Difference in Differences with pymc models#

Note

This example is in-progress! Further elaboration and explanation will follow soon.

import arviz as az

import causalpy as cp
%load_ext autoreload
%autoreload 2
%config InlineBackend.figure_format = 'retina'
seed = 42

Load data#

df = cp.load_data("did")
df.head()
group t unit post_treatment y
0 0 0.0 0 False 0.897122
1 0 1.0 0 True 1.961214
2 1 0.0 1 False 1.233525
3 1 1.0 1 True 2.752794
4 0 0.0 2 False 1.149207

Run the analysis#

Note

The random_seed keyword argument for the PyMC sampler is not necessary. We use it here so that the results are reproducible.

result = cp.DifferenceInDifferences(
    df,
    formula="y ~ 1 + group*post_treatment",
    time_variable_name="t",
    group_variable_name="group",
    model=cp.pymc_models.LinearRegression(sample_kwargs={"random_seed": seed}),
)
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [beta, sigma]


Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1 seconds.
Sampling: [beta, sigma, y_hat]
Sampling: [y_hat]
Sampling: [y_hat]
Sampling: [y_hat]
Sampling: [y_hat]
fig, ax = result.plot()
result.summary()
===========================Difference in Differences============================
Formula: y ~ 1 + group*post_treatment

Results:
Causal impact = 0.50$CI_{94\%}$[0.4, 0.6]
Model coefficients:
    Intercept                     1.1, 94% HDI [1, 1.1]
    post_treatment[T.True]        0.99, 94% HDI [0.92, 1.1]
    group                         0.16, 94% HDI [0.094, 0.23]
    group:post_treatment[T.True]  0.5, 94% HDI [0.4, 0.6]
    sigma                         0.082, 94% HDI [0.066, 0.1]
ax = az.plot_posterior(result.causal_impact, ref_val=0)
ax.set(title="Posterior estimate of causal impact");