Posterior interval for aggregate impact

[AJ]

Dear Kay,

Suppose you analyze multiple units using CausalImpact. How would you build a posterior interval for the sum of the impacts?

This is somewhat related to Nicolae's question on multi-level analysis, which CausalImpact doesn't support, but I don't care about fixed/random effects and just wonder if you can construct an interval without building a Gibbs sampler.

Thanks!

AJ

[Kay Brodersen]

Hi AJ,

One option would be to form the sum of the observed time series of your treated units, followed by a single CausalImpact analysis on this summed time series.

Another option would be to run individual analyses and then combine the results. Expectations are linear, so you can get the expected overall impact by simply adding up the individual impact series. To get the correct posterior intervals, you would add up the individual MCMC traces and then take, say, the 2.5th and 97.5th percentiles. For details on how to access the individual traces, see:

https://github.com/google/CausalImpact/blob/master/R/impact_inference.R#L44

Best wishes,

Kay

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