From f9dc804b39ceddf809e97453de818621a0ba7fe4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Laurent?= <francois.laurent@posteo.net>
Date: Wed, 22 Sep 2021 23:12:01 +0200
Subject: [PATCH] extra dataset + regression and non-linear regression sections

---
 data/patients.csv                 |  201 +++
 notebooks/scipy_cours.ipynb       |    6 -
 notebooks/statsmodels_cours.ipynb | 2304 +++++++++++++++++++++++++----
 3 files changed, 2192 insertions(+), 319 deletions(-)
 create mode 100644 data/patients.csv

diff --git a/data/patients.csv b/data/patients.csv
new file mode 100644
index 0000000..78b5260
--- /dev/null
+++ b/data/patients.csv
@@ -0,0 +1,201 @@
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diff --git a/notebooks/scipy_cours.ipynb b/notebooks/scipy_cours.ipynb
index ea9b183..78f76bf 100644
--- a/notebooks/scipy_cours.ipynb
+++ b/notebooks/scipy_cours.ipynb
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    "id": "3b30414c-6575-4dff-9637-664cb0f29a5a",
    "metadata": {
-    "heading_collapsed": true,
     "hidden": true
    },
    "source": [
@@ -3503,7 +3498,6 @@
    "cell_type": "markdown",
    "id": "700ff9a1-e4e9-4ef5-9559-f6d6740977ed",
    "metadata": {
-    "heading_collapsed": true,
     "hidden": true
    },
    "source": [
diff --git a/notebooks/statsmodels_cours.ipynb b/notebooks/statsmodels_cours.ipynb
index 23e89c1..7c043b6 100644
--- a/notebooks/statsmodels_cours.ipynb
+++ b/notebooks/statsmodels_cours.ipynb
@@ -17,13 +17,13 @@
      "output_type": "stream",
      "text": [
       "Requirement already satisfied: statsmodels in /home/flaurent/.local/lib/python3.8/site-packages (0.12.2)\n",
-      "Requirement already satisfied: patsy>=0.5 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (0.5.1)\n",
-      "Requirement already satisfied: scipy>=1.1 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.7.1)\n",
       "Requirement already satisfied: numpy>=1.15 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.21.1)\n",
+      "Requirement already satisfied: scipy>=1.1 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.7.1)\n",
       "Requirement already satisfied: pandas>=0.21 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.3.1)\n",
-      "Requirement already satisfied: six in /usr/lib/python3/dist-packages (from patsy>=0.5->statsmodels) (1.14.0)\n",
+      "Requirement already satisfied: patsy>=0.5 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (0.5.1)\n",
+      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas>=0.21->statsmodels) (2.7.3)\n",
       "Requirement already satisfied: pytz>=2017.3 in /usr/lib/python3/dist-packages (from pandas>=0.21->statsmodels) (2019.3)\n",
-      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas>=0.21->statsmodels) (2.7.3)\n"
+      "Requirement already satisfied: six in /usr/lib/python3/dist-packages (from patsy>=0.5->statsmodels) (1.14.0)\n"
      ]
     }
    ],
@@ -426,8 +426,8 @@
       "Dep. Variable:                      Y   R-squared:                       0.149\n",
       "Model:                            OLS   Adj. R-squared:                  0.086\n",
       "Method:                 Least Squares   F-statistic:                     2.358\n",
-      "Date:                Mon, 20 Sep 2021   Prob (F-statistic):              0.114\n",
-      "Time:                        13:22:16   Log-Likelihood:                -96.604\n",
+      "Date:                Wed, 22 Sep 2021   Prob (F-statistic):              0.114\n",
+      "Time:                        08:49:55   Log-Likelihood:                -96.604\n",
       "No. Observations:                  30   AIC:                             199.2\n",
       "Df Residuals:                      27   BIC:                             203.4\n",
       "Df Model:                           2                                         \n",
@@ -986,14 +986,14 @@
      "output_type": "stream",
      "text": [
       "Requirement already satisfied: formulaic in /home/flaurent/.local/lib/python3.8/site-packages (0.2.4)\n",
-      "Requirement already satisfied: numpy in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.21.1)\n",
-      "Requirement already satisfied: pandas in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.3.1)\n",
       "Requirement already satisfied: interface-meta>=1.2 in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.2.4)\n",
       "Requirement already satisfied: wrapt in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.12.1)\n",
-      "Requirement already satisfied: astor in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (0.8.1)\n",
       "Requirement already satisfied: scipy in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.7.1)\n",
-      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas->formulaic) (2.7.3)\n",
-      "Requirement already satisfied: pytz>=2017.3 in /usr/lib/python3/dist-packages (from pandas->formulaic) (2019.3)\n"
+      "Requirement already satisfied: astor in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (0.8.1)\n",
+      "Requirement already satisfied: pandas in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.3.1)\n",
+      "Requirement already satisfied: numpy in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.21.1)\n",
+      "Requirement already satisfied: pytz>=2017.3 in /usr/lib/python3/dist-packages (from pandas->formulaic) (2019.3)\n",
+      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas->formulaic) (2.7.3)\n"
      ]
     }
    ],
@@ -1323,10 +1323,10 @@
        "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2.358</td>\n",
        "</tr>\n",
        "<tr>\n",
-       "  <th>Date:</th>             <td>Mon, 20 Sep 2021</td> <th>  Prob (F-statistic):</th>  <td> 0.114</td> \n",
+       "  <th>Date:</th>             <td>Wed, 22 Sep 2021</td> <th>  Prob (F-statistic):</th>  <td> 0.114</td> \n",
        "</tr>\n",
        "<tr>\n",
-       "  <th>Time:</th>                 <td>13:22:20</td>     <th>  Log-Likelihood:    </th> <td> -96.604</td>\n",
+       "  <th>Time:</th>                 <td>08:49:58</td>     <th>  Log-Likelihood:    </th> <td> -96.604</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>   199.2</td>\n",
@@ -1381,8 +1381,8 @@
        "Dep. Variable:                      Y   R-squared:                       0.149\n",
        "Model:                            OLS   Adj. R-squared:                  0.086\n",
        "Method:                 Least Squares   F-statistic:                     2.358\n",
-       "Date:                Mon, 20 Sep 2021   Prob (F-statistic):              0.114\n",
-       "Time:                        13:22:20   Log-Likelihood:                -96.604\n",
+       "Date:                Wed, 22 Sep 2021   Prob (F-statistic):              0.114\n",
+       "Time:                        08:49:58   Log-Likelihood:                -96.604\n",
        "No. Observations:                  30   AIC:                             199.2\n",
