First step to measuring the long-term impact of Marketing: The Memory Effect

Why model the memory effect?

All marketers know that the impact of your advertising extends not just today, but also tomorrow, next week, and next month. But how best to measure that? That's where tracking the memory effect comes in.

In reality, we know that advertising memories and brand equity decay rather than vanish instantly. Measuring this will increase model accuracy and provide the best estimate of ROIs.

In an MMM (marketing mix model), we typically measure this impact with a memory effect or adstock. But this impact can take many forms. So let's look at three approaches we use to capture the Memory effect.

1. Geometric-decay adstock

Concept

The most simple of our examples, the geometric decay, assumes a “constant rate” reduction of effect over the coming days/ weeks.

To capture this, we use a single retention parameter θ (0 < θ < 1). This says what proportion of last period’s effect survives into the next. A high amount, then we get lots of ongoing impact, potentially an upper funnel campaign. A lower amount means most of the impact comes in day/ week 1.

Mathematically, for spend x​:

x̃_t = x_t + θ x_t-1 + θ² x_t-2 + …

2. Weibull adstock

Concept

Instead of a constant decay, the Weibull kernel lets the decay rate itself vary with time. This reflects that the impact in weeks 1-2 may be different to weeks 2-3 and so on.

With shape k and scale λ:

w_l = exp​[−(l ⁄ λ)^k],  l = 0, 1, 2, …

• k < 1 → fast initial drop, then long tail (good for quick-impact media).
• k > 1 → “S-shaped” build-up before decaying, capturing delayed awareness (e.g., TV bursts).

Advantages & cautions

• Greater flexibility reflects real funnel dynamics.
• Requires non-linear optimisation; risk of over-fitting if data are scarce.
• More parameters to estimate compared to geometric decay.

3. Delayed adstock

Concept

Unlike geometric adstock, which assumes media impact starts immediately and decays, delayed adstock models the case where the effect builds gradually to a peak and then fades symmetrically.

This is useful for media like TV or print, where response may be delayed as audiences take time to act.

Mathematically, the weights applied to past media are based on both a decay rate α and a delay parameter θ:

w_l = α^{(l − θ)²},  l = 0, 1, 2, …

So the transformed media variable becomes:

x̃_t = ∑_l=0^L−1 α^{(l − θ)²} · x_t − l

4. Split-variable (current + lagged geometric)

Concept

This allows us to separate the initial marketing from its subsequent decay. This is better used when there are known delays to the activity, e.g. direct mail (delayed by post) or an influencer activity (when activity is seen over time).

To build this, we use two variables in our analysis:

1. Current-week spend x_t – captures immediate “pop”.
2. Lagged geometric adstock x̃_t^(θ)​ – same θ as classic geometric.

This lets the model estimate separate coefficients, often revealing that short-term ROI differs sharply from long-term brand effect.

Pros & cons

• Pros: Extra flexibility; aids interpretability for campaign planners and addresses known delays (e.g. delivery).
• Cons: Adds collinearity risk and degrees of freedom

Choosing the right form

Criterion	Geometric	Weibull	Delayed	Split Variable
# Parameters	1	2	2	1 (θ) + extra β
Computation	Fast linear	Non-linear	Non-linear	Linear but multicollinear
Captures delay of media delivery?	No	Yes	Yes (peak delay)	Yes (via lag)
Risk of overfit	Low	Medium–High	Medium	Medium
When to prefer	Exploratory, digital	TV, upper-funnel, long memory	TV, Print, response peaks post-exposure	Stakeholders need to see short vs long-term

Take-aways

• Adstock is not optional; it’s fundamental to the valid measurement of your marketing campaigns.
• Geometric is the dependable baseline; Weibull offers realism when media build slowly; Delayed captures lagged peak response; Split-variable unveils distinct tactical pay-offs.
• Always cross-validate and check out-of-sample fit, not just in-sample R².
• Memory effects are the first tool in your ability to measure long-term impacts. See this article for how to get a more holistic viewpoint.