For the Robust Regression with Student-\(t\) distribution as the likelihood, we'll use a famous dataset called kidiq (Gelman & Hill, 2007), which is data from a survey of adult American women and their respective children. Dated from 2007, it has 434 observations and 4 variables:

  • kid_score: child's IQ

  • mom_hs: binary/dummy (0 or 1) if the child's mother has a high school diploma

  • mom_iq: mother's IQ

  • mom_age: mother's age

using CSV
using DataFrames
url = "https://github.com/TuringLang/TuringGLM.jl/raw/main/data/kidiq.csv";
kidiq = CSV.read(download(url), DataFrame)
kid_scoremom_hsmom_iqmom_age
1651121.11827
298189.361925
3851115.44327
483199.449625
5115192.745727
6980107.90218
7691138.89320
81061125.14523
9102181.619524
1095195.073119
...
43470191.253325
using TuringGLM

Using kid_score as dependent variable and mom_hs along with mom_iq as independent variables with a moderation (interaction) effect:

fm = @formula(kid_score ~ mom_hs * mom_iq)
FormulaTerm
Response:
  kid_score(unknown)
Predictors:
  mom_hs(unknown)
  mom_iq(unknown)
  mom_hs(unknown) & mom_iq(unknown)

We instantiate our model with turing_model passing a keyword argument model=TDist to indicate that the model is a robust regression with the Student's t-distribution:

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

References

Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge university press.