In modern retail contexts, retailers sell products from vast product assortments to a large and heterogeneous customer base. Understanding purchase behavior in such a context is very important. Standard models cannot be used due to the high dimensionality of the data. We propose a new model that creates an efficient dimension reduction through the idea of purchase motivations. We only require customer-level purchase history data, which is ubiquitous in modern retailing. The model handles large-scale data and even works in settings with shopping trips consisting of few purchases. As scalability of the model is essential for practical applicability, we develop a fast, custom-made inference algorithm based on variational inference. Essential features of our model are that it accounts for the product, customer and time dimensions present in purchase history data; relates the relevance of motivations to customer- and shopping-trip characteristics; captures interdependencies between motivations; and achieves superior predictive performance. Estimation results from this comprehensive model provide deep insights into purchase behavior. Such insights can be used by managers to create more intuitive, better informed, and more effective marketing actions. We illustrate the model using purchase history data from a Fortune 500 retailer involving more than 4,000 unique products
