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How to Recover Average Ad Position using Non-Linear Bayes and Weighted Ensembles

The Average Ad Position metric is a statistic that describes how ads are ranked on a Search engine result page (SERP) against competitors in a given space. For instance, in scenario-planning and bidding optimization, Average Position data can be enabled to forecast the expected change in the cost-per-click and the click-through-rate from our next budget or bidding action.   

In this blog post, I'll describe how to make an analysts’ work easier during the transition away from average position by building a predictive algorithm of average position from other Search auction share metrics – some recently introduced by Google, through an approach we would describe as an ensemble of Bayesian Hierarchical models.

Modeling Average Position

Ad position, as a statistic, poses certain challenges for modeling.

Domain. Ad position is bounded between one and a potentially large positive number.

Non-linearity. It is expected that the relationship between auction share metrics and ad position would be non-linear.

You can approach this problem as a non-linear curve fitting exercise with the non-linearity expressed in the following equation:
AvgPos = f(x) = α*e- β* x+ 1Image removed.

Where independent variable xImage removed. can be any of Google’s auction share or impression rate metrics that you want to use to model average position.

Ave Position vs Dependent Variable

Bayesian Hierarchical Models

Merkle’s analytics team recently made this model. In order to build our model, we collected data from a number of advertisers, which caused a few challenges.

First, not all advertisers were equal in size and they did not contribute the same amount of data to our modeling team.

Second, each advertiser may have expected somewhat different average position results given the same impression share metrics, depending on the particular Search space they operate in, their overall quality score, and their bidding strategies.

To ensure the generalizability of our insights, our purpose was to uncover the best model for the average advertiser and to reduce the bias caused by any one advertiser. Therefore, we resorted to Bayesian hierarchical models to identify the share of variation in the data due to advertiser specificities.

In our hierarchical model, while a separate set of parameters were estimated for each advertiser in the data, we assumed that these advertiser-level parameters were sampled from a shared prior distribution that broadly described how all advertisers should behave. The prior distribution could, therefore, be used as a direction for predicting the average advertiser’s ad position.

Ensemble Modeling

Some statistics perform better at predicting average position in certain situations and worse in others.

Instead of picking a single winning metric, you can resolve this to use a model averaging ensemble approach.

Simple model averaging combines the prediction from each model equally and often results in better predictive performance than any one model alone. However, this approach can be too limited, since certain models are expected to perform better in different situations.

For instance, you can expect that when the ad shows on an average, closer to the top position, the impression rate in the absolute top position would perform better than the rate in the top four positions. The absolute top impression rate can lose much of its predictive performance when falling under 40 percent. In the example below, we used a weighted average ensemble, which is an approach that allows multiple models to contribute to a prediction to different degree.

Simple ensemble model approach:

Ensemble model approach

Putting it into action

Advertisers derive multiple benefits from knowing where their ad ranks on the SERP.  First, ad position is an important metric in brand strategy, as it allows the advertiser to assess the brand’s ranking against competitors in that space. At the other end, in order to bring to the site high-quality traffic resulting in leads, conversions and sales, the ad position is a useful lever to balance the advertiser’s conversion goals against the media budget.  

This modeling approach allows you to maximize predictive accuracy on average ad position using other auction share statistics (provided by Google) in a way that is generalizable to advertisers who wants to continue assessing their ad position.

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