A comparison of generalized multinomial logit (GMNL) and latent class approaches to studying consumer heterogeneity with some extensions of the GMNL model by Peter J. Lenk

I wish to congratulate the authors on their comparison of the newly proposed generalized multinomial logit (GMNL) of Fiebig et al. [1], henceforth ‘FKLW,’ with the widely-used, latent class or finite mixture model of Kamakura and Russell [2]. Both models use the same logistic regression likelihood for product choice but differ in their distributions for individual parameter heterogeneity. I am agnostic about the ‘best’ model for parameter heterogeneity. Ultimately, it is an empirical issue. When models are nested, the smaller model may be preferred because of its simplicity. Conversely, even when the smaller model has better AIC or BIC, a practitioner may choose the larger model if it provides useful information for marketing strategy. When models are not nested, as in this paper, comparisons beyond fit are more nuanced because the models have different foundations and implications. Academics who propose new models tend to be more focused on improved fit, while practitioners tend to look for new models that extend the set of functional problems that can be addressed. Aitchison and Bennet [3] introduced the probit model for product choice based on maximizing random ‘enjoyment,’ which has normal distributions. Partly because of limitations in computing power at the time and partly because of lack of visibility among economist, this work was superseded by the logistic random utility model of McFadden [4]. The random utility for subject i , product j , and choice occasion t is