International Choice Modelling Conference, International Choice Modelling Conference 2017

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Personalized Recommendations using Discrete Choice Models with Inter-and Intra-Consumer Heterogeneity
Mazen Danaf

Last modified: 28 March 2017


This paper proposes a methodology for estimating and continuously updating consumer preferences utilizing discrete choice models in the context of an app-based recommendation system which predicts user responses to options. The recommendation systems of interest are those where users are repeatedly presented with menus of alternatives to choose from. Individual-specific preferences are stored for each user, and retrieved once the user is identified (i.e. upon logging in to the system).

In order to estimate user preferences, we use the Hierarchical Bayes (HB) estimator proposed by Becker et al. (2016a) and Ben-Akiva et al. (2016). This estimator extends the Allenby-Train procedure (Train, 2009) to include intra-consumer heterogeneity, i.e., preference heterogeneity for a given individual, by adding two additional Gibbs sampling steps. Studies in the literature mostly address the heterogeneity across individuals, namely inter-consumer heterogeneity.

We propose a methodology in which individual-specific parameters are updated after each choice via a continuously running Monte Carlo Markov Chain (MCMC). Furthermore, data from multiple individuals are pooled periodically, and sample level parameters are updated to account for trends in the population.

The parameters of the proposed double-mixture model are classified into:

1.Sample level parameters representing the average tastes/preferences in the sample and the inter-consumer variance-covariance matrix respectively;

2.Individual level parameters representing the average tastes/preferences of a specific individual and the intra-consumer variance-covariance matrix respectively; and

3.Menu level parameters which reflect the choice situation specific tastes/preferences.

These parameters are estimated and updated through two interacting and repeated steps: the online and the offline procedures. The online estimation procedure updates users’ preferences in real time as they make new choices via a continuously running Monte Carlo Markov Chain. The individual specific parameters are updated after every choice, assuming that the sample parameters are fixed. This update is computationally inexpensive, as it can be done for the individual making the choice only. The offline estimation procedure updates individual as well as sample level parameters for all individuals. Periodically (e.g. overnight or once every week), data are pooled and all coefficients are updated to reflect the effects of all choices made by all individuals since the last update. Updating sample level parameters enables to account for population trends in estimating individual level coefficients.

The offline and online procedures result in updated individual and sample level parameters, which are stored in a database along with users’ characteristics and alternative attributes. These are then used as inputs to an online optimizer performing menu/assortment optimization. The optimization is therefore capable of offering personalized menu of alternatives to the user in real time.   The objective function of such optimization models can be tailored to the context, e.g., maximization of revenue and/or user benefit, and is expected to provide better solutions as it takes into account heterogeneity appropriately through the proposed procedure.

The proposed procedure is tested with the Monte-Carlo CBC Grapes data (Ben-Akiva et al, 2016, Becker et al, 2016a). The data assumes that 1000 subjects experience eight choice situations each, i.e., each is presented with eight menus. The menu includes three different bunches of grapes with varying prices and attributes and an opt-out alternative. Thus the dependent variable is the choice between different bunches, or not buying grapes at all.

The model has been estimated for menus 1-7 using two procedures: 1. full-offline procedure, where all the data is used for the offline procedure, 2. offline-online procedure, in which offline procedure is applied to a subset of menus (e.g. menus 1-5) and online procedure then follows with the data from the remaining menus. The eighth menu was used as the test data.

The estimation results indicate that the full-offline procedure achieves the highest final log-likelihood values and probabilities of the chosen alternatives for the test data as expected. However, this procedure would be infeasible in real-time, since updating the sample level estimates is computationally expensive. On the other hand, the offline-online procedure yields results that are very close to those obtained by the full offline procedure. The offline-online procedure is also feasible and efficient in real time, because it can be performed for the individual making the choice only rather than the whole sample.

Moreover, we evaluate the importance of accounting for intra-consumer heterogeneity compared to the case where only inter-consumer heterogeneity is modeled. Finally, we analyze the effects of accounting for individual level parameters, namely the impact of personalization, on the predicted choice probabilities. The results indicate that these probabilities decrease by about 4% if we do not account for personalization.

The proposed methodology can be applied to various online recommendations such as suggesting to users what items to buy, movies to watch, music to listen to, or news to read. It also applies to transport applications such as app-based services (Atasoy et al., 2015) and personalized travel advisors, e.g., MeMOT that is being designed at MIT.

The proposed Bayesian estimation outperforms standard maximum likelihood estimation (MLE) methods in recommender systems in two aspects. First, the proposed HB estimator is computationally more efficient compared to the ML estimator since it avoids the maximization of complex likelihood functions (using numerical simulation from multiple integrals in this case). Especially in the case of intra-consumer heterogeneity, where multi-dimensional integration is required, the added value is more evident. Second, individual-specific parameters can directly be obtained from the Markov Chains and used in forecasting and personalized optimization.



Atasoy, B., Ikeda, T., Song, X., and Ben-Akiva, M. (2015). ‘The concept and impact analysis of a flexible mobility on demand system’, Transportation Research Part C: Emerging Technologies, Vol. 56, pp. 373-392.

Becker, F. (2016). Bayesian Estimation of Mixed Logit Models with Inter- and Intra-Personal Heterogeneity. Thesis submitted for the Master of Science in Business Information Systems, Freie Universitaet Berlin.

Ben-Akiva, M., McFadden, D., and Train, K. (2016). Foundations of stated preference elicitation, consumer choice behavior and choice-based conjoint analysis, University of California, Berkeley.

Train, K. (2009). Discrete Choice Methods with Simulation, Cambridge University Press, Chapter 12.


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