IDEAS home Printed from https://ideas.repec.org/a/bpj/jossai/v2y2014i5p437-450n5.html
   My bibliography  Save this article

A Robust Factor Analysis Model for Dichotomous Data

Author

Listed:
  • Yang Yixin

    (School of the Gifted Young, University of Science and Technology of China, Hefei230026, China)

  • Lü Xin

    (Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing100190, China)

  • Ma Jian

    (Department of Information Systems, City University of Hong Kong, Hong Kong, China)

  • Qiao Han

    (Management School, University of Chinese Academy of Sciences, Beijing100180, China)

Abstract

Factor analysis is widely used in psychology, sociology and economics, as an analytically tractable method of reducing the dimensionality of the data in multivariate statistical analysis. The classical factor analysis model in which the unobserved factor scores and errors are assumed to follow the normal distributions is often criticized because of its lack of robustness. This paper introduces a new robust factor analysis model for dichotomous data by using robust distributions such as multivariate t-distribution. After comparing the fitting results of the normal factor analysis model and the robust factor analysis model for dichotomous data, it can been seen that the robust factor analysis model can get more accurate analysis results in some cases, which indicates this model expands the application range and practical value of the factor analysis model.

Suggested Citation

  • Yang Yixin & Lü Xin & Ma Jian & Qiao Han, 2014. "A Robust Factor Analysis Model for Dichotomous Data," Journal of Systems Science and Information, De Gruyter, vol. 2(5), pages 437-450, October.
    • Handle: RePEc:bpj:jossai:v:2:y:2014:i:5:p:437-450:n:5
    DOI: 10.1515/JSSI-2014-0437
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/JSSI-2014-0437
    Download Restriction: no
    File URL: https://libkey.io/10.1515/JSSI-2014-0437?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
    ---><---

    References listed on IDEAS

    as
    1. Bartholomew, D. J., 1983. "Latent variable models for ordered categorical data," Journal of Econometrics, Elsevier, vol. 22(1-2), pages 229-243.
    2. Bengt Muthén, 1978. "Contributions to factor analysis of dichotomous variables," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 551-560, December.
    3. Stanislav Kolenikov & Gustavo Angeles, 2009. "Socioeconomic Status Measurement With Discrete Proxy Variables: Is Principal Component Analysis A Reliable Answer?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(1), pages 128-165, March.
    4. Yoshio Takane & Jan Leeuw, 1987. "On the relationship between item response theory and factor analysis of discretized variables," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 393-408, September.
    5. repec:ucp:bkecon:9780226316529 is not listed on IDEAS
    6. Rizopoulos, Dimitris, 2006. "ltm: An R Package for Latent Variable Modeling and Item Response Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i05).
    7. Anders Christoffersson, 1975. "Factor analysis of dichotomized variables," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 5-32, March.
    Full references (including those not matched with items on IDEAS)

    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. Edward Haertel, 1990. "Continuous and discrete latent structure models for item response data," Psychometrika, Springer;The Psychometric Society, vol. 55(3), pages 477-494, September.
    2. Steffen Grønneberg & Jonas Moss & Njål Foldnes, 2020. "Partial Identification of Latent Correlations with Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 1028-1051, December.
    3. Jonas Moss & Steffen Grønneberg, 2023. "Partial Identification of Latent Correlations with Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 241-252, March.
    4. Mark Reiser, 1996. "Analysis of residuals for the multionmial item response model," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 509-528, September.
    5. Maydeu-Olivares, Albert, 2002. "Limited information estimation and testing of Thurstonian models for preference data," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 467-483, July.
    6. Henry Brady, 1989. "Factor and ideal point analysis for interpersonally incomparable data," Psychometrika, Springer;The Psychometric Society, vol. 54(2), pages 181-202, June.
    7. Alexander Robitzsch, 2024. "A Comparison of Limited Information Estimation Methods for the Two-Parameter Normal-Ogive Model with Locally Dependent Items," Stats, MDPI, vol. 7(3), pages 1-16, June.
    8. Jochen Ranger & Kay Brauer, 2022. "On the Generalized S − X 2 –Test of Item Fit: Some Variants, Residuals, and a Graphical Visualization," Journal of Educational and Behavioral Statistics, , vol. 47(2), pages 202-230, April.
    9. Albert Maydeu-Olivares & Harry Joe, 2006. "Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 713-732, December.
    10. Njål Foldnes & Steffen Grønneberg, 2019. "On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1000-1017, December.
    11. Yoshio Takane & Jan Leeuw, 1987. "On the relationship between item response theory and factor analysis of discretized variables," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 393-408, September.
    12. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    13. Albert Maydeu-Olivares, 2001. "Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 209-227, June.
    14. Kamel Jedidi & Wayne DeSarbo, 1991. "A stochastic multidimensional scaling procedure for the spatial representation of three-mode, three-way pick any/J data," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 471-494, September.
    15. Ulf Böckenholt, 1990. "Multivariate thurstonian models," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 391-403, June.
    16. Beth Reboussin & Kung-Yee Liang, 1998. "An estimating equations approach for the LISCOMP model," Psychometrika, Springer;The Psychometric Society, vol. 63(2), pages 165-182, June.
    17. Bouguila, Nizar, 2010. "On multivariate binary data clustering and feature weighting," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 120-134, January.
    18. Wayne DeSarbo & Jaewun Cho, 1989. "A stochastic multidimensional scaling vector threshold model for the spatial representation of “pick any/n” data," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 105-129, March.
    19. Guirong Li & Jiajia Xu & Liying Li & Zhaolei Shi & Hongmei Yi & James Chu & Elena Kardanova & Yanyan Li & Prashant Loyalka & Scott Rozelle, 2020. "The Impacts of Highly Resourced Vocational Schools on Student Outcomes in China," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 28(6), pages 125-150, November.
    20. Paschalis Arvanitidis & Athina Economou & Christos Kollias, 2016. "Terrorism’s effects on social capital in European countries," Public Choice, Springer, vol. 169(3), pages 231-250, 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:bpj:jossai:v:2:y:2014:i:5:p:437-450:n:5. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.