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Regularized nonsymmetric correspondence analysis

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  • Takane, Yoshio
  • Jung, Sunho

Abstract

Nonsymmetric correspondence analysis (NSCA) is designed to analyze two-way contingency tables in which rows and columns assume an asymmetric role, e.g.,columns depend on rows, but not vice versa. A ridge type of regularization was incorporated into a variety of NSCA: Ordinary NSCA, and Partial and/or Constrained NSCA. The regularization has proven useful in obtaining estimates of parameters, which are on average closer to the true population values. An optimal value of the regularization parameter is found by a G-fold cross validation method, and the best dimensionality of the solution space is determined by permutation tests. A bootstrap method is used to evaluate the stability of the solution. A small Monte Carlo study and an illustrative example demonstrate the usefulness of the proposed procedures.

Suggested Citation

  • Takane, Yoshio & Jung, Sunho, 2009. "Regularized nonsymmetric correspondence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3159-3170, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3159-3170
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    References listed on IDEAS

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    1. Heungsun Hwang & Yoshio Takane, 2002. "Generalized constrained multiple correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 211-224, June.
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    1. Blasius, J. & Greenacre, M. & Groenen, P.J.F. & van de Velden, M., 2009. "Special issue on correspondence analysis and related methods," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3103-3106, June.
    2. Takane, Yoshio & Jung, Kwanghee & Hwang, Heungsun, 2011. "Regularized reduced rank growth curve models," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1041-1052, February.
    3. Yoshio Takane & Sunho Jung, 2009. "Tests of ignoring and eliminating in nonsymmetric correspondence analysis," 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. 3(3), pages 315-340, December.
    4. D'Ambra, Luigi & Amenta, Pietro & D'Ambra, Antonello & de Tibeiro, Jules S., 2021. "A study of the family service expenditures and the socio-demographic characteristics via fixed marginals correspondence analysis," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).

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