Interdependences of Products in Market Baskets: Comparing the Conditional Restricted Boltzmann Machine to the Multivariate Logit Model

Abstract We analyze market baskets of individual households in two consumer durables categories (music, computer related products) by the multivariate logit (MVL) model, its finite mixture extension (FM-MVL) and the conditional restricted Boltzmann machine (CRBM). The CRBM attains a vastly better out-of-sample performance than MVL and FM-MVL models. Based on simulation-based likelihood ratio tests we prefer the CRBM to the FM-MVL model. To interpret hidden variables of conditional Boltzmann machines we look at their average probability differences between purchase and non-purchases of any sub-category across all baskets. To measure interdependences we compute cross effects between sub-categories for the best performing FM-MVL model and CRBM. In both product categories the CRBM indicates more or higher positive cross effects than the FM-MVL model. Finally, we suggest appropriate future research based on larger and more detailed data sets.