A generalised discrete mixture model to better capture preference heterogeneity in discrete choice data

Abstract: Arguably the key issue in modelling discrete choice data is capturing preference heterogeneity. This can be through observed characteristics, and/or using techniques for capturing random heterogeneity across respondents. On the latter, in health economics, the two main approaches are the mixed multinomial logit (MMNL) and the latent class (LC) model. In this paper, we revisit the discrete mixture (DM) model as a third alternative to these. The DM model is similar to LC but allows for any combination of preferences across attributes, rather than grouping preferences as is the case in LC. We next develop a generalised discrete mixture (GDM) model. Additional boosting parameters in the class allocation component allow the model to collapse to a standard DM or LC structure as best fits the data at hand. This means that the model, by definition, performs at least as well as the best of a standard DM and a LC model; or better than both. Additional benefits include that it (a) allows the data to tell us the underlying correlations of preferences, (b) does not rely on distributions as is the case for mixed logit models, meaning estimation times are reduced and it does not require assumptions on the distribution of preferences. Exercises on simulated data show the unlikely conditions under which a LC model would be preferred to a DM. The convention of labelling latent classes, we believe, is questionable in many cases. The GDM is suitable in all cases. We show in empirical data that the GDM substantially outperforms LC models, granting a more detailed depiction of respondents' preferences.