From fb636842460af5019ec343a0d056b1e92693ed75 Mon Sep 17 00:00:00 2001
From: "Benjamin T. Vincent" <inferencelab@gmail.com>
Date: Thu, 3 Nov 2022 08:51:37 +0000
Subject: [PATCH] #50 #44 alcohol RD example and update corresponding plots

---
 causalpy/pymc_experiments.py          |   51 +-
 causalpy/skl_experiments.py           |   56 +-
 img/regression_discontinuity_pymc.svg | 6102 ++++++++-----------------
 img/regression_discontinuity_skl.svg  | 2025 ++------
 notebooks/pymc_demos.ipynb            | 1910 +++++++-
 notebooks/skl_demos.ipynb             |   58 +-
 6 files changed, 4044 insertions(+), 6158 deletions(-)

diff --git a/causalpy/pymc_experiments.py b/causalpy/pymc_experiments.py
index 825e35e0..7ad96f54 100644
--- a/causalpy/pymc_experiments.py
+++ b/causalpy/pymc_experiments.py
@@ -308,14 +308,22 @@ def __init__(
         self.score = self.prediction_model.score(X=self.X, y=self.y)
 
         # get the model predictions of the observed data
-        xi = np.linspace(np.min(self.data["x"]), np.max(self.data["x"]), 200)
-        self.x_pred = pd.DataFrame({"x": xi, "treated": self._is_treated(xi)})
+        xi = np.linspace(
+            np.min(self.data[self.running_variable_name]),
+            np.max(self.data[self.running_variable_name]),
+            200,
+        )
+        self.x_pred = pd.DataFrame(
+            {self.running_variable_name: xi, "treated": self._is_treated(xi)}
+        )
         (new_x,) = build_design_matrices([self._x_design_info], self.x_pred)
         self.pred = self.prediction_model.predict(X=np.asarray(new_x))
 
         # calculate the counterfactual
         xi = xi[xi > self.treatment_threshold]
-        self.x_counterfact = pd.DataFrame({"x": xi, "treated": np.zeros(xi.shape)})
+        self.x_counterfact = pd.DataFrame(
+            {self.running_variable_name: xi, "treated": np.zeros(xi.shape)}
+        )
         (new_x,) = build_design_matrices([self._x_design_info], self.x_counterfact)
         self.pred_counterfac = self.prediction_model.predict(X=np.asarray(new_x))
 
@@ -323,48 +331,21 @@ def _is_treated(self, x):
         return np.greater_equal(x, self.treatment_threshold)
 
     def plot(self):
-        fig, ax = plt.subplots(2, 1, figsize=(7, 8))
+        fig, ax = plt.subplots()
         # Plot raw data
         sns.scatterplot(
             self.data,
             x=self.running_variable_name,
             y=self.outcome_variable_name,
             c="k",  # hue="treated",
-            ax=ax[0],
+            ax=ax,
         )
         # Plot model fit to data
         plot_xY(
             self.x_pred[self.running_variable_name],
             self.pred["posterior_predictive"].y_hat,
-            ax=ax[0],
-        )
-        # # Plot counterfactual
-        plot_xY(
-            self.x_counterfact[self.running_variable_name],
-            self.pred_counterfac["posterior_predictive"].y_hat,
-            ax=ax[0],
-            plot_hdi_kwargs={"color": "C2"},
-        )
-        # Shaded causal effect
-        # TODO
-        # Intervention line
-        ax[0].axvline(
-            x=self.treatment_threshold,
-            ls="-",
-            lw=3,
-            color="r",
-            label="treatment threshold",
-        )
-        ax[0].set(title=f"$R^2$ on all data = {self.score:.3f}")
-        ax[0].legend(fontsize=LEGEND_FONT_SIZE)
-
-        # Plot causal effect estimate ------------------------
-        coeff_name = (
-            "treated[T.True]"  # NOTE: get rid of this hard coded variable name!
