考虑需求-营销交互的媒体混合模型估计：一种约束遗传算法方法
Estimating Media Mix Models with Demand-Marketing Interactions: A Constrained Genetic Algorithm Approach
浏览论文内容
中文总结 AI 辅助
本文针对媒体混合模型的可识别性与参数估计偏差问题，提出带需求-营销乘性交互的扩展模型，采用约束遗传算法优化，经模拟与真实数据验证可提升估计准确性，助力预算分配决策。
中文摘要 AI 辅助
本文对媒体混合模型（Media Mix Modeling，MMM）提出了一种新颖扩展，引入了营销活动与潜在消费者需求之间的乘性交互作用。与标准MMM框架假设媒体和基线需求驱动因素具有加性且独立的效应不同，我们的设定允许营销有效性随当前需求条件而变化。然而，所提出的结构带来了显著的统计挑战，尤其是可识别性问题，这可能导致参数估计不稳定且有偏。我们通过全面的模拟研究，结合偏差评估分析了这些可识别性问题的性质和严重程度，及其对统计推断的影响。为解决这些问题，我们开发了一种约束遗传算法优化方法，该方法可实现稳健估计，同时减轻上述问题导致的偏差。所提出的方法还具有灵活性，可纳入具有经济意义的参数约束。最后，将该方法应用于真实数据，以证明其在考虑额外商业约束的同时提高估计准确性的有效性，从而为预算分配决策提供支持。
英文摘要
This paper proposes a novel extension to Media Mix Modeling (MMM) that introduces a multiplicative interaction between marketing activity and underlying consumer demand. Unlike standard MMM frameworks that assume additive and independent effects of media and baseline demand drivers, our specification allows marketing effectiveness to vary with prevailing demand conditions. However, the proposed structure introduces significant statistical challenges, particularly identifiability issues that can lead to unstable and biased parameter estimates. Using comprehensive simulation studies, we analyze the nature and severity of these identification issues through bias assessment and their implications for statistical inference. To address these issues, we develop a constrained genetic algorithm optimization approach which facilitates robust estimation that simultaneously mitigates biases arising from the aforementioned issues. The proposed approach also offers flexibility to incorporate economically meaningful parameter constraints. Finally, the proposed methodology is applied to real-world data to demonstrate its effectiveness in enhancing estimation accuracy while taking into account additional commercial constraints, facilitating budget allocation decisions.
