Response shrinkage estimation in multinomial logit models

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• 作者：Faisal Maqbool Zahid ; ^{faisal-maqbool.zahid@stat.uni-muenchen.de} ; Christian Heumann ^{christian.heumann@stat.uni-muenchen.de}
• 关键词：Logistic regression ; Shrinkage ; Response shrinkage estimator ; Shadow data ; Resistant fitting ; Multinomial logit
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2012
• 出版时间：January, 2012
• 年：2012
• 卷：142
• 期：1
• 页码：95-109
• 全文大小：298 K

文摘

A shrinkage estimation method for multinomial logit models is developed. The proposed method is based on shrinking the responses for each category towards the underlying probabilities. The estimator is also used in combination with Pregibon's resistant fitting. The resulting estimator can also be used to control the over-estimation of Pregibon's resistant estimator. The proposed method handles not only the problem of separation in multinomial logit models but estimates also exist when the number of covariates is large relative to the sample size. Estimates exist even when the MLE does not exist. Estimates can be easily computed with all commonly used statistical packages supporting the fitting procedures with weights. Estimates are compared with the usual MLE and Firth's bias reduction technique in a simulation study and an application.