Latent Ordering Conjoint Model Under Lexicographic Preferences

Consumer's preference structure varies over product categories. For some durable goods, such as laptops and smartphones, consumers tend to distinguish a product from its competing ones by differences in several features ordered in their importance. This preference structure, so called lexicographic preference, does not allow us to simply find the optimal marketing mix strategy because of two reasons: First, there is no simple utility function that captures the cardinal link with a continuous price variable as well as the ordinal preference structure. Secondly, the latent process of ordering attributes according to their importance cannot be easily calibrated in the conventional manners, such as MLE, GMM, and Bayesian methods. In this paper, we propose an economic framework that takes into account the ordinal lexicographic preference, the cardinal link with prices, and the latent ordering process by introducing a recursive utility specification and a data augmentation technique that employs multinomial-Dirichlet conjugacy.