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Multiple correspondence analysis and the multilogit bilinear model

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  • Fithian, William
  • Josse, Julie

Abstract

Multiple correspondence analysis is a dimension reduction technique which plays a large role in the analysis of tables with categorical nominal variables, such as survey data. Though it is usually motivated and derived using geometric considerations, we prove that in fact, it can be seen as a single proximal Newton step of a natural bilinear exponential family model for categorical data: the multinomial logit bilinear model. We compare and contrast the behavior of multiple correspondence analysis with that of this model on simulated data, and discuss new insights into both approaches and their cognate models. Consequently, multiple correspondence analysis can be used to approximate the parameters of the multilogit model. Indeed, estimating the model’s parameters is non-trivial, whereas multiple correspondence analysis has the advantage of being easily solved by a singular value decomposition, and scalable to large data sets. We illustrate the methods on a survey of the drinking habits in France in the context of European policies against the harmful effects of alcohol on society.

Suggested Citation

  • Fithian, William & Josse, Julie, 2017. "Multiple correspondence analysis and the multilogit bilinear model," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 87-102.
    • Handle: RePEc:eee:jmvana:v:157:y:2017:i:c:p:87-102
    DOI: 10.1016/j.jmva.2017.02.009
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    References listed on IDEAS

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    1. Julie Josse & Marie Chavent & Benot Liquet & François Husson, 2012. "Handling Missing Values with Regularized Iterative Multiple Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 29(1), pages 91-116, April.
    2. Mark Rooij & Willem Heiser, 2005. "Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 99-122, March.
    3. Mark de Rooij, 2008. "The analysis of change, Newton's law of gravity and association models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 137-157, January.
    4. Genevera I. Allen & Logan Grosenick & Jonathan Taylor, 2014. "A Generalized Least-Square Matrix Decomposition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 145-159, March.
    5. Husson, François & Josse, Julie & Saporta, Gilbert, 2016. "Jan de Leeuw and the French School of Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i06).
    6. Peter Heijden & Jan Leeuw, 1985. "Correspondence analysis used complementary to loglinear analysis," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 429-447, December.
    7. de Leeuw, Jan, 2006. "Principal component analysis of binary data by iterated singular value decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 21-39, January.
    8. Irini Moustaki & Martin Knott, 2000. "Generalized latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 391-411, September.
    9. Henk Kiers, 1991. "Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 197-212, June.
    10. Michel Tenenhaus & Forrest Young, 1985. "An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 91-119, March.
    11. Jean‐Baptiste Denis & John C. Gower, 1996. "Asymptotic Confidence Regions for Biadditive Models: Interpreting Genotype‐Environment Interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 479-493, December.
    12. Peter D. Hoff, 2009. "Multiplicative latent factor models for description and prediction of social networks," Computational and Mathematical Organization Theory, Springer, vol. 15(4), pages 261-272, December.
    13. Vartan Choulakian, 1996. "Generalized bilinear models," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 271-283, June.
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    Cited by:

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