-        )
-        beta = self.prediction_model.idata["posterior"]["beta"].sel(
-            {"coeffs": coeff_name}
+            ax=ax,
         )
-        az.plot_posterior(beta, ref_val=0, ax=ax[1])
-        ax[1].set(title=f"Causal impact", xlabel=coeff_name)
+        ax.set(title=f"$R^2$ on all data = {self.score:.3f}")
+        ax.legend(fontsize=LEGEND_FONT_SIZE)
         return (fig, ax)
diff --git a/causalpy/skl_experiments.py b/causalpy/skl_experiments.py
index 32d0383b..5e055704 100644
--- a/causalpy/skl_experiments.py
+++ b/causalpy/skl_experiments.py
@@ -339,65 +339,31 @@ def _is_treated(self, x):
         return np.greater_equal(x, self.treatment_threshold)
 
     def plot(self):
-        fig, ax = plt.subplots(2, 1, sharex=True, figsize=(7, 8))
+        fig, ax = plt.subplots()
         # Plot raw data
         sns.scatterplot(
             self.data,
             x=self.running_variable_name,
             y=self.outcome_variable_name,
             c="k",  # hue="treated",
-            ax=ax[0],
+            ax=ax,
         )
         # Plot model fit to data
-        ax[0].plot(
+        ax.plot(
             self.x_pred[self.running_variable_name],
             self.pred,
             "k",
             markersize=10,
             label="model fit",
         )
-        # Plot counterfactual
-        ax[0].plot(
-            self.x_counterfact[self.running_variable_name],
-            self.pred_counterfac,
-            markersize=10,
-            ls=":",
-            c="k",
-            label="counterfactual",
-        )
-        # Shaded causal effect
-        ax[0].fill_between(
-            self.x_counterfact[self.running_variable_name],
-            y1=np.squeeze(self.pred_counterfac),
-            y2=np.squeeze(self.pred[-len(np.squeeze(self.pred_counterfac)) :]),
-            color="C0",
-            alpha=0.25,
-            label="inferred causal impact",
-        )
-        ax[0].set(title=f"$R^2$ on all data = {self.score:.3f}")
-
-        # Plot causal effect ------------------------
-        # NOTE: plotting residual data point requires another call to self.prediction_model.predict() for the treated unit x-values.
-        ax[1].plot(
-            self.x_counterfact[self.running_variable_name],
-            self.causal_impact,
-            markersize=10,
+        ax.set(title=f"$R^2$ on all data = {self.score:.3f}")
+        # Intervention line
+        ax.axvline(
+            x=self.treatment_threshold,
             ls="-",
-            c="k",
-            label="causal impact",
+            lw=3,
+            color="r",
+            label="treatment threshold",
         )
-        ax[1].axhline(y=0, c="k")
-        ax[1].set(title=f"Causal impact", xlabel=self.running_variable_name)
-
-        # Intervention line
-        for i in [0, 1]:
-            ax[i].axvline(
-                x=self.treatment_threshold,
-                ls="-",
-                lw=3,
-                color="r",
-                label="treatment threshold",
-            )
-            ax[i].legend(fontsize=LEGEND_FONT_SIZE)
-
+        ax.legend(fontsize=LEGEND_FONT_SIZE)
         return (fig, ax)
diff --git a/img/regression_discontinuity_pymc.svg b/img/regression_discontinuity_pymc.svg
index 9d7cb1d4..ed964535 100644
--- a/img/regression_discontinuity_pymc.svg
+++ b/img/regression_discontinuity_pymc.svg
@@ -1,16 +1,16 @@
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    <cc:Work>
     <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
-    <dc:date>2022-10-29T15:28:07.972164</dc:date>
+    <dc:date>2022-11-03T08:46:26.030547</dc:date>
     <dc:format>image/svg+xml</dc:format>
     <dc:creator>
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@@ -21,33 +21,33 @@
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diff --git a/notebooks/pymc_demos.ipynb b/notebooks/pymc_demos.ipynb
index 0a5583a9..b81b82a3 100644
--- a/notebooks/pymc_demos.ipynb
+++ b/notebooks/pymc_demos.ipynb
@@ -1,239 +1,1675 @@
 {
-    "cells": [
-        {
-            "cell_type": "markdown",
-            "metadata": {},
-            "source": [
-                "# Demo of PyMC models"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "import arviz as az\n",
-                "import matplotlib.pyplot as plt\n",
-                "import pandas as pd\n",
-                "import pathlib"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "%config InlineBackend.figure_format = 'svg'\n",
-                "az.style.use(\"arviz-darkgrid\")"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "%load_ext autoreload\n",
