Considering a hypothetical example, we have samples from Twitter and Facebook across US counties during the same time period. Say we asked a different question on the different platforms.
People on Facebook were asked if they liked Apple Pie answering yes/no. People on Twitter were asked if they liked Pumpkin Pie answering on a scale 1-5.
For county x we know the number of Twitter respondents T(x), Facebook respondents F(x), the size S(x) of the county and the numbers of apple pie fans A(x) and pumpkin pie scores for each Twitter user.
We would like to know if there is a correlation between people liking Apple Pie to those liking Pumpkin Pie across US counties.
We have identified a few issues…
- There are widely varying numbers of people responding to the questions from each county, and widely different sizes of US counties.
- Twitter and Facebook might not be representative samples, with inherent biases toward people from Twitter / Facebook to liking one type of pie over the other.
- There might also be biases according to those who respond to the question or not.
- Finally, we might want to add confounding factors - possibly voting Republican is the main factor in liking apple pie. We have good recent numbers of Republican voters per county.
What is the best model (it could be frequentist or Bayesian) we could use to incorporate all the information, and especially the uncertainty, we have to predict the correlation?