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

WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.

%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 neccessary. We use it here so that the results are reproducible.

result = cp.pymc_experiments.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]

100.00% [8000/8000 00:01<00:00 Sampling 4 chains, 0 divergences]

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 = 0.5, $CI_{94\%}$[0.4, 0.6]
Model coefficients:
Intercept                     1.08, 94% HDI [1.03, 1.13]
post_treatment[T.True]        0.99, 94% HDI [0.92, 1.06]
group                         0.16, 94% HDI [0.09, 0.23]
group:post_treatment[T.True]  0.50, 94% HDI [0.40, 0.60]
sigma                         0.08, 94% HDI [0.07, 0.10]

ax = az.plot_posterior(result.causal_impact, ref_val=0)
ax.set(title="Posterior estimate of causal impact");