Overall, brand media has 3 impacts:
Direct - Direct impact onto sales, which is the short to medium term impact
Brand health - Impact on to developing people's perceptions of the brand, via brand health and subsequent composite metrics
Activation - boosting performance channels such as paid search - i.e. people become aware of the brand via brand media, they search on google for the brand, then click on a paid search link. That interaction therefore didnt come from paid search, but from brand, as it you took the paid search link away, they will still get through.
(there are also other impacts, but these are very hard to measure, such as reducing price elasticity and ability to increase availability of the product)
Most clients we see concentrate on the Direct impact, which is only roughly a third of the actual impact. More often than not, clients are therefore overspending on channels such paid search, which is just harvesting demand they would have got anyway.
The way you can model this is:
Brand driver analysis to identify the brand themes and composite brand health variables
Sales modelling (MMM) to identify the direct impact of channels onto sales
Using the sales model in (2) to identify the brand health metric which tracks base sales growth, which you can then model to derive the base building effect of brand media
Modelling large activation channels (such as paid search clicks) to identify the brand impact onto boosting these channels
Then you can work out the short, medium and long term effect of all media channels.
This then means you can get much more out of your budget by optimising spend more accurately, but also to hit different KPIs (i.e. short term sales, long term base, etc).