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Ridge estimation for multinomial logit models with symmetric side constraints

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  • Faisal Zahid
  • Gerhard Tutz

Abstract

In multinomial logit models, the identifiability of parameter estimates is typically obtained by side constraints that specify one of the response categories as reference category. When parameters are penalized, shrinkage of estimates should not depend on the reference category. In this paper we investigate ridge regression for the multinomial logit model with symmetric side constraints, which yields parameter estimates that are independent of the reference category. In simulation studies the results are compared with the usual maximum likelihood estimates and an application to real data is given. Copyright Springer-Verlag 2013

Suggested Citation

  • Faisal Zahid & Gerhard Tutz, 2013. "Ridge estimation for multinomial logit models with symmetric side constraints," Computational Statistics, Springer, vol. 28(3), pages 1017-1034, June.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:3:p:1017-1034
    DOI: 10.1007/s00180-012-0341-1
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    References listed on IDEAS

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    1. Gerhard Tutz & Harald Binder, 2006. "Generalized Additive Modeling with Implicit Variable Selection by Likelihood-Based Boosting," Biometrics, The International Biometric Society, vol. 62(4), pages 961-971, December.
    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
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    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Hans Nyquist, 1991. "Restricted Estimation of Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 133-141, March.
    6. S. le Cessie & J. C. van Houwelingen, 1992. "Ridge Estimators in Logistic Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 191-201, March.
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    1. Faisal Zahid & Gerhard Tutz, 2013. "Multinomial logit models with implicit variable selection," 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. 7(4), pages 393-416, December.
    2. Mohamed R. Abonazel & Rasha A. Farghali, 2019. "Liu-Type Multinomial Logistic Estimator," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 203-225, December.

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    More about this item

    Keywords

    Cross-validation; L2 penalty; Logistic regression ; Multicategory response; Penalization; Reference category;
    All these keywords.

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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