Reach and frequency modeling is an option for any channel with reach and
frequency data. Meridian models each channel according to the data
provided, so you only input reach and frequency data for the channels that you
want to model this way. For more information, see [Model specification](https://developers.google.com/meridian/docs/advanced-modeling/model-spec).

The [MMM Data Platform](https://developers.google.com/meridian/docs/pre-modeling/using-mmm-data-platform)
provides reach and frequency data for YouTube. If you have access to reach and
frequency data for other channels, you can also use that data.

## Reach and frequency data

For modeling purposes, the reach and frequency data must be at the same level of
geo and time granularity as the KPI and controls data.

Additionally:

- The reach data should be the number of unique individuals exposed to the
  channels' ad within each time period instead of the cumulative number of
  individuals reached over consecutive time periods.

- The frequency data should be the total number of impressions divided by the
  reach for each time period.

## Reach and frequency modeling

The use of reach and frequency is a crucial factor in effective ad campaigns,
but it is not often considered in current marketing mix models (MMMs) due to
the lack of accurate reach and frequency metrics for some traditional media
channels. Typically, MMMs rely on impressions as input, neglecting the fact that
individuals can be exposed to ads multiple times, and the impact can vary with
exposure frequency. To overcome this limitation, Meridian offers the
option to model any media channel's effect based on reach and frequency data,
instead of a single execution metric. This approach can potentially yield more
precise estimates of marketing impact on business outcomes and aid in optimizing
campaign execution through frequency recommendations.

The *media effect* is the additive contribution to expected outcome. For
channels with reach and frequency data, the media effect of the \\(i\^{th}\\)
channel within geo \\(g\\) and time period \\(t\\) is modeled as follows:
$$ \\beta_{g,i}\^{\[RF\]} \\text{Adstock} \\left(\\left\\{ r_{g,t-s,i}\^{\[RF\]} \\text{Hill} \\left( f_{g,t-s,i}\^{\[RF\]};\\ ec_i\^{\[RF\]}, \\text{slope}_i\^{\[RF\]} \\right) \\right\\}_{s=0} \^L;\\ \\alpha_i\^{\[RF\]} \\right) $$

Where:

- \\(f_{g,t,i}\^{\[RF\]}\\) is the average frequency
- \\(r_{g,t,i}\^{\[RF\]}=L_{g,i}\^{\[RF\]}(\\overset {\\cdot \\cdot} r_{g,t,i})\^{\[RF\]}\\) is the transformed reach. This is scaled by population and the median value for the channel. For more information, see [Input
  data](https://developers.google.com/meridian/docs/advanced-modeling/input-data).

This effect is calculated by first applying the Hill function to the average
frequency \\(f_{g,t,i}\^{\[RF\]}\\) to adjust for saturation effects. The
Hill-transformed frequency for each geo and week is multiplied by transformed
reach. These values are then weighted by the Adstock function to capture lagged
effects of media exposure over time.

The Hill function allows for the media effect to be *S* shaped as a function of
frequency, which means that the optimal average reach for cost effectiveness may
be greater than one. The *S* shaped curve reflects the intuition that there
might be an optimal frequency for incremental outcome value per impression. A
certain minimum frequency might be necessary to reinforce brand recall, while
excessive frequency can result in ad fatigue and diminishing returns.

Reach is assumed to have a linear relationship with the KPI, while holding
frequency fixed. This means that each additional individual reached has the
same effect on the KPI as those reached previously. This assumption is a
reasonable approximation as long as the media channel does not reach individuals
well beyond its intended target audience, who may be less affected by the
channel. The linear reach assumption also helps avoid model
overparameterization, parameter non-identifiability, and Markov Chain Monte
Carlo (MCMC) convergence issues. Be careful about extrapolating this linear
effect far outside the range of reach values observed in the data.

For more information about reach and frequency, see [Bayesian Hierarchical Media
Mix Model Incorporating Reach and Frequency
Data](https://research.google/pubs/bayesian-hierarchical-media-mix-model-incorporating-reach-and-frequency-data/).

## Differences between assumed frequency for ROI and for optimization

There are differences between the assumed frequency for ROI and for
optimization. You can adjust the assumed frequency for optimization if needed.

As discussed in [ROI, mROI, and response
curves](https://developers.google.com/meridian/docs/post-modeling/roi-mroi-response-curves), ROI measures the
return of investment of a channel as it was executed during the time window for
which the MMM has data. How a channel was executed includes how impressions are
allocated across geos and time, and also includes the historical frequency of
that channel.

Optimization assumes that future campaigns will be executed at the optimal
frequency, since frequency is something often in an advertiser's control,
especially for digital channels. If the optimal frequency is different from the
historical frequency, a channel's performance in optimized budget allocation
might not match the channel's historical performance according to ROI. This can
be exacerbated if the current frequency is far from the optimal frequency.

If future campaigns won't be executed at the optimal frequency, you can use the
optimization option to change the assumed frequency. This can be helpful for
channels that cannot be executed at a specific average frequency.