带符号约束的分层营销组合模型
Hierarchical Marketing Mix Models with Sign Constraints
摘要：
营销组合模型（MMM）是用于测量各种营销活动（如促销，媒体广告等）的有效性的统计模型。在这项研究中，我们提出了一个全面的营销组合模型，捕捉层次结构和结转，形状和规模效应的某些营销活动，以及签署限制某些系数是符合商业常识。在实践中，通常采用的方法，估计参数在一个多阶段的过程中，所提出的方法估计所有的未知参数/系数同时使用约束极大似然法和解决的哈密顿蒙特卡罗算法。我们目前的结果，真实的数据集来说明使用所提出的解决方案的算法。
英文摘要：
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/coefficients simultaneously using a constrained maximum likelihood approach and solved with the Hamiltonian Monte Carlo algorithm. We present results on real datasets to illustrate the use of the proposed solution algorithm.
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