-                "%autoreload 2"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "export_images = True"
-            ]
-        },
-        {
-            "cell_type": "markdown",
-            "metadata": {},
-            "source": [
-                "## Synthetic Control"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "sc_data_path = pathlib.Path.cwd().parents[0] / 'causalpy' / 'data' / 'synthetic_control.csv'\n",
-                "df = pd.read_csv(sc_data_path)\n",
-                "treatment_time = 70"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "from causalpy.pymc_experiments import SyntheticControl\n",
-                "from causalpy.pymc_models import WeightedSumFitter\n",
-                "\n",
-                "# Note, we do not want an intercept in this model\n",
-                "thing = SyntheticControl(df,\n",
-                "                         treatment_time,\n",
-                "                         formula = \"actual ~ 0 + a + b + c + d + e + f + g\",\n",
-                "                         prediction_model=WeightedSumFitter())\n",
-                "\n",
-                "thing.plot();\n",
-                "\n",
-                "if export_images:\n",
-                "    plt.savefig(pathlib.Path.cwd().parents[0] / 'img' / 'synthetic_control_pymc.svg', bbox_inches='tight', format=\"svg\")"
-            ]
-        },
-        {
-            "cell_type": "markdown",
-            "metadata": {},
-            "source": [
-                "## Interrupted time series"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "its_data_path = pathlib.Path.cwd().parents[0] / 'causalpy' / 'data' / 'its.csv'\n",
-                "df = pd.read_csv(its_data_path, parse_dates=[\"date\"])\n",
-                "df.set_index(\"date\", inplace=True)\n",
-                "treatment_time = pd.to_datetime(\"2017-01-01\")"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "from causalpy.pymc_experiments import InterruptedTimeSeries\n",
-                "from causalpy.pymc_models import LinearRegression\n",
-                "\n",
-                "thing = InterruptedTimeSeries(df, \n",
-                "                              treatment_time, \n",
-                "                              formula = 'y ~ 1 + t + C(month)', \n",
-                "                              prediction_model=LinearRegression())\n",
-                "\n",
-                "fig, ax = thing.plot()\n",
-                "\n",
-                "if export_images:\n",
-                "    plt.savefig(pathlib.Path.cwd().parents[0] / 'img' / 'interrupted_time_series_pymc.svg', bbox_inches='tight', format=\"svg\")"
-            ]
-        },
-        {
-            "cell_type": "markdown",
-            "metadata": {},
-            "source": [
-                "## Difference in differences"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "did_data_path = pathlib.Path.cwd().parents[0] / 'causalpy' / 'data' / 'did.csv'\n",
-                "\n",
-                "df = pd.read_csv(did_data_path)"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "from causalpy.pymc_experiments import DifferenceInDifferences\n",
-                "from causalpy.pymc_models import LinearRegression\n",
-                "\n",
-                "# NOTE: `treated` is a deterministic function of `t` and `group`. So add this function into the formula.\n",
-                "\n",
-                "thing = DifferenceInDifferences(df, \n",
-                "                                formula = 'y ~ 1 + group + t + treated:group',\n",
-                "                                prediction_model=LinearRegression())\n",
-                "fig, ax = thing.plot()\n",
-                "\n",
-                "if export_images:\n",
-                "    plt.savefig(pathlib.Path.cwd().parents[0] / 'img' / 'difference_in_differences_pymc.svg', bbox_inches='tight', format=\"svg\")"
-            ]
-        },
-        {
-            "cell_type": "markdown",
-            "metadata": {},
-            "source": [
-                "## Regression discontinuity"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "rd_data_path = pathlib.Path.cwd().parents[0] / 'causalpy' / 'data' / 'regression_discontinuity.csv'\n",
-                "df = pd.read_csv(rd_data_path)\n",
-                "df"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": [
-                "from causalpy.pymc_experiments import RegressionDiscontinuity\n",