        "Df Residuals:                      27   BIC:                             203.4\n",
        "Df Model:                           2                                         \n",
@@ -1479,8 +1479,8 @@
       "Dep. Variable:                      Y   R-squared:                       0.149\n",
       "Model:                            OLS   Adj. R-squared:                  0.086\n",
       "Method:                 Least Squares   F-statistic:                     2.358\n",
-      "Date:                Mon, 20 Sep 2021   Prob (F-statistic):              0.114\n",
-      "Time:                        13:22:21   Log-Likelihood:                -96.604\n",
+      "Date:                Wed, 22 Sep 2021   Prob (F-statistic):              0.114\n",
+      "Time:                        08:49:59   Log-Likelihood:                -96.604\n",
       "No. Observations:                  30   AIC:                             199.2\n",
       "Df Residuals:                      27   BIC:                             203.4\n",
       "Df Model:                           2                                         \n",
@@ -2173,14 +2173,14 @@
   {
    "cell_type": "code",
    "execution_count": 43,
-   "id": "76d3083a",
+   "id": "8642f0e6",
    "metadata": {},
    "outputs": [
     {
      "data": {
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+      "image/png": "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\n",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 957.6x295.2 with 2 Axes>"
       ]
      },
      "metadata": {
@@ -2193,11 +2193,17 @@
     "power = 0.8\n",
     "type1_error = 0.05\n",
     "\n",
+    "true_grid = np.zeros((20, 60), dtype=bool)\n",
+    "true_grid[:10,-10:] = True\n",
+    "\n",
     "rejection_grid = np.array([[ np.random.rand() <= type1_error for _ in range(60) ] for _ in range(20)])\n",
     "rejection_grid[:10,-10:] = [[ np.random.rand() <= power for _ in range(10)] for _ in range(10)]\n",
     "\n",
-    "plt.imshow(rejection_grid, cmap='seismic')\n",
-    "plt.gca().axis(\"off\");"
+    "_, axes = plt.subplots(1, 2, figsize=(13.3,4.1))\n",
+    "for ax, title, grid in zip(axes[::-1], ('true', 'observed'), (true_grid, rejection_grid)):\n",
+    "    ax.imshow(grid, cmap='seismic')\n",
+    "    ax.set_title(title)\n",
+    "    ax.axis(\"off\");"
    ]
   },
   {
@@ -2528,16 +2534,12 @@
     "\n",
     "Designs are balanced.\n",
     "\n",
-    "`statsmodels` features [AnovaRM](https://www.statsmodels.org/stable/generated/statsmodels.stats.anova.AnovaRM.html) but corrections for departure from sphericity are not implemented and we should first perform a Mauchly's test for sphericity, for example with [pingouin.sphericity](https://pingouin-stats.org/generated/pingouin.sphericity.html).\n",
-    "\n",
-    "[rm_anova](https://pingouin-stats.org/generated/pingouin.rm_anova.html) from `pingouin` does implement Greenhouse-Geiser correction.\n",
-    "\n",
     "Let us borrow an example from `pingouin` documentation:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 48,
    "id": "5bbe2b04",
    "metadata": {},
    "outputs": [
@@ -2641,7 +2643,7 @@
        "31        2  Post  Product            6"
       ]
      },
-     "execution_count": 82,
+     "execution_count": 48,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2653,16 +2655,37 @@
     "data.loc[[0,1,10,11,20,21,30,31]]"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "9d6d7c4c",
+   "metadata": {},
+   "source": [
+    "In this example, each subject (`Subject`) has undergone all possible measurements, for all levels of the `Time` and `Metric` factors.\n",
+    "As a consequence, the observations for each subject are not independent, and this must be accounted for by the model.\n",
+    "\n",
+    "In a standard repeated measures ANOVA, the covariance structure is just assumed to exhibit a property called sphericity.\n",
+    "\n",
+    "`Time` and `Metric` are called *within-subject* factors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2f4b9c1d",
+   "metadata": {},
+   "source": [
+    "`statsmodels` features [AnovaRM](https://www.statsmodels.org/stable/generated/statsmodels.stats.anova.AnovaRM.html) but corrections for departure from sphericity are not implemented and we should first perform a Mauchly's test for sphericity, for example with [pingouin.sphericity](https://pingouin-stats.org/generated/pingouin.sphericity.html):"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "21f450d5",
+   "id": "4a695145",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "SpherResults(spher=True, W=0.9681178957928578, chi2=0.25921124757845354, dof=2, pval=0.8784417991645136)"
+       "SpherResults(spher=True, W=0.6247989838343564, chi2=3.762602454747652, dof=2, pval=0.15239168046050933)"
       ]
      },
      "execution_count": 49,
@@ -2671,19 +2694,73 @@
     }
    ],
    "source": [
-    "pg.sphericity(data, dv='Performance', subject='Subject', within=['Metric'])"
+    "pg.sphericity(data, dv='Performance', subject='Subject', within=['Time', 'Metric'])"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 50,
-   "id": "4a695145",
+   "id": "d60b902e",
    "metadata": {},
    "outputs": [
     {
      "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>F Value</th>\n",
+       "      <th>Num DF</th>\n",
+       "      <th>Den DF</th>\n",
+       "      <th>Pr &gt; F</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>Time</th>\n",
+       "      <td>33.85228</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>9.0</td>\n",
+       "      <td>0.000254</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Metric</th>\n",
+       "      <td>26.95919</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>18.0</td>\n",
+       "      <td>0.000004</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Time:Metric</th>\n",
+       "      <td>12.63227</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>18.0</td>\n",
+       "      <td>0.000373</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
       "text/plain": [
-       "SpherResults(spher=True, W=0.6247989838343564, chi2=3.762602454747652, dof=2, pval=0.15239168046050933)"
+       "              F Value  Num DF  Den DF    Pr > F\n",
+       "Time         33.85228     1.0     9.0  0.000254\n",
+       "Metric       26.95919     2.0    18.0  0.000004\n",
+       "Time:Metric  12.63227     2.0    18.0  0.000373"
       ]
      },
      "execution_count": 50,
@@ -2692,7 +2769,17 @@
     }
    ],
    "source": [
-    "pg.sphericity(data, dv='Performance', subject='Subject', within=['Time', 'Metric'])"
+    "from statsmodels.stats import anova\n",
+    "result = anova.AnovaRM(data, depvar='Performance', subject='Subject', within=['Time', 'Metric']).fit()\n",
+    "result.anova_table"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5c4e709f",
+   "metadata": {},
+   "source": [
+    "In contrast, [rm_anova](https://pingouin-stats.org/generated/pingouin.rm_anova.html) from `pingouin` does implement Greenhouse-Geiser correction."
