Hierarchical marketing mix models with sign constraints

Marketing mix models (MMMs) are statistical models for measuring the effectiveness of various marketing activities such as promotion, media advertisement, etc. In this research, we propose a comprehensive marketing mix model that captures the hierarchical structure and the carryover, shape and scale effects of certain marketing activities, as well as sign restrictions on certain coefficients that are consistent with common business sense. In contrast to commonly adopted approaches in practice, which estimate parameters in a multi-stage process, the proposed approach estimates all the unknown parameters simultaneously using a constrained maximum likelihood approach and a Hamiltonian Monte Carlo algorithm. We present results on real datasets to illustrate the use of the proposed solution algorithms.