how does the intercept of the Meridian MMM get calculated?

[mikeh3636]

Hi Meridian Support team,

From the doc and the GitHub repo, it is clear that the mu_t is coming from w*b, where b is the user inputs on integer or time indices, and w is the weight on inversely proportional to the neighborhood knots. However, this would only create a matrix with ratio (e.g. 0-1). Could you help clarify how does it scale back to the "intercept"? and what is the relationship does it have with "tau g"? I am trying to better understand how does the "intercept" of the model consists of and how was it derived.

Thank you

[dattatreyam23]

Hi @mikeh3636,

Thank you for reaching out to the Google Meridian support team.

We have updated the intercept documentation to make it more precise.

I believe you are referencing the equation for $\mu_t$, which is a weighted average of the two neighboring knots closest to time $t$. The knot values $b_k$ are not restricted to the interval [0, 1]. They can take any real value and by default are assigned independent Normal(0, 5) prior distributions.

The Meridian intercept varies by geo and time period and can be defined as $\mu_t + \tau_g$. The intercept is the expected model response when all 1) media variables are set to zero and 2) all non-media treatments and controls are set to their mean observed values. Note that:

• The model response is a transformation of KPI. The KPI is scaled by geo population and then centered and scaled to have mean=0 and std=1.
• The non-media treatments and control variables are transformed to have mean=0 and std=1, which is why the intercept corresponds to having these variables set to their mean values.

Feel free to reach out if you have any questions or suggestions regarding Meridian.

Thank you,

Google Meridian Support Team