IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v95y2005i2p370-384.html
   My bibliography  Save this article

Mixtures of factor analyzers: an extension with covariates

Author

Listed:
  • Fokoué, Ernest

Abstract

This paper examines the analysis of an extended finite mixture of factor analyzers (MFA) where both the continuous latent variable (common factor) and the categorical latent variable (component label) are assumed to be influenced by the effects of fixed observed covariates. A polytomous logistic regression model is used to link the categorical latent variable to its corresponding covariate, while a traditional linear model with normal noise is used to model the effect of the covariate on the continuous latent variable. The proposed model turns out be in various ways an extension of many existing related models, and as such offers the potential to address some of the issues not fully handled by those previous models. A detailed derivation of an EM algorithm is proposed for parameter estimation, and latent variable estimates are obtained as by-products of the overall estimation procedure.

Suggested Citation

  • Fokoué, Ernest, 2005. "Mixtures of factor analyzers: an extension with covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 370-384, August.
    • Handle: RePEc:eee:jmvana:v:95:y:2005:i:2:p:370-384
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00158-7
    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. 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.
    2. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    3. Yiu-Fai Yung, 1997. "Finite mixtures in confirmatory factor-analysis models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 297-330, September.
    4. 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.
    5. 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.
    6. Mary Dupuis Sammel & Louise M. Ryan & Julie M. Legler, 1997. "Latent Variable Models for Mixed Discrete and Continuous Outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 667-678.
    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. Zhou, Xingcai & Liu, Xinsheng, 2008. "The EM algorithm for the extended finite mixture of the factor analyzers model," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3939-3953, April.
    2. James C. Slaughter & Amy H. Herring & John M. Thorp, 2009. "A Bayesian Latent Variable Mixture Model for Longitudinal Fetal Growth," Biometrics, The International Biometric Society, vol. 65(4), pages 1233-1242, December.

    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. 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.
    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. Williams, John & Temme, Dirk & Hildebrandt, Lutz, 2002. "A Monte Carlo study of structural equation models for finite mixtures," SFB 373 Discussion Papers 2002,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. 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.
    5. 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.
    6. Zhou, Xingcai & Liu, Xinsheng, 2008. "The EM algorithm for the extended finite mixture of the factor analyzers model," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3939-3953, April.
    7. 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.
    8. Sy-Miin Chow & Guangjian Zhang, 2013. "Nonlinear Regime-Switching State-Space (RSSS) Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 740-768, October.
    9. 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.
    10. Silvia Cagnone & Cinzia Viroli, 2014. "A factor mixture model for analyzing heterogeneity and cognitive structure of dementia," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(1), pages 1-20, January.
    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. Casey Codd & Robert Cudeck, 2014. "Nonlinear Random-Effects Mixture Models for Repeated Measures," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 60-83, January.
    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. Anindita Chakravarty & Rajdeep Grewal & V. Sambamurthy, 2013. "Information Technology Competencies, Organizational Agility, and Firm Performance: Enabling and Facilitating Roles," Information Systems Research, INFORMS, vol. 24(4), pages 976-997, December.
    15. Heike Heidemeier & Anja Göritz, 2013. "Individual Differences in How Work and Nonwork Life Domains Contribute to Life Satisfaction: Using Factor Mixture Modeling for Classification," Journal of Happiness Studies, Springer, vol. 14(6), pages 1765-1788, December.
    16. Jolynn Pek & R. Philip Chalmers & Bethany E. Kok & Diane Losardo, 2015. "Visualizing Confidence Bands for Semiparametrically Estimated Nonlinear Relations Among Latent Variables," Journal of Educational and Behavioral Statistics, , vol. 40(4), pages 402-423, August.
    17. Asokan Mulayath Variyath & Anita Brobbey, 2020. "Variable selection in multivariate multiple regression," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-15, July.
    18. 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.
    19. Yang Lu, 2019. "Flexible (panel) regression models for bivariate count–continuous data with an insurance application," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1503-1521, October.
    20. Wang, Zihan & Daeipour, Mohamad & Xu, Hongyi, 2023. "Quantification and propagation of Aleatoric uncertainties in topological structures," Reliability Engineering and System Safety, Elsevier, vol. 233(C).

    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:jmvana:v:95:y:2005:i:2:p:370-384. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.