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Multinomial logit models with implicit variable selection

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  • Faisal Zahid
  • Gerhard Tutz

Abstract

The multinomial logit model is the most widely used model for the unordered multi-category responses. However, applications are typically restricted to the use of few predictors because in the high-dimensional case maximum likelihood estimates frequently do not exist. In this paper we are developing a boosting technique called multinomBoost that performs variable selection and fits the multinomial logit model also when predictors are high-dimensional. Since in multi-category models the effect of one predictor variable is represented by several parameters one has to distinguish between variable selection and parameter selection. A special feature of the approach is that, in contrast to existing approaches, it selects variables not parameters. The method can also distinguish between mandatory predictors and optional predictors. Moreover, it adapts to metric, binary, nominal and ordinal predictors. Regularization within the algorithm allows to include nominal and ordinal variables which have many categories. In the case of ordinal predictors the order information is used. The performance of boosting technique with respect to mean squared error, prediction error and the identification of relevant variables is investigated in a simulation study. The method is applied to the national Indonesia contraceptive prevalence survey and the identification of glass. Results are also compared with the Lasso approach which selects parameters. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
  • Handle: RePEc:spr:advdac:v:7:y:2013:i:4:p:393-416
    DOI: 10.1007/s11634-013-0136-4
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    References listed on IDEAS

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    1. Jan Gertheiss & Gerhard Tutz, 2009. "Penalized Regression with Ordinal Predictors," International Statistical Review, International Statistical Institute, vol. 77(3), pages 345-365, December.
    2. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    3. 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.
    4. 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.
    5. Buhlmann P. & Yu B., 2003. "Boosting With the L2 Loss: Regression and Classification," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 324-339, January.
    6. 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).
    7. Tutz, Gerhard & Binder, Harald, 2007. "Boosting ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6044-6059, August.
    8. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    9. 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.
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    Cited by:

    1. Paz, Alexander & Arteaga, Cristian & Cobos, Carlos, 2019. "Specification of mixed logit models assisted by an optimization framework," Journal of choice modelling, Elsevier, vol. 30(C), pages 50-60.
    2. Moritz Berger & Thomas Welchowski & Steffen Schmitz-Valckenberg & Matthias Schmid, 2019. "A classification tree approach for the modeling of competing risks in discrete time," 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. 13(4), pages 965-990, December.
    3. Faisal Maqbool Zahid & Gerhard Tutz, 2013. "Proportional Odds Models with High‐Dimensional Data Structure," International Statistical Review, International Statistical Institute, vol. 81(3), pages 388-406, December.
    4. Bayerstadler, Andreas & van Dijk, Linda & Winter, Fabian, 2016. "Bayesian multinomial latent variable modeling for fraud and abuse detection in health insurance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 244-252.

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