# Compute conditional independencies from a directed graphical model
# Uses this library
# https://github.com/ijmbarr/causalgraphicalmodels
# Code is based on
# https://fehiepsi.github.io/rethinking-numpyro/06-the-haunted-dag-and-the-causal-terror.html
from causalgraphicalmodels import CausalGraphicalModel
dag = CausalGraphicalModel(
nodes=["X", "Y", "C", "U", "B", "A"],
edges=[
("X", "Y"),
("U", "X"),
("A", "U"),
("A", "C"),
("C", "Y"),
("U", "B"),
("C", "B"),
],
)
all_independencies = dag.get_all_independence_relationships()
print(all_independencies)
print('\n')
"""
Treatment appears to have negligible effect even though βF posterior indicates fungus impacts
growth.
The problem is that fungus is a consequence of treatment; i.e. fungus is a post-treatment variable.
The model asked the question "Once we know fungus is present does treatment matter?" ⇒ No.
The next model ignores the fungus variable
"""
with pm.Model() as m8:
σ = pm.Exponential('σ', 1)
α = pm.Lognormal('α', 0, 0.2)
βT = pm.Normal('βT', 0, 0.5)
p = α + βT * d.treatment.values
μ = d.h0.values * p
h1 = pm.Normal('h1', mu=μ, sd=σ, observed=d.h1.values)
trc8 = pm.sample(tune=1000)
pm.summary(trc8)
"""
Now the treatment effect is plain to see. Note that:
1. It makes sense to control for pre-treatment differences such as initial height, h0, here.
2. Including post-treatment variables can mask the treatment itself.
3. Note that model m7 is still useful to identify the causal mechanism!
"""
plant_dag = CausalGraphicalModel(nodes=['H0', 'H1', 'T', 'F'],
edges=[('H0', 'H1'), ('T', 'F'), ('F', 'H1')])
plant_dag.draw()
plant_dag.is_d_separated('T', 'H1')
plant_dag.is_d_separated('T', 'H1', 'F')
plant_dag.get_all_independence_relationships()