    ]
   },
   {
@@ -2799,89 +2886,14 @@
     "pg.rm_anova(data, dv='Performance', subject='Subject', within=['Time', 'Metric'])"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "id": "d60b902e",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>F Value</th>\n",
-       "      <th>Num DF</th>\n",
-       "      <th>Den DF</th>\n",
-       "      <th>Pr &gt; F</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>Time</th>\n",
-       "      <td>33.85228</td>\n",
-       "      <td>1.0</td>\n",
-       "      <td>9.0</td>\n",
-       "      <td>0.000254</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Metric</th>\n",
-       "      <td>26.95919</td>\n",
-       "      <td>2.0</td>\n",
-       "      <td>18.0</td>\n",
-       "      <td>0.000004</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Time:Metric</th>\n",
-       "      <td>12.63227</td>\n",
-       "      <td>2.0</td>\n",
-       "      <td>18.0</td>\n",
-       "      <td>0.000373</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "              F Value  Num DF  Den DF    Pr > F\n",
-       "Time         33.85228     1.0     9.0  0.000254\n",
-       "Metric       26.95919     2.0    18.0  0.000004\n",
-       "Time:Metric  12.63227     2.0    18.0  0.000373"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "from statsmodels.stats import anova\n",
-    "result = anova.AnovaRM(data, depvar='Performance', subject='Subject', within=['Time', 'Metric']).fit()\n",
-    "result.anova_table"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "6a895941",
    "metadata": {},
    "source": [
-    "Mixed effects models are increasingly popular and preferred over the standard repeated measures ANOVA."
+    "Note that neither `AnovaRM` nor `rm_anova` give access to the model's coefficients.\n",
+    "\n",
+    "Mixed effects models are increasingly popular and preferred over the standard repeated measures ANOVA, especially because sphericity simply cannot be expected from the data in most cases."
    ]
   },
   {
@@ -2897,140 +2909,107 @@
    "id": "d14b605d-5737-4d22-9a37-4bd6df7dffb0",
    "metadata": {},
    "source": [
-    "The [mixedlm](https://www.statsmodels.org/stable/generated/statsmodels.formula.api.mixedlm.html) function and underlying [MixedLM](https://www.statsmodels.regression.mixed_linear_model.MixedLM ) class offer a flexible framework for defining models with random effects (`re`) and variance components (`vc`):"
+    "The previously mentioned procedures model *fixed effects*. Fixed effects define the expected values of the observations (or responses).\n",
+    "\n",
+    "In contrast, the variance and covariances of the observations can be modelled as *random effects*.\n",
+    "\n",
+    "Mixed effects models combine both fixed and random effects and allows choosing how to treat each factor.\n",
+    "\n",
+    "The [mixedlm](https://www.statsmodels.org/stable/generated/statsmodels.formula.api.mixedlm.html) function and underlying [MixedLM](https://www.statsmodels.regression.mixed_linear_model.MixedLM ) take a `groups` argument, plus other arguments prefixed `re_` for random effects and `vc_` for variance components.\n",
+    "\n",
+    "To begin with, we can introduce a random intercept for each subject, and keep all the factors fixed:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": 52,
    "id": "c368c19e",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>Coef.</th>\n",
-       "      <th>Std.Err.</th>\n",
-       "      <th>z</th>\n",
-       "      <th>P&gt;|z|</th>\n",
-       "      <th>[0.025</th>\n",
-       "      <th>0.975]</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>Intercept</th>\n",
-       "      <td>33.000</td>\n",
-       "      <td>2.123</td>\n",
-       "      <td>15.543</td>\n",
-       "      <td>0.000</td>\n",
-       "      <td>28.839</td>\n",
-       "      <td>37.161</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Time[T.Pre]</th>\n",
-       "      <td>-10.700</td>\n",
-       "      <td>1.928</td>\n",
-       "      <td>-5.551</td>\n",
-       "      <td>0.000</td>\n",
-       "      <td>-14.478</td>\n",
-       "      <td>-6.922</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Metric[T.Client]</th>\n",
-       "      <td>-3.100</td>\n",
-       "      <td>1.928</td>\n",
-       "      <td>-1.608</td>\n",
-       "      <td>0.108</td>\n",
-       "      <td>-6.878</td>\n",
-       "      <td>0.678</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Metric[T.Product]</th>\n",
-       "      <td>-15.500</td>\n",
-       "      <td>1.928</td>\n",
-       "      <td>-8.041</td>\n",
-       "      <td>0.000</td>\n",
-       "      <td>-19.278</td>\n",
-       "      <td>-11.722</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Time[T.Pre]:Metric[T.Client]</th>\n",
-       "      <td>1.100</td>\n",
-       "      <td>2.726</td>\n",
-       "      <td>0.404</td>\n",
-       "      <td>0.687</td>\n",
-       "      <td>-4.243</td>\n",
-       "      <td>6.443</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Time[T.Pre]:Metric[T.Product]</th>\n",
-       "      <td>8.700</td>\n",
-       "      <td>2.726</td>\n",
-       "      <td>3.191</td>\n",
-       "      <td>0.001</td>\n",
-       "      <td>3.357</td>\n",
-       "      <td>14.043</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Group Var</th>\n",
-       "      <td>26.497</td>\n",
-       "      <td>3.545</td>\n",
-       "      <td></td>\n",
-       "      <td></td>\n",
-       "      <td></td>\n",
-       "      <td></td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td> <td>Performance</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>No. Observations:</td>   <td>60</td>          <td>Method:</td>          <td>REML</td>    \n",
+       "</tr>\n",
+       "<tr>\n",
+       "     <td>No. Groups:</td>      <td>10</td>          <td>Scale:</td>          <td>18.5783</td>  \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>Min. group size:</td>     <td>6</td>      <td>Log-Likelihood:</td>    <td>-172.5821</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>Max. group size:</td>     <td>6</td>        <td>Converged:</td>          <td>Yes</td>    \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>Mean group size:</td>    <td>6.0</td>            <td></td>                <td></td>      \n",
