Analyzing market baskets by restricted Boltzmann machines

We introduce a model which differs from the well-known multivariate logit model (MVL) used to analyze the cross-category dependence in market baskets by the addition of binary hidden variables. This model is called restricted Boltzmann machine (RBM) and new to the marketing literature. Extant applications of the MVL model for higher numbers of categories typically follow a two-step approach as simultaneous maximum likelihood estimation is computationally infeasible. In contrast to the MVL, the RBM can be simultaneously estimated by maximum likelihood even for a higher number of categories as long as the number of hidden variables is moderate. We measure the cross-category dependence by pairwise marginal cross effects which are obtained using estimated coefficients and sampling of baskets. In the empirical study, we analyze market baskets consisting of the 60 most frequently purchased categories of the assortment of a supermarket. For a validation data set, the RBM performs better than the MVL model estimated by maximum pseudo-likelihood. For our data, about 75 % of the baskets are reproduced by the model without cross-category dependence, but 25 % of the baskets cannot be adequately modeled if cross effects are ignored. Moreover, it turns out that both the number of significant cross effects and their relationships can be grasped rather easily.