-                "from causalpy.pymc_models import LinearRegression\n",
-                "\n",
-                "thing = RegressionDiscontinuity(df, \n",
-                "                                formula = 'y ~ 1 + bs(x, df=6) + treated',\n",
-                "                                prediction_model=LinearRegression(), \n",
-                "                                treatment_threshold=0.5)\n",
-                "thing.plot()\n",
-                "\n",
-                "if export_images:\n",
-                "    plt.savefig(pathlib.Path.cwd().parents[0] / 'img' / 'regression_discontinuity_pymc.svg', bbox_inches='tight', format=\"svg\")"
-            ]
-        },
-        {
-            "cell_type": "code",
-            "execution_count": null,
-            "metadata": {},
-            "outputs": [],
-            "source": []
-        }
-    ],
-    "metadata": {
-        "kernelspec": {
-            "display_name": "Python 3.10.6 ('CausalPy')",
-            "language": "python",
-            "name": "python3"
-        },
-        "language_info": {
-            "codemirror_mode": {
-                "name": "ipython",
-                "version": 3
-            },
-            "file_extension": ".py",
-            "mimetype": "text/x-python",
-            "name": "python",
-            "nbconvert_exporter": "python",
-            "pygments_lexer": "ipython3",
-            "version": "3.10.6"
-        },
-        "orig_nbformat": 4,
-        "vscode": {
-            "interpreter": {
-                "hash": "02f5385db19eab57520277c5168790c7855381ee953bdbb5c89c321e1f17586e"
-            }
-        }
-    },
-    "nbformat": 4,
-    "nbformat_minor": 2
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Demo of PyMC models"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import arviz as az\n",
+    "import matplotlib.pyplot as plt\n",
+    "import pandas as pd\n",
+    "import pathlib"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_format = 'svg'\n",
+    "az.style.use(\"arviz-darkgrid\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "export_images = True"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Synthetic Control"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sc_data_path = (\n",
+    "    pathlib.Path.cwd().parents[0] / \"causalpy\" / \"data\" / \"synthetic_control.csv\"\n",
+    ")\n",
+    "df = pd.read_csv(sc_data_path)\n",
+    "treatment_time = 70"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "NUTS: [beta, sigma]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
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+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [8000/8000 00:06&lt;00:00 Sampling 4 chains, 208 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 7 seconds.\n",
+      "Sampling: [beta, sigma, y_hat]\n",
+      "Sampling: [y_hat]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
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+       "    /* Turns off some styling */\n",
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+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
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+       "    <div>\n",
+       "      <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [4000/4000 00:00&lt;00:00]\n",
+       "    </div>\n",
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+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling: [y_hat]\n"
+     ]
+    },
+    {
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+       "        border: none;\n",
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+      "text/plain": [
+       "<Figure size 700x800 with 3 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from causalpy.pymc_experiments import SyntheticControl\n",
+    "from causalpy.pymc_models import WeightedSumFitter\n",
+    "\n",
+    "# Note, we do not want an intercept in this model\n",
+    "thing = SyntheticControl(\n",
+    "    df,\n",
+    "    treatment_time,\n",
+    "    formula=\"actual ~ 0 + a + b + c + d + e + f + g\",\n",
+    "    prediction_model=WeightedSumFitter(),\n",
+    ")\n",
+    "\n",
+    "thing.plot()\n",
+    "\n",
+    "if export_images:\n",
+    "    plt.savefig(\n",
+    "        pathlib.Path.cwd().parents[0] / \"img\" / \"synthetic_control_pymc.svg\",\n",
+    "        bbox_inches=\"tight\",\n",
+    "        format=\"svg\",\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Interrupted time series"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "its_data_path = pathlib.Path.cwd().parents[0] / \"causalpy\" / \"data\" / \"its.csv\"\n",
