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Currently, TuringGLM only supports hierarchical models with a single random-intercept. This is done by using the (1 | group) inside the @formula macro.

For our Hierarchical Model example, let's use a famous dataset called cheese (Boatwright, McCulloch & Rossi, 1999), which is data from cheese ratings. A group of 10 rural and 10 urban raters rated 4 types of different cheeses (A, B, C and D) in two samples. So we have \(4 \cdot 20 \cdot 2 = 160\) observations and 4 variables:

  • cheese: type of cheese from A to D

  • rater: id of the rater from 1 to 10

  • background: type of rater, either rural or urban

  • y: rating of the cheese

using CSV
using DataFrames
url = "https://github.com/TuringLang/TuringGLM.jl/raw/main/data/cheese.csv";
cheese = CSV.read(download(url), DataFrame)
cheeseraterbackgroundy
1"A"1"rural"67
2"A"1"rural"66
3"B"1"rural"51
4"B"1"rural"53
5"C"1"rural"75
6"C"1"rural"70
7"D"1"rural"68
8"D"1"rural"66
9"A"2"rural"76
10"A"2"rural"76
...
160"D"10"urban"83
using TuringGLM

Using y as dependent variable and background is independent variable with a varying-intercept per cheese type:

fm = @formula(y ~ (1 | cheese) + background)
FormulaTerm
Response:
  y(unknown)
Predictors:
  background(unknown)
  (cheese)->1 | cheese

We instantiate our model with turing_model without specifying any model, thus the default model will be used (model=Normal):

model = turing_model(fm, cheese);
chn = sample(model, NUTS(), 2_000);
plot_chains(chn)

References

Boatwright, P., McCulloch, R., & Rossi, P. (1999). Account-level modeling for trade promotion: An application of a constrained parameter hierarchical model. Journal of the American Statistical Association, 94(448), 1063–1073.