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Variable selection in general multinomial logit models

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  • Tutz, Gerhard
  • Pößnecker, Wolfgang
  • Uhlmann, Lorenz

Abstract

The use of the multinomial logit model is typically restricted to applications with few predictors, because in high-dimensional settings maximum likelihood estimates tend to deteriorate. A sparsity-inducing penalty is proposed that accounts for the special structure of multinomial models by penalizing the parameters that are linked to one variable in a grouped way. It is devised to handle general multinomial logit models with a combination of global predictors and those that are specific to the response categories. A proximal gradient algorithm is used that efficiently computes stable estimates. Adaptive weights and a refitting procedure are incorporated to improve variable selection and predictive performance. The effectiveness of the proposed method is demonstrated by simulation studies and an application to the modeling of party choice of voters in Germany.

Suggested Citation

  • Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:207-222
    DOI: 10.1016/j.csda.2014.09.009
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    References listed on IDEAS

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    1. Rui Wang & Naihua Xiu & Kim-Chuan Toh, 2021. "Subspace quadratic regularization method for group sparse multinomial logistic regression," Computational Optimization and Applications, Springer, vol. 79(3), pages 531-559, July.
    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. Nibbering, Didier & Hastie, Trevor J., 2022. "Multiclass-penalized logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    4. Mauerer, Ingrid & Pößnecker, Wolfgang & Thurner, Paul W. & Tutz, Gerhard, 2015. "Modeling electoral choices in multiparty systems with high-dimensional data: A regularized selection of parameters using the lasso approach," Journal of choice modelling, Elsevier, vol. 16(C), pages 23-42.
    5. Raja Chakir & Thibault Laurent & Anne Ruiz-Gazen & Christine Thomas-Agnan & Céline Vignes, 2017. "Prédiction de l’usage des sols sur un zonage régulier à différentes résolutions et à partir de covariables facilement accessibles," Revue économique, Presses de Sciences-Po, vol. 68(3), pages 435-469.
    6. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.

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