加入新推出的
Discord 社区,展开实时讨论,获得同行支持,并直接与 Meridian 团队互动!
媒体饱和度与滞后
使用集合让一切井井有条
根据您的偏好保存内容并对其进行分类。
通常情况下,媒体渠道对销售的影响具有滞后效应,随着时间的推移会慢慢减弱。Meridian 的模型结构旨在通过几何衰减 Adstock 函数来捕捉这种效应。如需了解详情,请参阅“A Hierarchical Bayesian Approach to Improve Media Mix Models Using Category Data”(使用类别数据改进媒体组合模型的分层贝叶斯方法)和“Bayesian Methods for Media Mix Modeling with Carryover and Shape Effects”(利用延滞效应和形状效应进行媒体组合建模的贝叶斯方法)。
Adstock 函数
Adstock 函数的定义如下:
$$
\text{AdStock}(x_t, x_{t-1}, \cdots, x_{t-L};\ \alpha)\ =
\dfrac{\sum\limits_{s=0}^L\ \alpha^sx_{t-s}}
{\sum\limits _{s=0}^L\ \alpha^s}
$$
其中:
\(x_s \geq 0; s = t, t-1, \cdots, t-L\)
\(\alpha\ \in\ [0, 1]\) 是几何衰减率
\(L\) 是最大滞后时长
同样直观的是,随着给定时间段内给定媒体渠道的支出不断增加,您最终会看到边际回报递减,例如达到饱和。Meridian 通过一个双形参函数(名为“Hill 函数”)来模拟这种饱和效应。
Hill 函数
Hill 函数的定义如下:
$$
\text{Hill}(x; ec, \text{slope}) = \frac{1}{1+\left( \frac{x}{ec} \right)^
{- \text{slope}}}
$$
其中:
\(x \geq 0\)
\(ec > 0\) 是半饱和点,这意味着\(\text{Hill}(x=ec; ec, \text{slope}) = 0.5\)
\(\text{slope} > 0\) 是一个形参,用于控制函数形状:
- \(\text{slope} \leq 1\) 对应于凹形
- \(\text{slope} > 1\) 对应于 S 形函数,当 \( x < ec \) 时为凸函数,当 \( x > ec \)时为凹函数
重要提示:Hill 函数形参的模型估计值基于观测到的媒体数据范围。拟合的响应曲线可外推至此范围之外,但在解读基于外推的结果时应保持适当的谨慎。
Hill 函数可以在 Adstock 转换之前或之后应用,具体取决于 ModelSpec
的布尔值 hill_before_adstock
实参。默认设置为 hill_before_adstock = False
,这会使渠道 \(m\) 在地理位置 \(g\) 和时间段 \(t\)的媒体效应等于\(\beta_{g,m} \text{Hill}(\text{Adstock}(x_t,x_{t-1},\cdots,x_{t-L};\ \alpha_m)
;ec_m, \text{slope}_m)\)。
如未另行说明,那么本页面中的内容已根据知识共享署名 4.0 许可获得了许可,并且代码示例已根据 Apache 2.0 许可获得了许可。有关详情,请参阅 Google 开发者网站政策。Java 是 Oracle 和/或其关联公司的注册商标。
最后更新时间 (UTC):2025-08-04。
[null,null,["最后更新时间 (UTC):2025-08-04。"],[[["\u003cp\u003eMeridian utilizes an Adstock function to model the lagged and tapering effects of media channels on sales.\u003c/p\u003e\n"],["\u003cp\u003eThe Hill function is employed to capture the diminishing marginal returns, or saturation, of media spending.\u003c/p\u003e\n"],["\u003cp\u003eThe Hill function can be applied before or after the Adstock transformation, offering flexibility in modeling media effects.\u003c/p\u003e\n"],["\u003cp\u003eThe model estimates parameters based on observed data, and extrapolation beyond this range requires caution in interpretation.\u003c/p\u003e\n"],["\u003cp\u003eDetails on the Adstock and Hill functions, including formulas and parameter explanations, are provided within the content.\u003c/p\u003e\n"]]],["Meridian's model captures the lagged effect of media on sales using a geometric decay Adstock function, defined by decay rate (α) and maximum lag (L). It also accounts for diminishing returns through the Hill function, characterized by half saturation point (ec) and slope. The Hill function can be applied before or after the Adstock transformation, defaulting to after. The model estimates Hill function parameters based on the observed media data range.