Frequentist Model Averaging in the Generalized Multinomial Logit Model

The generalized multinomial logit (GMNL) model nests the random parameters logit (RPL) model and the scale heterogeneity logit (SMNL) model. The RPL model captures the preference heterogeneity among individuals by allowing the coefficients to be random with any distribution. It has been often used to analyze and predict people' choices in many fields, such as health economics, agriculture economics, marketing and transportation research. However, more and more researchers stated that much of the preference heterogeneity in most choice context can be better described as "scale" heterogeneity, which takes the form of coefficients of observed attributes scaled down or up proportionately over individuals. The random coefficients of the RPL model cannot adequately account for such scale heterogeneity. The GMNL model accommodates scale heterogeneity to the preference heterogeneity in the RPL model. Incorporating the scaling parameter to the preference heterogeneity in the RPL model makes the maximization of the simulated likelihood function of GMNL model become more difficult and the corresponding estimated parameters have bigger variance. In this paper, we use frequentist model average estimator to reduce the estimation and prediction risks of the GMNL estimators. The model average estimator in this study is a weighted combination of GMNL-I and GMNL-II estimators. The weight is selected by minimizing the asymptotic squared error risk of the model average estimator. The results of our Monte Carlo experiments show that the frequentist model average estimator provides smaller mean squared error (MSE) than the GMNL estimator. The accuracy of the predicted choices are higher based on the model average estimates compared to the results based on the GMNL estimates. In the empirical analyses, using model average estimator improves the percentage of correct predicted choices by 10% compared to the results with GMNL estimate