+       "</tr>\n",
        "</table>\n",
-       "</div>"
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "                <td></td>                 <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>   <th>P>|z|</th> <th>[0.025</th>  <th>0.975]</th> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Intercept</th>                     <td>33.000</td>    <td>2.123</td>  <td>15.543</td> <td>0.000</td> <td>28.839</td>  <td>37.161</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time[T.Pre]</th>                   <td>-10.700</td>   <td>1.928</td>  <td>-5.551</td> <td>0.000</td> <td>-14.478</td> <td>-6.922</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Metric[T.Client]</th>              <td>-3.100</td>    <td>1.928</td>  <td>-1.608</td> <td>0.108</td> <td>-6.878</td>   <td>0.678</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Metric[T.Product]</th>             <td>-15.500</td>   <td>1.928</td>  <td>-8.041</td> <td>0.000</td> <td>-19.278</td> <td>-11.722</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time[T.Pre]:Metric[T.Client]</th>   <td>1.100</td>    <td>2.726</td>   <td>0.404</td> <td>0.687</td> <td>-4.243</td>   <td>6.443</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time[T.Pre]:Metric[T.Product]</th>  <td>8.700</td>    <td>2.726</td>   <td>3.191</td> <td>0.001</td>  <td>3.357</td>  <td>14.043</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Subject Var</th>                   <td>26.497</td>    <td>3.545</td>     <td></td>      <td></td>       <td></td>        <td></td>    \n",
+       "</tr>\n",
+       "</table>"
       ],
       "text/plain": [
-       "                                 Coef. Std.Err.       z  P>|z|   [0.025  \\\n",
-       "Intercept                       33.000    2.123  15.543  0.000   28.839   \n",
-       "Time[T.Pre]                    -10.700    1.928  -5.551  0.000  -14.478   \n",
-       "Metric[T.Client]                -3.100    1.928  -1.608  0.108   -6.878   \n",
-       "Metric[T.Product]              -15.500    1.928  -8.041  0.000  -19.278   \n",
-       "Time[T.Pre]:Metric[T.Client]     1.100    2.726   0.404  0.687   -4.243   \n",
-       "Time[T.Pre]:Metric[T.Product]    8.700    2.726   3.191  0.001    3.357   \n",
-       "Group Var                       26.497    3.545                           \n",
+       "<class 'statsmodels.iolib.summary2.Summary'>\n",
+       "\"\"\"\n",
+       "                   Mixed Linear Model Regression Results\n",
+       "===========================================================================\n",
+       "Model:                  MixedLM       Dependent Variable:       Performance\n",
+       "No. Observations:       60            Method:                   REML       \n",
+       "No. Groups:             10            Scale:                    18.5783    \n",
+       "Min. group size:        6             Log-Likelihood:           -172.5821  \n",
+       "Max. group size:        6             Converged:                Yes        \n",
+       "Mean group size:        6.0                                                \n",
+       "---------------------------------------------------------------------------\n",
+       "                               Coef.  Std.Err.   z    P>|z|  [0.025  0.975]\n",
+       "---------------------------------------------------------------------------\n",
+       "Intercept                      33.000    2.123 15.543 0.000  28.839  37.161\n",
+       "Time[T.Pre]                   -10.700    1.928 -5.551 0.000 -14.478  -6.922\n",
+       "Metric[T.Client]               -3.100    1.928 -1.608 0.108  -6.878   0.678\n",
+       "Metric[T.Product]             -15.500    1.928 -8.041 0.000 -19.278 -11.722\n",
+       "Time[T.Pre]:Metric[T.Client]    1.100    2.726  0.404 0.687  -4.243   6.443\n",
+       "Time[T.Pre]:Metric[T.Product]   8.700    2.726  3.191 0.001   3.357  14.043\n",
+       "Subject Var                    26.497    3.545                             \n",
+       "===========================================================================\n",
        "\n",
-       "                                0.975]  \n",
-       "Intercept                       37.161  \n",
-       "Time[T.Pre]                     -6.922  \n",
-       "Metric[T.Client]                 0.678  \n",
-       "Metric[T.Product]              -11.722  \n",
-       "Time[T.Pre]:Metric[T.Client]     6.443  \n",
-       "Time[T.Pre]:Metric[T.Product]   14.043  \n",
-       "Group Var                               "
+       "\"\"\""
       ]
      },
-     "execution_count": 84,
+     "execution_count": 52,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "me_model = smf.mixedlm(\"Performance ~ Time * Metric\", data, groups=data[\"Subject\"]).fit()\n",
-    "me_model.summary().tables[1]"
+    "random_intercept_model = smf.mixedlm(\"Performance ~ Time * Metric\", data, groups=\"Subject\").fit()\n",
+    "random_intercept_model.summary()"
    ]
   },
   {
@@ -3043,7 +3022,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 53,
    "id": "1d278355",
    "metadata": {},
    "outputs": [
@@ -3078,7 +3057,7 @@
        "<class 'statsmodels.iolib.table.SimpleTable'>"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3089,20 +3068,1515 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": 75,
-   "id": "e3391f0c",
+   "cell_type": "markdown",
+   "id": "ad998bc8",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
+   "source": [
+    "The differences between subject means are not reflected by the coefficients. Only variance is affected and, consequently, the statistics and $p$-values for fixed-effect coefficients.\n",
+    "\n",
+    "Specifying a grouping factor introduces in the model a random intercept. Basically, denoting $\\beta$ the coefficients for fixed effects, for each observation $i$ and corresponding subject $j$:\n",
+    "\n",
+    "$$\n",
