Conditional Independence Approximation to Cross-media Incremental Reach

An independence assumption has been used as a solution to
calculate cross-media ads reach when cross-media panel data are
unavailable. In this paper, we introduce restricted conditional
independence assumption (RCIA) and apply it to calculate the digital
video incremental reach on top of TV. By conducting
large-scale simulation studies based on the cross-media
universes in a single source panel, we show that RCIA based incremental reach
is close to the standard calculation based on the
cross-media universes. Moreover, substantial variance reduction is achieved
from RCIA with single-media panel data compared to the standard calculation based on the cross-media universes. We use distance correlation to measure the strength of dependence
between ad impressions of TV campaigns and digital
video.
The magnutudes of distance correlation between these two types of ad impressions are small, and only ~2% TV campaigns show statistically significant dependence.
As a summary, because of its high accuracy, low variance, simplicity and low cost, we recommend that the RCIA approximation as a preferred
solution than the standard cross-media universe calculation.

• Algorithms and Theory