Liu And Bias-Corrected Liu Estimator For The Multinomial Logit Model

Abstract

The multinomial logit Liu estimator and the bias-corrected multinomial logit Liu estimator are proposed as solutions to mitigate the issue of multicollinearity in the multinomial logit model. Furthermore, the superior properties of these estimators in terms of mean squared error are presented when compared to both the maximum likelihood estimator and the ridge estimator. The optimal values of the biasing parameter for the proposed estimators [1]are derived. A simulation is conducted to demonstrate the effectiveness of proposed estimators against ridge and traditional MLE using MSE and bias as performance criteria. The performance of estimators is judged by varying different factors such as the number of values, the number of predictors, levels of the response variable, and the multicollinearity levels. The result of the Monte-Carlo simulation and real data applications reveal that proposed estimators have lower MSE and bias compared to the MLE and ridge estimator.