    18. Lu, Xiaosun & Huang, Yangxin & Zhu, Yiliang, 2016. "Finite mixture of nonlinear mixed-effects joint models in the presence of missing and mismeasured covariate, with application to AIDS studies," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 119-130.
    19. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    20. Jost Reinecke & Daniel Seddig, 2011. "Growth mixture models in longitudinal research," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(4), pages 415-434, December.

    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:71:y:2014:i:c:p:220-240. 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.