+    "df = pd.read_csv(its_data_path, parse_dates=[\"date\"])\n",
+    "df.set_index(\"date\", inplace=True)\n",
+    "treatment_time = pd.to_datetime(\"2017-01-01\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "NUTS: [beta, sigma]\n"
+     ]
+    },
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+       "      100.00% [8000/8000 00:02&lt;00:00 Sampling 4 chains, 0 divergences]\n",
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+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 2 seconds.\n",
+      "Sampling: [beta, sigma, y_hat]\n",
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+      "text/plain": [
+       "<Figure size 700x800 with 3 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from causalpy.pymc_experiments import InterruptedTimeSeries\n",
+    "from causalpy.pymc_models import LinearRegression\n",
+    "\n",
+    "thing = InterruptedTimeSeries(\n",
+    "    df,\n",
+    "    treatment_time,\n",
+    "    formula=\"y ~ 1 + t + C(month)\",\n",
+    "    prediction_model=LinearRegression(),\n",
+    ")\n",
+    "\n",
+    "fig, ax = thing.plot()\n",
+    "\n",
+    "if export_images:\n",
+    "    plt.savefig(\n",
+    "        pathlib.Path.cwd().parents[0] / \"img\" / \"interrupted_time_series_pymc.svg\",\n",
+    "        bbox_inches=\"tight\",\n",
+    "        format=\"svg\",\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Difference in differences"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "did_data_path = pathlib.Path.cwd().parents[0] / \"causalpy\" / \"data\" / \"did.csv\"\n",
+    "\n",
+    "df = pd.read_csv(did_data_path)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "NUTS: [beta, sigma]\n"
+     ]
+    },
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+       "      100.00% [8000/8000 00:01&lt;00:00 Sampling 4 chains, 0 divergences]\n",
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+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1 seconds.\n",
+      "Sampling: [beta, sigma, y_hat]\n",
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+      "text/plain": [
+       "<Figure size 720x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from causalpy.pymc_experiments import DifferenceInDifferences\n",
+    "from causalpy.pymc_models import LinearRegression\n",
+    "\n",
+    "# NOTE: `treated` is a deterministic function of `t` and `group`. So add this function into the formula.\n",
+    "\n",
+    "thing = DifferenceInDifferences(\n",
+    "    df, formula=\"y ~ 1 + group + t + treated:group\", prediction_model=LinearRegression()\n",
+    ")\n",
+    "fig, ax = thing.plot()\n",
+    "\n",
+    "if export_images:\n",
+    "    plt.savefig(\n",
+    "        pathlib.Path.cwd().parents[0] / \"img\" / \"difference_in_differences_pymc.svg\",\n",
+    "        bbox_inches=\"tight\",\n",
+    "        format=\"svg\",\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Regression discontinuity"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rd_data_path = (\n",
+    "    pathlib.Path.cwd().parents[0] / \"causalpy\" / \"data\" / \"regression_discontinuity.csv\"\n",
+    ")\n",
+    "df = pd.read_csv(rd_data_path)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "NUTS: [beta, sigma]\n"
+     ]
+    },
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+      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 3 seconds.\n",
+      "Sampling: [beta, sigma, y_hat]\n",
+      "Sampling: [y_hat]\n"
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+      "Sampling: [y_hat]\n"
+     ]
+    },
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+      "text/html": [
+       "\n",
+       "<style>\n",
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+      "text/plain": [
+       "<Figure size 720x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from causalpy.pymc_experiments import RegressionDiscontinuity\n",
+    "from causalpy.pymc_models import LinearRegression\n",
+    "\n",
+    "thing = RegressionDiscontinuity(\n",
+    "    df,\n",
+    "    formula=\"y ~ 1 + bs(x, df=6) + treated\",\n",
+    "    prediction_model=LinearRegression(),\n",
+    "    treatment_threshold=0.5,\n",
+    ")\n",
+    "thing.plot()\n",
+    "\n",
+    "if export_images:\n",
+    "    plt.savefig(\n",
+    "        pathlib.Path.cwd().parents[0] / \"img\" / \"regression_discontinuity_pymc.svg\",\n",
+    "        bbox_inches=\"tight\",\n",
