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.

营销组合模型 (MMM) 是用于衡量各种营销活动（如促销、媒体广告等）有效性的统计模型。在本研究中，我们提出了一个综合营销组合模型，该模型捕捉了层次结构以及结转、形状和规模效应某些营销活动，以及对某些符合商业常识的系数进行符号限制。与实践中普遍采用的方法（在多阶段过程中估计参数）相比，所提出的方法使用约束最大似然方法和哈密顿蒙特卡罗算法同时估计所有未知参数。我们展示了真实数据集的结果，以说明所提出的解决方案算法的使用。