\n"],null,["# Media saturation and lagging\n\nTypically the effect of a media channel on sales has a lagged effect that tapers\noff slowly over time. Meridian's model architecture is designed to\ncapture this effect through a geometric decay Adstock function. For more\ninformation, see [A Hierarchical Bayesian Approach to Improve Media Mix Models\nUsing Category\nData](https://research.google/pubs/a-hierarchical-bayesian-approach-to-improve-media-mix-models-using-category-data/)\nand [Bayesian Methods for Media Mix Modeling with Carryover and Shape\nEffects](https://research.google/pubs/bayesian-methods-for-media-mix-modeling-with-carryover-and-shape-effects/).\n\nAdstock function\n----------------\n\nThe Adstock function is defined as follows: \n$$ \\\\text{AdStock}(x_t, x_{t-1}, \\\\cdots, x_{t-L};\\\\ \\\\alpha)\\\\ = \\\\dfrac{\\\\sum\\\\limits_{s=0}\\^L\\\\ \\\\alpha\\^sx_{t-s}} {\\\\sum\\\\limits _{s=0}\\^L\\\\ \\\\alpha\\^s} $$\n\nWhere:\n\n- \\\\(x_s \\\\geq 0; s = t, t-1, \\\\cdots, t-L\\\\)\n\n- \\\\(\\\\alpha\\\\ \\\\in\\\\ \\[0, 1\\]\\\\) is the geometric decay rate\n\n- \\\\(L\\\\) is the maximum lag duration\n\nIt is also intuitive that as spending on a given media channel within any given\ntime period increases, you eventually see diminishing marginal returns, for\nexample, saturation. Meridian models this saturation effect through a\ntwo-parameter function known as the Hill function.\n\nHill function\n-------------\n\nThe Hill function is defined as follows: \n$$ \\\\text{Hill}(x; ec, \\\\text{slope}) = \\\\frac{1}{1+\\\\left( \\\\frac{x}{ec} \\\\right)\\^ {- \\\\text{slope}}} $$\n\nWhere:\n\n- \\\\(x \\\\geq 0\\\\)\n\n- \\\\(ec \\\u003e 0\\\\) is the half saturation point, meaning that\n \\\\(\\\\text{Hill}(x=ec; ec, \\\\text{slope}) = 0.5\\\\)\n\n- \\\\(\\\\text{slope} \\\u003e 0\\\\) is a parameter that controls the function shape:\n\n - \\\\(\\\\text{slope} \\\\leq 1\\\\) corresponds to a concave shape\n - \\\\(\\\\text{slope} \\\u003e 1\\\\) corresponds to an *S* shaped function that is convex for \\\\( x \\\u003c ec \\\\) and concave for \\\\( x \\\u003e ec \\\\)\n\n**Important:** The model's estimation of the Hill function parameters is based\non the observed range of media data. The fitted response curve can be\nextrapolated outside this range, but results based on extrapolation should be\ninterpreted with an appropriate level of caution.\n\nThe Hill function can be applied either before or after the Adstock\ntransformation, depending on the boolean `hill_before_adstock` argument of the\n`ModelSpec`. The default setting is `hill_before_adstock = False`, which makes\nthe media effect of channel \\\\(m\\\\) within geo \\\\(g\\\\) and time period \\\\(t\\\\)\nequal to\n\\\\(\\\\beta_{g,m} \\\\text{Hill}(\\\\text{Adstock}(x_t,x_{t-1},\\\\cdots,x_{t-L};\\\\ \\\\alpha_m)\n;ec_m, \\\\text{slope}_m)\\\\)."]]