{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Difference in Differences with `pymc` models\n",
"\n",
":::{note}\n",
"This example is in-progress! Further elaboration and explanation will follow soon.\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import arviz as az\n",
"\n",
"import causalpy as cp"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%load_ext autoreload\n",
"%autoreload 2\n",
"%config InlineBackend.figure_format = 'retina'\n",
"seed = 42"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load data"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" group | \n",
" t | \n",
" unit | \n",
" post_treatment | \n",
" y | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0 | \n",
" 0.0 | \n",
" 0 | \n",
" False | \n",
" 0.897122 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0 | \n",
" 1.0 | \n",
" 0 | \n",
" True | \n",
" 1.961214 | \n",
"
\n",
" \n",
" | 2 | \n",
" 1 | \n",
" 0.0 | \n",
" 1 | \n",
" False | \n",
" 1.233525 | \n",
"
\n",
" \n",
" | 3 | \n",
" 1 | \n",
" 1.0 | \n",
" 1 | \n",
" True | \n",
" 2.752794 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0 | \n",
" 0.0 | \n",
" 2 | \n",
" False | \n",
" 1.149207 | \n",
"
\n",
" \n",
"
\n",
"
"
]
},
"metadata": {
"image/png": {
"height": 491,
"width": 731
}
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = result.plot()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"===========================Difference in Differences============================\n",
"Formula: y ~ 1 + group*post_treatment\n",
"\n",
"Results:\n",
"Causal impact = 0.50$CI_{94\\%}$[0.4, 0.6]\n",
"Model coefficients:\n",
" Intercept 1.1, 94% HDI [1, 1.1]\n",
" post_treatment[T.True] 0.99, 94% HDI [0.92, 1.1]\n",
" group 0.16, 94% HDI [0.094, 0.23]\n",
" group:post_treatment[T.True] 0.5, 94% HDI [0.4, 0.6]\n",
" y_hat_sigma 0.082, 94% HDI [0.066, 0.1]\n"
]
}
],
"source": [
"result.summary()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"ax = az.plot_posterior(result.causal_impact, ref_val=0)\n",
"ax.set(title=\"Posterior estimate of causal impact\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Effect Summary Reporting\n",
"\n",
"For decision-making, you often need a concise summary of the causal effect. The `effect_summary()` method provides a decision-ready report with key statistics. Note that for Difference-in-Differences, the effect is a single scalar (average treatment effect), unlike time-series experiments where effects vary over time.\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" mean | \n",
" median | \n",
" hdi_lower | \n",
" hdi_upper | \n",
" p_gt_0 | \n",
"
\n",
" \n",
" \n",
" \n",
" | treatment_effect | \n",
" 0.503779 | \n",
" 0.504367 | \n",
" 0.401661 | \n",
" 0.607651 | \n",
" 1.0 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" mean | \n",
" median | \n",
" hdi_lower | \n",
" hdi_upper | \n",
" p_two_sided | \n",
" prob_of_effect | \n",
" p_rope | \n",
"
\n",
" \n",
" \n",
" \n",
" | treatment_effect | \n",
" 0.503779 | \n",
" 0.504367 | \n",
" 0.401661 | \n",
" 0.607651 | \n",
" 0.0 | \n",
" 1.0 | \n",
" 0.99925 | \n",
"
\n",
" \n",
"
\n",
"