+    "\\texttt{Performance}_i = (\\beta_{0} + u_{0j}) + \\beta_{1}\\texttt{Time[T.Pre]} + \\beta_{2}\\texttt{Metric[T.Client]} + \\beta_{3}\\texttt{Metric[T.Product]} + ...\n",
+    "$$\n",
+    "\n",
+    "with for example $\\beta_{0}=33$ the fixed intercept and, notably, $u_{0j}$ the random intercept for subject $j$.\n",
+    "Each $u_{0j}$ is a draw from $u_{0} \\sim \\mathcal{N}(0, 26.497)$. The population mean for random coefficients is always $0$.\n",
+    "\n",
+    "A downside of mixed-effects models is that we can no longer rely on an omnibus statistic to tell us whether there is any significant effect. Some [procedures](https://www.ssc.wisc.edu/sscc/pubs/MM/MM_TestEffects.html) exist, but are computationally expensive."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "id": "0f17cdbd",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td> <td>Performance</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>No. Observations:</td>   <td>60</td>          <td>Method:</td>          <td>REML</td>    \n",
+       "</tr>\n",
+       "<tr>\n",
+       "     <td>No. Groups:</td>       <td>1</td>          <td>Scale:</td>          <td>18.5783</td>  \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>Min. group size:</td>    <td>60</td>      <td>Log-Likelihood:</td>    <td>-172.5821</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>Max. group size:</td>    <td>60</td>        <td>Converged:</td>          <td>Yes</td>    \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <td>Mean group size:</td>   <td>60.0</td>            <td></td>                <td></td>      \n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "                <td></td>                 <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>   <th>P>|z|</th> <th>[0.025</th>  <th>0.975]</th> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Intercept</th>                     <td>33.000</td>    <td>2.123</td>  <td>15.543</td> <td>0.000</td> <td>28.839</td>  <td>37.161</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time[T.Pre]</th>                   <td>-10.700</td>   <td>1.928</td>  <td>-5.551</td> <td>0.000</td> <td>-14.478</td> <td>-6.922</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Metric[T.Client]</th>              <td>-3.100</td>    <td>1.928</td>  <td>-1.608</td> <td>0.108</td> <td>-6.878</td>   <td>0.678</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Metric[T.Product]</th>             <td>-15.500</td>   <td>1.928</td>  <td>-8.041</td> <td>0.000</td> <td>-19.278</td> <td>-11.722</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time[T.Pre]:Metric[T.Client]</th>   <td>1.100</td>    <td>2.726</td>   <td>0.404</td> <td>0.687</td> <td>-4.243</td>   <td>6.443</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time[T.Pre]:Metric[T.Product]</th>  <td>8.700</td>    <td>2.726</td>   <td>3.191</td> <td>0.001</td>  <td>3.357</td>  <td>14.043</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Subject Var</th>                   <td>26.497</td>    <td>3.545</td>     <td></td>      <td></td>       <td></td>        <td></td>    \n",
+       "</tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "<class 'statsmodels.iolib.summary2.Summary'>\n",
+       "\"\"\"\n",
+       "                   Mixed Linear Model Regression Results\n",
+       "===========================================================================\n",
+       "Model:                  MixedLM       Dependent Variable:       Performance\n",
+       "No. Observations:       60            Method:                   REML       \n",
+       "No. Groups:             1             Scale:                    18.5783    \n",
+       "Min. group size:        60            Log-Likelihood:           -172.5821  \n",
+       "Max. group size:        60            Converged:                Yes        \n",
+       "Mean group size:        60.0                                               \n",
+       "---------------------------------------------------------------------------\n",
+       "                               Coef.  Std.Err.   z    P>|z|  [0.025  0.975]\n",
+       "---------------------------------------------------------------------------\n",
+       "Intercept                      33.000    2.123 15.543 0.000  28.839  37.161\n",
+       "Time[T.Pre]                   -10.700    1.928 -5.551 0.000 -14.478  -6.922\n",
+       "Metric[T.Client]               -3.100    1.928 -1.608 0.108  -6.878   0.678\n",
+       "Metric[T.Product]             -15.500    1.928 -8.041 0.000 -19.278 -11.722\n",
+       "Time[T.Pre]:Metric[T.Client]    1.100    2.726  0.404 0.687  -4.243   6.443\n",
+       "Time[T.Pre]:Metric[T.Product]   8.700    2.726  3.191 0.001   3.357  14.043\n",
+       "Subject Var                    26.497    3.545                             \n",
+       "===========================================================================\n",
+       "\n",
+       "\"\"\""
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "vc = {'Subject': '0 + C(Subject)'}\n",
+    "random_intercept_model = smf.mixedlm(\"Performance ~ Time * Metric\", data, groups=np.ones(len(data)), vc_formula=vc).fit()\n",
+    "random_intercept_model.summary()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a5f2e5a4-1119-4379-8b02-abde4828eb02",
+   "metadata": {},
+   "source": [
+    "### Nested designs"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f999ae16",
+   "metadata": {},
+   "source": [
+    "\"Sometimes, constraints prevent us from crossing every level of one factor with every level of the other factor. In these cases we are forced into what is known as a nested layout. We say we have a nested layout when fewer than all levels of one factor occur within each level of the other factor.\"\n",
+    "[Engineering Statistics Handbook](https://www.itl.nist.gov/div898/handbook/ppc/section2/ppc233.htm)\n",
+    "\n",
+    "Examples: Students in classrooms in schools; mice in breeding cages\n",
+    "\n",
+    "Terminology: the `student` factor is nested in `classroom`, that in turn is nested in `school`. `classroom` is a grouping factor for `student`, and `school` is a grouping factor for `classroom`.\n",
