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Conditional Independence Approximation to Cross-media Incremental Reach

Xinyang Shen
Yunwen Yang
Jim Koehler
Lu Zhang
Google Inc (2019) (to appear)


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.