I recently published a short note that uses a multilevel model with a GP component for causal inference and thought that it may be of interest to some of you.
The data comes from the Morrow Plots. This is the second oldest continuous agricultural experiment in the world, started in 1876 in Illinois USA. The treatments are crop rotations and the outcomes are crop yield and soil health, with a focus in the present analysis on soil organic carbon stocks.
This 150 year old “experiment” lacks replication and isn’t even fully randomized, which as you can imagine creates issues. We tried to mitigate these issues by taking measurements in the grass perimeter around the experiment and including them in the model as an additional treatment level. This is a small data problem, the full experimental design and data are contained in figure 1:
You can download the data on figshare along with a markdown file that should fully reproduce the brms modeling and figures.
Let me know if you have any feedback. Thanks for reading and thank you to the stan and brms developers for making this kind of analysis so easy!