+    "\n",
+    "Again, it is possible to treat these factors as *fixed effect* factors in the model, introducing the grouping factors in interaction terms only. For example:\n",
+    "\n",
+    "`test_score ~ student_age + student_age:C(classroom) + C(classroom):C(school)`\n",
+    "\n",
+    "However, it becomes more common to treat the grouping factors as *random effect* factors instead.\n",
+    "Models with both fixed and random effects are called [linear *mixed effects* models](https://www.statsmodels.org/stable/mixed_linear.html)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "id": "d4c6a6ac",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>y</th>\n",
+       "      <th>age</th>\n",
+       "      <th>group1</th>\n",
+       "      <th>group2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>3.724447</td>\n",
+       "      <td>28</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2.517394</td>\n",
+       "      <td>21</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>6.146888</td>\n",
+       "      <td>35</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>3.725873</td>\n",
+       "      <td>19</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>2.826362</td>\n",
+       "      <td>32</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>115</th>\n",
+       "      <td>9.094052</td>\n",
+       "      <td>19</td>\n",
+       "      <td>3</td>\n",
+       "      <td>23</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>116</th>\n",
+       "      <td>9.837780</td>\n",
+       "      <td>28</td>\n",
+       "      <td>3</td>\n",
+       "      <td>23</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>117</th>\n",
+       "      <td>7.241901</td>\n",
+       "      <td>37</td>\n",
+       "      <td>3</td>\n",
+       "      <td>23</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>118</th>\n",
+       "      <td>6.820161</td>\n",
+       "      <td>32</td>\n",
+       "      <td>3</td>\n",
+       "      <td>23</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>119</th>\n",
+       "      <td>11.594506</td>\n",
+       "      <td>32</td>\n",
+       "      <td>3</td>\n",
+       "      <td>23</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>120 rows × 4 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "             y  age  group1  group2\n",
+       "0     3.724447   28       0       0\n",
+       "1     2.517394   21       0       0\n",
+       "2     6.146888   35       0       0\n",
+       "3     3.725873   19       0       0\n",
+       "4     2.826362   32       0       0\n",
+       "..         ...  ...     ...     ...\n",
+       "115   9.094052   19       3      23\n",
+       "116   9.837780   28       3      23\n",
+       "117   7.241901   37       3      23\n",
+       "118   6.820161   32       3      23\n",
+       "119  11.594506   32       3      23\n",
+       "\n",
+       "[120 rows x 4 columns]"
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def randint(low, high, size, dist):\n",
+    "    ret = []\n",
+    "    while len(ret) < size:\n",
+    "        ints = np.round(dist.rvs(size))\n",
+    "        ints = ints[(low<=ints)&(ints<=high)]\n",
+    "        ret = np.r_[ret, ints] if len(ret) else ints\n",
+    "    return ret[:size].astype(int)\n",
+    "\n",
+    "def generate_nested(\n",
+    "    n_group1=4, n_group2=6, n_rep=5,\n",
+    "    group1_sd=1, group2_sd=2, unexplained_sd=3\n",
+    "):\n",
+    "    # Group 1 indicators\n",
+    "    group1 = np.repeat(np.arange(n_group1), n_group2 * n_rep)\n",
+    "\n",
+    "    # Group 1 effects\n",
+    "    u = group1_sd * np.random.normal(size=n_group1)\n",
+    "    effects1 = np.kron(u, np.ones(n_group2 * n_rep))\n",
+    "\n",
+    "    # Group 2 indicators\n",
+    "    group2 = np.repeat(np.arange(n_group2*n_group1), n_rep)\n",
+    "\n",
+    "    # Group 2 effects\n",
+    "    u = group2_sd * np.random.normal(size=n_group1 * n_group2)\n",
+    "    effects2 = np.kron(u, np.ones(n_rep))\n",
+    "\n",
+    "    age = np.concatenate([randint(17, 40, n_group2 * n_rep, stats.norm(mu, 10)) for mu in np.linspace(20, 30, n_group1)])\n",
+    "    e = unexplained_sd * np.random.normal(size=n_group1 * n_group2 * n_rep)\n",
+    "    y = np.log(age) + effects1 + effects2 + e\n",
+    "\n",
+    "    df = pd.DataFrame({\"y\": y, \"age\": age, \"group1\": group1, \"group2\": group2})\n",
+    "    return df\n",
+    "\n",
+    "df = generate_nested()\n",
+    "df"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "id": "bce17647",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "         Mixed Linear Model Regression Results\n",
+      "=======================================================\n",
+      "Model:            MixedLM Dependent Variable: y        \n",
+      "No. Observations: 120     Method:             REML     \n",
+      "No. Groups:       4       Scale:              9.0703   \n",
+      "Min. group size:  30      Log-Likelihood:     -320.0019\n",
+      "Max. group size:  30      Converged:          Yes      \n",
+      "Mean group size:  30.0                                 \n",
+      "-------------------------------------------------------\n",
+      "               Coef. Std.Err.   z   P>|z| [0.025 0.975]\n",
+      "-------------------------------------------------------\n",
+      "Intercept      3.479    1.486 2.342 0.019  0.567  6.390\n",
+      "age            0.007    0.050 0.139 0.890 -0.092  0.106\n",
+      "group2 Var     5.472    0.795                          \n",
+      "=======================================================\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "vc = {'group2': '0 + C(group2)'}\n",
+    "print(sm.MixedLM.from_formula('y ~ age', df, groups='group1', vc_formula=vc).fit().summary())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d807d633",
+   "metadata": {},
+   "source": [
+    "\\[DISCONTINUED\\]\n",
+    "\n",
+    "[More about mixed-effects models](https://ourcodingclub.github.io/tutorials/mixed-models/)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8cd7dd0-9c93-427f-b254-8098bd95e3c3",
