{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Interrupted Time Series (ITS) with scikit-learn models\n",
"\n",
"This notebook shows an example of using interrupted time series, where we do not have untreated control units of a similar nature to the treated unit and we just have a single time series of observations and the predictor variables are simply time and month."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"import causalpy as cp"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%config InlineBackend.figure_format = 'retina'"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load data"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" month \n",
" year \n",
" t \n",
" y \n",
" \n",
" \n",
" date \n",
" \n",
" \n",
" \n",
" \n",
" 2010-01-31 \n",
" 1 \n",
" 2010 \n",
" 0 \n",
" 25.058186 \n",
" \n",
" \n",
" 2010-02-28 \n",
" 2 \n",
" 2010 \n",
" 1 \n",
" 27.189812 \n",
" \n",
" \n",
" 2010-03-31 \n",
" 3 \n",
" 2010 \n",
" 2 \n",
" 26.487551 \n",
" \n",
" \n",
" 2010-04-30 \n",
" 4 \n",
" 2010 \n",
" 3 \n",
" 31.241716 \n",
" \n",
" \n",
" 2010-05-31 \n",
" 5 \n",
" 2010 \n",
" 4 \n",
" 40.753973 \n",
" \n",
" \n",
"
\n",
"
"
]
},
"metadata": {
"image/png": {
"height": 811,
"width": 711
}
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = result.plot()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"==================================Pre-Post Fit==================================\n",
"Formula: y ~ 1 + t + C(month)\n",
"Model coefficients:\n",
" Intercept \t 0\n",
" C(month)[T.2] \t 2.85\n",
" C(month)[T.3] \t 1.16\n",
" C(month)[T.4] \t 7.15\n",
" C(month)[T.5] \t 15\n",
" C(month)[T.6] \t 24.8\n",
" C(month)[T.7] \t 18.2\n",
" C(month)[T.8] \t 33.5\n",
" C(month)[T.9] \t 16.2\n",
" C(month)[T.10]\t 9.19\n",
" C(month)[T.11]\t 6.28\n",
" C(month)[T.12]\t 0.578\n",
" t \t 0.21\n"
]
}
],
"source": [
"result.summary(round_to=3)"
]
},
{
"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.\n",
"\n",
":::{note}\n",
"**OLS vs PyMC Models**: When using OLS models (scikit-learn), the `effect_summary()` provides **confidence intervals** and **p-values** (frequentist inference), rather than the posterior distributions, HDI intervals, and tail probabilities provided by PyMC models (Bayesian inference). OLS tables include: mean, CI_lower, CI_upper, and p_value, but do not include median, tail probabilities (P(effect>0)), or ROPE probabilities.\n",
":::\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" mean \n",
" ci_lower \n",
" ci_upper \n",
" p_value \n",
" relative_mean \n",
" relative_ci_lower \n",
" relative_ci_upper \n",
" \n",
" \n",
" \n",
" \n",
" average \n",
" 1.845561 \n",
" 0.161437 \n",
" 3.529686 \n",
" 0.032645 \n",
" 3.366709 \n",
" 0.150601 \n",
" 6.582817 \n",
" \n",
" \n",
" cumulative \n",
" 66.440209 \n",
" 5.811718 \n",
" 127.068701 \n",
" 0.032645 \n",
" 121.201506 \n",
" 5.421618 \n",
" 236.981394 \n",
" \n",
" \n",
"
\n",
"