Hidden Variable Models for Market Basket Data. Statistical Performance and Managerial Implications

We compare the performance of several hidden variable models, namely binary factor analysis, topic models (latent Dirichlet allocation, correlated topic model), the restricted Boltzmann machine and the deep belief net. We shortly present these models and outline their estimation. Performance is measured by log likelihood values of these models for a holdout data set of market baskets. For each model we estimate and evaluate variants with increasing numbers of hidden variables. Binary factor analysis vastly outperforms topic models. The restricted Boltzmann machine and the deep belief net on the other hand attain a similar performance advantage over binary factor analysis. For each model we interpret the relationships between the most important hidden variables and observed category purchases. To demonstrate managerial implications we compute relative basket size increase due to promoting each category for the better performing models. Recommendations based on the restricted Boltzmann machine and the deep belief net not only have lower uncertainty due to their statistical performance, they also have more managerial appeal than those derived for binary factor analysis. The impressive performances of the restricted Boltzmann machine and the deep belief net suggest to continue research by extending these models, e.g., by including marketing variables as predictors.