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Meta-analyses using information reweighting: An application to online advertising

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Abstract

Because technology-enabled marketing research has led to information arriving at a rapid pace, methods in marketing that allow for coherent, sequential and fast information integration are needed. We propose in this research a new approach to information integration: Information Reweighted Priors (IRPs). It is a sample reweighting approach which utilizes the output from a Bayesian model fit using Markov Chain Monte Carlo, with no restrictions on the likelihood, prior distributions, or data structure; hence a general purpose tool. We demonstrate the approach with simulated datasets and an online advertising dataset with external information obtained from i) previous advertising studies in the industry from a major online advertising portal, ii) past academic studies of online adverting and iii) out-of-sample summaries of the dataset.

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Notes

  1. For example, the external information might be about an aggregate quantity (market share within a population) but interest might be about individual-level predictions.

  2. The results are robust to the exact number of days, but discussions with Organic Inc. determined the time window.

  3. In industry there is generally some indicator of customer's interest and/or intent of purchase. The exact probability may not be readily available, but we use this case as an example to demonstrate how IRP can incorporate information of various shapes.

  4. For the sake of computation ease, if the estimated \({p^{e}_{i}}\) is 0 or 1, it is jittered with a small number (1/10th of the smallest \({p^{e}_{i}}\) or \(1-{p^{e}_{i}}\) where \({p^{e}_{i}}\neq 0~ or~ 1\)), and hence the posterior samples would not receive 0 weight in the reweighting stage. A sensitivity study about the jittering value was conducted, where the jittering value was ranged from 1/100th of the smallest \({p^{e}_{i}}\) or \(1-{p^{e}_{i}}\) where \({p^{e}_{i}}\neq 0~ or~ 1\) to 1/5, and the inference results were not observably affected.

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Authors and Affiliations

  1. University of Pennsylvania, Philadelphia, PA, 19104-6340, Pennsylvania

    Pengyuan Wang, Eric T. Bradlow & Edward I. George

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  1. Pengyuan Wang
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  2. Eric T. Bradlow
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Correspondence to Pengyuan Wang.

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We thank Organic, Inc. and the Wharton Customer Analytics Initiative for providing the data.

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Wang, P., Bradlow, E.T. & George, E.I. Meta-analyses using information reweighting: An application to online advertising. Quant Mark Econ 12, 209–233 (2014). https://doi.org/10.1007/s11129-014-9145-7

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