Negative Binomial Regression

For our example on Negative Binomial Regression, let's use a famous dataset called roaches (Gelman & Hill, 2007), which is data on the efficacy of a pest management system at reducing the number of roaches in urban apartments. It has 262 observations and the following variables:

y – number of roaches caught.
roach1 – pretreatment number of roaches.
treatment – binary/dummy (0 or 1) for treatment indicator.
senior – binary/dummy (0 or 1) for only elderly residents in building.
exposure2 – number of days for which the roach traps were used

using CSV

using DataFrames

url = "https://github.com/TuringLang/TuringGLM.jl/raw/main/data/roaches.csv";

roaches = CSV.read(download(url), DataFrame)

	y	roach1	treatment	senior	exposure2
1	153	308.0	1	0	0.8
2	127	331.25	1	0	0.6
3	7	1.67	1	0	1.0
4	7	3.0	1	0	1.0
5	0	2.0	1	0	1.14286
6	0	0.0	1	0	1.0
7	73	70.0	1	0	0.8
8	24	64.56	1	0	1.14286
9	2	1.0	0	0	1.0
10	2	14.0	0	0	1.14286
...
262	8	0.0	0	1	1.0

using TuringGLM

Using y as dependent variable and roach1, treatment, and senior as independent variables:

fm = @formula(y ~ roach1 + treatment + senior)

FormulaTerm
Response:
  y(unknown)
Predictors:
  roach1(unknown)
  treatment(unknown)
  senior(unknown)

We instantiate our model with turing_model passing a keyword argument model=NegativeBinomial to indicate that the model is a negative binomial regression:

model = turing_model(fm, roaches; model=NegativeBinomial);

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.