Example Interrupted Time Series (ITS) with sci-kit learn models

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.

import pandas as pd
from sklearn.linear_model import LinearRegression

import causalpy as cp

%config InlineBackend.figure_format = 'retina'

Load data

df = (
    cp.load_data("its")
    .assign(date=lambda x: pd.to_datetime(x["date"]))
    .set_index("date")
)

treatment_time = pd.to_datetime("2017-01-01")
df.head()

	month	year	t	y
date
2010-01-31	1	2010	0	25.058186
2010-02-28	2	2010	1	27.189812
2010-03-31	3	2010	2	26.487551
2010-04-30	4	2010	3	31.241716
2010-05-31	5	2010	4	40.753973

Run the analysis

result = cp.InterruptedTimeSeries(
    df,
    treatment_time,
    formula="y ~ 1 + t + C(month)",
    model=LinearRegression(),
)

Examine the results

fig, ax = result.plot()

/Users/benjamv/opt/mambaforge/envs/CausalPy/lib/python3.11/site-packages/IPython/core/pylabtools.py:77: DeprecationWarning: backend2gui is deprecated since IPython 8.24, backends are managed in matplotlib and can be externally registered.
  warnings.warn(
/Users/benjamv/opt/mambaforge/envs/CausalPy/lib/python3.11/site-packages/matplotlib_inline/config.py:68: DeprecationWarning: InlineBackend._figure_format_changed is deprecated in traitlets 4.1: use @observe and @unobserve instead.
  def _figure_format_changed(self, name, old, new):
/Users/benjamv/opt/mambaforge/envs/CausalPy/lib/python3.11/site-packages/IPython/core/pylabtools.py:77: DeprecationWarning: backend2gui is deprecated since IPython 8.24, backends are managed in matplotlib and can be externally registered.
  warnings.warn(
/Users/benjamv/opt/mambaforge/envs/CausalPy/lib/python3.11/site-packages/IPython/core/pylabtools.py:77: DeprecationWarning: backend2gui is deprecated since IPython 8.24, backends are managed in matplotlib and can be externally registered.
  warnings.warn(

result.summary(round_to=3)

==================================Pre-Post Fit==================================
Formula: y ~ 1 + t + C(month)
Model coefficients:
  Intercept     	         0
  C(month)[T.2] 	      2.85
  C(month)[T.3] 	      1.16
  C(month)[T.4] 	      7.15
  C(month)[T.5] 	        15
  C(month)[T.6] 	      24.8
  C(month)[T.7] 	      18.2
  C(month)[T.8] 	      33.5
  C(month)[T.9] 	      16.2
  C(month)[T.10]	      9.19
  C(month)[T.11]	      6.28
  C(month)[T.12]	     0.578
  t             	      0.21