Capturing Heterogeneity in the Multinomial Logit Model by Implementing the Bagging Method

When a multinomial logit model (MNL) is constructed by selecting the best (e.g. the highest t-values) subset of independent variables using the Maximum Likelihood (ML) approach the stability of parameters is not guaranteed and has not been discussed in the literature. The definition of instability by Breiman (1) implies that when a model is unstable a small change in its train dataset results in considerable changes in the structure of the model. Thereby, instability results in biased prediction error. The bagging method, i.e. utilizing an ensemble of models instead of a single model has been introduced in the literature to be effective in reducing instability for some modelling formulations. Bagging can also increase the overall model’s goodness-of-fit. This paper investigates the effectiveness of implementing the bagging method in MNL. It also discusses the required condition where the ensemble of MNLs, called Random MNL (RMNL), improves the log-likelihood value compared to a single MNL. Furthermore, the capability of RMNL in capturing taste variation is explained and the prediction accuracy of RMNL is compared against mixed logit (MMNL) as a well-known model for addressing heterogeneity. A publicly available dataset of “college distance” is used to demonstrate the impacts of the bagging method on MNL