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ROI values are found by imputing a future promotional period with a trend, such as last year sales then calculating the difference between the Stan model prediction and the trend prediction. This difference is what media mix modelers would identify as the lift due to the media (probably debatable, but this is what is sometimes used). ROI is a function of this incremental lift and media spend.
Regression with autoregressive features for the y and the media values. The Stan model takes a really long time and I felt like it did not provide that much extra useable information for real business problems. If I were to look at this again I would just do regression with some thought put into lagging the y and media variables.
Hello Alex,
I would like to start off by stating that I found your code very helpful, I had a few questions regarding your approach to media mix modeling.
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