Response shrinkage estimation in multinomial logit models

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 Pregibonʹs resistant fitting. The resulting estimator can also be used to control the over-estimation of Pregibonʹs 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 Firthʹs bias reduction technique in a simulation study and an application.