+    "        format=\"svg\",\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Run the 'drinking example' from the RDD chapter of [Causal Inference for the Brave and True](https://matheusfacure.github.io/python-causality-handbook/16-Regression-Discontinuity-Design.html)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rd_data_path = pathlib.Path.cwd().parents[0] / \"causalpy\" / \"data\" / \"drinking.csv\"\n",
+    "df = (\n",
+    "    pd.read_csv(rd_data_path)[[\"agecell\", \"all\", \"mva\", \"suicide\"]]\n",
+    "    .rename(columns={\"agecell\": \"age\"})\n",
+    "    .assign(treated=lambda df_: df_.age > 21)\n",
+    "    .dropna(axis=0)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "NUTS: [beta, sigma]\n"
+     ]
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+       "    <div>\n",
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+       "      100.00% [8000/8000 00:16&lt;00:00 Sampling 4 chains, 1 divergences]\n",
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+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 17 seconds.\n",
+      "Sampling: [beta, sigma, y_hat]\n",
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+      "text/plain": [
+       "<Figure size 720x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from causalpy.pymc_experiments import RegressionDiscontinuity\n",
+    "from causalpy.pymc_models import LinearRegression\n",
+    "\n",
+    "thing = RegressionDiscontinuity(\n",
+    "    df,\n",
+    "    formula=\"all ~ 1 + age + treated + age:treated\",\n",
+    "    running_variable_name=\"age\",\n",
+    "    outcome_variable_name=\"all\",\n",
+    "    prediction_model=LinearRegression(),\n",
+    "    treatment_threshold=21,\n",
+    ")\n",
+    "thing.plot();"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3.10.6 ('CausalPy')",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.6"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "02f5385db19eab57520277c5168790c7855381ee953bdbb5c89c321e1f17586e"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
 }
diff --git a/notebooks/skl_demos.ipynb b/notebooks/skl_demos.ipynb
index 4c9a2c78..8ec2000e 100644
--- a/notebooks/skl_demos.ipynb
+++ b/notebooks/skl_demos.ipynb
@@ -41,11 +41,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [],
    "source": [
-    "export_images = False"
+    "export_images = True"
    ]
   },
   {
@@ -82,7 +82,7 @@
    "outputs": [
     {
      "data": {
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-       "<Figure size 700x800 with 2 Axes>"
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       "text/plain": [
-       "<Figure size 700x800 with 2 Axes>"
+       "<Figure size 720x480 with 1 Axes>"
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      "metadata": {},
@@ -416,14 +416,14 @@
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   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
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       "text/plain": [
-       "<Figure size 700x800 with 2 Axes>"
+       "<Figure size 720x480 with 1 Axes>"
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@@ -465,24 +465,24 @@
    "outputs": [],
    "source": [
     "rd_data_path = pathlib.Path.cwd().parents[0] / \"causalpy\" / \"data\" / \"drinking.csv\"\n",
-    "df = pd.read_csv(rd_data_path)[[\"agecell\", \"all\", \"mva\", \"suicide\"]]\n",
-    "df[\"agecell\"] = df[\"agecell\"] - 21\n",
-    "# create dummy variable\n",
-    "df = df.assign(treated=(df[\"agecell\"] > 0))\n",
-    "# drop rows with missing data\n",
-    "df = df.dropna(axis=0)"
+    "df = (\n",
+    "    pd.read_csv(rd_data_path)[[\"agecell\", \"all\", \"mva\", \"suicide\"]]\n",
+    "    .rename(columns={\"agecell\": \"age\"})\n",
+    "    .assign(treated=lambda df_: df_.age > 21)\n",
+    "    .dropna(axis=0)\n",
+    ")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
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       "text/plain": [
-       "<Figure size 700x800 with 2 Axes>"
+       "<Figure size 720x480 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -495,11 +495,11 @@
     "\n",
     "thing = RegressionDiscontinuity(\n",
     "    df,\n",
-    "    formula=\"all ~ 1 + agecell + treated + agecell:treated\",\n",
-    "    running_variable_name=\"agecell\",\n",
+    "    formula=\"all ~ 1 + age + treated + age:treated\",\n",
+    "    running_variable_name=\"age\",\n",
     "    outcome_variable_name=\"all\",\n",
     "    prediction_model=LinearRegression(),\n",
-    "    treatment_threshold=0,\n",
+    "    treatment_threshold=21,\n",
     ")\n",
     "thing.plot();"
    ]