IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i11p2889-2907.html
   My bibliography  Save this article

A mixture of generalized latent variable models for mixed mode and heterogeneous data

Author

Listed:
  • Cai, Jing-Heng
  • Song, Xin-Yuan
  • Lam, Kwok-Hap
  • Ip, Edward Hak-Sing

Abstract

In the behavioral, biomedical, and social-psychological sciences, mixed data types such as continuous, ordinal, count, and nominal are common. Subpopulations also often exist and contribute to heterogeneity in the data. In this paper, we propose a mixture of generalized latent variable models (GLVMs) to handle mixed types of heterogeneous data. Different link functions are specified to model data of multiple types. A Bayesian approach, together with the Markov chain Monte Carlo (MCMC) method, is used to conduct the analysis. A modified DIC is used for model selection of mixture components in the GLVMs. A simulation study shows that our proposed methodology performs satisfactorily. An application of mixture GLVM to a data set from the National Longitudinal Surveys of Youth (NLSY) is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:11:p:2889-2907
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311001770
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. 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.
    3. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
    4. Fruhwirth-Schnatter S., 2001. "Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 194-209, March.
    5. Yiu-Fai Yung, 1997. "Finite mixtures in confirmatory factor-analysis models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 297-330, 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. Philippe Huber & Elvezio Ronchetti & Maria‐Pia Victoria‐Feser, 2004. "Estimation of generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 893-908, November.
    8. 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.
    9. Gerhard Arminger & Petra Stein & Jörg Wittenberg, 1999. "Mixtures of conditional mean- and covariance-structure models," Psychometrika, Springer;The Psychometric Society, vol. 64(4), pages 475-494, December.
    10. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    11. Hong-Tu Zhu & Sik-Yum Lee, 2001. "A Bayesian analysis of finite mixtures in the LISREL model," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 133-152, March.
    12. Irini Moustaki & Martin Knott, 2000. "Generalized latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 391-411, September.
    13. Moustaki, Irini & Victoria-Feser, Maria-Pia, 2006. "Bounded-Influence Robust Estimation in Generalized Linear Latent Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 644-653, June.
    14. Mingan Yang & David Dunson, 2010. "Bayesian Semiparametric Structural Equation Models with Latent Variables," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 675-693, December.
    15. Philippe HUBER & Olivier SCAILLET & Maria-Pia VICTORIA-FESER, 2008. "Assessing multivariate predictors of financial market movements: A latent factor framework for ordinal data," Swiss Finance Institute Research Paper Series 08-45, Swiss Finance Institute.
    16. Meyer, Renate & Cai, Bo & Perron, François, 2008. "Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3408-3423, March.
    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. Xin-Yuan Song & Zhao-Hua Lu & Jing-Heng Cai & Edward Ip, 2013. "A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 624-647, October.
    2. Christian Carmona & Luis Nieto-Barajas & Antonio Canale, 2019. "Model-based approach for household clustering with mixed scale variables," 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. 13(2), pages 559-583, June.
    3. Zhang, Q. & Ip, E.H., 2014. "Variable assessment in latent class models," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 146-156.
    4. Ye, Mao & Lu, Zhao-Hua & Li, Yimei & Song, Xinyuan, 2019. "Finite mixture of varying coefficient model: Estimation and component selection," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 452-474.
    5. Damien McParland & Isobel Claire Gormley, 2016. "Model based clustering for mixed data: clustMD," 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. 10(2), pages 155-169, June.
    6. Leila Amiri & Mojtaba Khazaei & Mojtaba Ganjali, 2017. "General location model with factor analyzer covariance matrix structure and its applications," 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. 11(3), pages 593-609, September.
    7. 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.
    8. Daniel Fernández & Richard Arnold & Shirley Pledger & Ivy Liu & Roy Costilla, 2019. "Finite mixture biclustering of discrete type multivariate 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. 13(1), pages 117-143, March.
    9. Ranalli, Monia & Rocci, Roberto, 2017. "Mixture models for mixed-type data through a composite likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 87-102.

    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. Xin-Yuan Song & Zhao-Hua Lu & Jing-Heng Cai & Edward Ip, 2013. "A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 624-647, October.
    2. 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.
    3. Li, Yun-Xian & Kano, Yutaka & Pan, Jun-Hao & Song, Xin-Yuan, 2012. "A criterion-based model comparison statistic for structural equation models with heterogeneous data," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 92-107.
    4. Yanyuan Ma & Marc G. Genton, 2010. "Explicit estimating equations for semiparametric generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 475-495, September.
    5. Xiong, Yingge & Mannering, Fred L., 2013. "The heterogeneous effects of guardian supervision on adolescent driver-injury severities: A finite-mixture random-parameters approach," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 39-54.
    6. Assaf, A. George & Tsionas, Mike & Oh, Haemoon, 2018. "The time has come: Toward Bayesian SEM estimation in tourism research," Tourism Management, Elsevier, vol. 64(C), pages 98-109.
    7. Hong-Tu Zhu & Sik-Yum Lee, 2001. "A Bayesian analysis of finite mixtures in the LISREL model," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 133-152, March.
    8. Fokoué, Ernest, 2005. "Mixtures of factor analyzers: an extension with covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 370-384, August.
    9. Chen, Yunxiao & Lu, Yan & Moustaki, Irini, 2022. "Detection of two-way outliers in multivariate data and application to cheating detection in educational tests," LSE Research Online Documents on Economics 112499, London School of Economics and Political Science, LSE Library.
    10. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    11. Temme, Dirk & Williams, John R. & Hildebrandt, Lutz, 2002. "Structural equation models for finite mixtures: Simulation results and empirical applications," SFB 373 Discussion Papers 2002,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Dylan Molenaar & Paul Boeck, 2018. "Response Mixture Modeling: Accounting for Heterogeneity in Item Characteristics across Response Times," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 279-297, June.
    13. Xia, Ye-Mao & Tang, Nian-Sheng, 2019. "Bayesian analysis for mixture of latent variable hidden Markov models with multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 190-211.
    14. 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.
    15. Yang Li & Asim Ansari, 2014. "A Bayesian Semiparametric Approach for Endogeneity and Heterogeneity in Choice Models," Management Science, INFORMS, vol. 60(5), pages 1161-1179, May.
    16. Emilio Augusto Coelho-Barros & Jorge Alberto Achcar & Josmar Mazucheli, 2010. "Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(5), pages 865-880.
    17. Vitoratou, Silia & Ntzoufras, Ioannis & Moustaki, Irini, 2016. "Explaining the behavior of joint and marginal Monte Carlo estimators in latent variable models with independence assumptions," LSE Research Online Documents on Economics 57685, London School of Economics and Political Science, LSE Library.
    18. Zhang, Q. & Ip, E.H., 2014. "Variable assessment in latent class models," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 146-156.
    19. Bacci, Silvia & Bartolucci, Francesco & Pieroni, Luca, 2012. "A causal analysis of mother’s education on birth inequalities," MPRA Paper 38754, University Library of Munich, Germany.
    20. Yuan Fang & Dimitris Karlis & Sanjeena Subedi, 2022. "Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 510-552, November.

    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:55:y:2011:i:11:p:2889-2907. 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.