+   "metadata": {},
+   "source": [
+    "## Regression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "929d319e",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "What if -- instead of factors -- our independent variables are continuous variables?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a8bf953c",
+   "metadata": {},
+   "source": [
+    "### Ordinary Least Squares"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 173,
+   "id": "b350dec1",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Response</th>\n",
+       "      <th>MARCO</th>\n",
+       "      <th>TLR8</th>\n",
+       "      <th>PSMB5</th>\n",
+       "      <th>HAVCR2</th>\n",
+       "      <th>LILRA2</th>\n",
+       "      <th>MS4A1</th>\n",
+       "      <th>ITGAE</th>\n",
+       "      <th>FCGRT</th>\n",
+       "      <th>NFKB1</th>\n",
+       "      <th>...</th>\n",
+       "      <th>IL13RA1</th>\n",
+       "      <th>TMEM173</th>\n",
+       "      <th>TRAF6</th>\n",
+       "      <th>IKBKB</th>\n",
+       "      <th>IL12RB1</th>\n",
+       "      <th>B2M</th>\n",
+       "      <th>LEF1</th>\n",
+       "      <th>PRDM1</th>\n",
+       "      <th>HLA.C</th>\n",
+       "      <th>CCL20</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>0.348895</td>\n",
+       "      <td>6.628041</td>\n",
+       "      <td>5.451410</td>\n",
+       "      <td>12.765834</td>\n",
+       "      <td>14.004527</td>\n",
+       "      <td>3.672567</td>\n",
+       "      <td>13.609538</td>\n",
+       "      <td>-1.291865</td>\n",
+       "      <td>7.737586</td>\n",
+       "      <td>14.977723</td>\n",
+       "      <td>...</td>\n",
+       "      <td>3.500934</td>\n",
+       "      <td>7.429266</td>\n",
+       "      <td>11.254056</td>\n",
+       "      <td>18.621722</td>\n",
+       "      <td>12.067877</td>\n",
+       "      <td>6.713297</td>\n",
+       "      <td>5.373240</td>\n",
+       "      <td>4.179533</td>\n",
+       "      <td>11.793683</td>\n",
+       "      <td>17.192958</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0.062775</td>\n",
+       "      <td>7.434965</td>\n",
+       "      <td>15.983178</td>\n",
+       "      <td>0.293150</td>\n",
+       "      <td>5.041096</td>\n",
+       "      <td>14.223888</td>\n",
+       "      <td>15.333888</td>\n",
+       "      <td>0.732892</td>\n",
+       "      <td>9.179190</td>\n",
+       "      <td>14.577946</td>\n",
+       "      <td>...</td>\n",
+       "      <td>17.132192</td>\n",
+       "      <td>6.349028</td>\n",
+       "      <td>7.435596</td>\n",
+       "      <td>17.324485</td>\n",
+       "      <td>17.576044</td>\n",
+       "      <td>6.477195</td>\n",
+       "      <td>3.490226</td>\n",
+       "      <td>13.702533</td>\n",
+       "      <td>5.336035</td>\n",
+       "      <td>13.813157</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>-0.203249</td>\n",
+       "      <td>6.600255</td>\n",
+       "      <td>3.098568</td>\n",
+       "      <td>4.850231</td>\n",
+       "      <td>1.087381</td>\n",
+       "      <td>2.526257</td>\n",
+       "      <td>6.331897</td>\n",
+       "      <td>2.443893</td>\n",
+       "      <td>7.195147</td>\n",
+       "      <td>7.718794</td>\n",
+       "      <td>...</td>\n",
+       "      <td>12.630984</td>\n",
+       "      <td>6.335089</td>\n",
+       "      <td>13.074254</td>\n",
+       "      <td>9.196277</td>\n",
+       "      <td>11.556602</td>\n",
+       "      <td>5.124115</td>\n",
+       "      <td>7.739951</td>\n",
+       "      <td>11.442156</td>\n",
+       "      <td>11.219388</td>\n",
+       "      <td>-0.290347</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>1.609151</td>\n",
+       "      <td>8.760969</td>\n",
+       "      <td>12.544481</td>\n",
+       "      <td>16.560668</td>\n",
+       "      <td>14.646189</td>\n",
+       "      <td>8.661329</td>\n",
+       "      <td>10.293389</td>\n",
+       "      <td>-3.245664</td>\n",
+       "      <td>6.490695</td>\n",
+       "      <td>-1.381632</td>\n",
+       "      <td>...</td>\n",
+       "      <td>8.081113</td>\n",
+       "      <td>6.423302</td>\n",
+       "      <td>-3.322394</td>\n",
+       "      <td>4.470948</td>\n",
+       "      <td>18.348316</td>\n",
+       "      <td>13.384904</td>\n",
+       "      <td>15.261042</td>\n",
+       "      <td>17.193111</td>\n",
+       "      <td>1.124725</td>\n",
+       "      <td>-1.044398</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>0.508908</td>\n",
+       "      <td>7.379778</td>\n",
+       "      <td>10.360622</td>\n",
+       "      <td>11.389056</td>\n",
+       "      <td>6.076842</td>\n",
+       "      <td>7.255451</td>\n",
+       "      <td>17.260926</td>\n",
+       "      <td>14.943879</td>\n",
+       "      <td>0.158889</td>\n",
+       "      <td>7.968893</td>\n",
+       "      <td>...</td>\n",
+       "      <td>4.980194</td>\n",
+       "      <td>7.365077</td>\n",
+       "      <td>4.547918</td>\n",
+       "      <td>3.884870</td>\n",
+       "      <td>15.489645</td>\n",
+       "      <td>-0.660620</td>\n",
+       "      <td>5.110488</td>\n",
+       "      <td>18.508337</td>\n",
+       "      <td>7.551574</td>\n",
+       "      <td>8.716116</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5 rows × 31 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   Response     MARCO       TLR8      PSMB5     HAVCR2     LILRA2      MS4A1  \\\n",
+       "0  0.348895  6.628041   5.451410  12.765834  14.004527   3.672567  13.609538   \n",
+       "1  0.062775  7.434965  15.983178   0.293150   5.041096  14.223888  15.333888   \n",
+       "2 -0.203249  6.600255   3.098568   4.850231   1.087381   2.526257   6.331897   \n",
+       "3  1.609151  8.760969  12.544481  16.560668  14.646189   8.661329  10.293389   \n",
+       "4  0.508908  7.379778  10.360622  11.389056   6.076842   7.255451  17.260926   \n",
+       "\n",
+       "       ITGAE     FCGRT      NFKB1  ...    IL13RA1   TMEM173      TRAF6  \\\n",
+       "0  -1.291865  7.737586  14.977723  ...   3.500934  7.429266  11.254056   \n",
+       "1   0.732892  9.179190  14.577946  ...  17.132192  6.349028   7.435596   \n",
+       "2   2.443893  7.195147   7.718794  ...  12.630984  6.335089  13.074254   \n",
+       "3  -3.245664  6.490695  -1.381632  ...   8.081113  6.423302  -3.322394   \n",
+       "4  14.943879  0.158889   7.968893  ...   4.980194  7.365077   4.547918   \n",
+       "\n",
+       "       IKBKB    IL12RB1        B2M       LEF1      PRDM1      HLA.C      CCL20  \n",
+       "0  18.621722  12.067877   6.713297   5.373240   4.179533  11.793683  17.192958  \n",
+       "1  17.324485  17.576044   6.477195   3.490226  13.702533   5.336035  13.813157  \n",
+       "2   9.196277  11.556602   5.124115   7.739951  11.442156  11.219388  -0.290347  \n",
+       "3   4.470948  18.348316  13.384904  15.261042  17.193111   1.124725  -1.044398  \n",
+       "4   3.884870  15.489645  -0.660620   5.110488  18.508337   7.551574   8.716116  \n",
+       "\n",
+       "[5 rows x 31 columns]"
+      ]
+     },
+     "execution_count": 173,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "patients = pd.read_csv('../data/patients.csv')\n",
+    "patients.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 174,
+   "id": "67e86aec",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.scatterplot(data=patients, x='CHUK', y='Response', label='Patient');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 194,
+   "id": "8bd68586",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "                            OLS Regression Results                            \n",
+      "==============================================================================\n",
+      "Dep. Variable:               Response   R-squared:                       0.642\n",
+      "Model:                            OLS   Adj. R-squared:                  0.640\n",
+      "Method:                 Least Squares   F-statistic:                     354.9\n",
+      "Date:                Wed, 22 Sep 2021   Prob (F-statistic):           4.97e-46\n",
+      "Time:                        12:43:55   Log-Likelihood:                -103.52\n",
+      "No. Observations:                 200   AIC:                             211.0\n",
+      "Df Residuals:                     198   BIC:                             217.6\n",
+      "Df Model:                           1                                         \n",
+      "Covariance Type:            nonrobust                                         \n",
+      "==============================================================================\n",
+      "==============================================================================\n",
+      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
+      "------------------------------------------------------------------------------\n",
+      "Intercept    -11.2792      0.599    -18.838      0.000     -12.460     -10.098\n",
+      "CHUK           0.9727      0.052     18.839      0.000       0.871       1.075\n",
+      "==============================================================================\n"
+     ]
+    }
+   ],
+   "source": [
+    "model = smf.ols('Response ~ CHUK', patients).fit()\n",
+    "print(model.summary().tables[0])\n",
+    "print(model.summary().tables[1])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "634c5b3f",
+   "metadata": {},
+   "source": [
+    "<p style=\"font-size: x-small;\">Data set and choice of an explanatory variable inspired by the RS3 session about linear models on <a href=\"https://moodle01.hosting.pasteur.fr\">Institut Pasteur's Moodle</a></p>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0c7020dd",
+   "metadata": {},
+   "source": [
+    "### Regression plot"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 196,
+   "id": "50155198",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ax = sns.scatterplot(data=patients, x='CHUK', y='Response', label='Patient')\n",
+    "sm.graphics.abline_plot(model_results=model, ax=ax, label='Model prediction')\n",
+    "plt.legend()\n",
+    "\n",
+    "example_patient = 173#np.argmax(model.resid)\n",
+    "x = patients.loc[example_patient, 'CHUK']\n",
+    "expected_value = patients.loc[example_patient, 'Response']\n",
+    "predicted_value = model.fittedvalues[example_patient]\n",
+    "ax.plot([x, x], [predicted_value, expected_value], 'r-', zorder=0);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "65111a8d",
+   "metadata": {},
+   "source": [
+    "Similarly to previous OLS applications, the coefficients of the model can be found in the `coef` column.\n",
+    "\n",
+    "$\n",
+    "\\texttt{Response} = a + b\\mbox{ }\\texttt{CHUK} + \\epsilon\n",
+    "$\n",
+    "\n",
+    "with intercept $a = -11.2792$ and slope $b = 0.9727$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d69a88dd",
+   "metadata": {},
+   "source": [
+    "### Residual plot"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0bbd0e7",
+   "metadata": {},
+   "source": [
+    "To assess the adequacy of the model, we inspect the residuals $\\epsilon_i$ in various.\n",
+    "First, we plot the residuals *vs* the explanatory variable:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 197,
+   "id": "bc471543",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ax = sns.scatterplot(x='CHUK', y='residuals', label='Patient',\n",
+    "    data={'CHUK': patients['CHUK'], 'residuals': model.resid})\n",
+    "ax.axhline(0, linestyle=':', lw=1, label='Model prediction')\n",
+    "plt.legend()\n",
+    "\n",
+    "example_patient_residual = model.resid[example_patient]\n",
+    "ax.plot([x, x], [0, example_patient_residual], 'r-', zorder=0);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "777daba8",
+   "metadata": {},
+   "source": [
+    "The most distant points may be outliers.\n",
+    "\n",
+    "The dispersion of the residuals should not greatly vary with the explanatory variable(s) (homoscedasticity).\n",
+    "\n",
+    "In addition, structured residuals, *e.g.* systematic positive-only or negative-only errors on subdomains of the explanatory variable, are indicative of the model not being flexible enough.\n",
+    "\n",
+    "Key criterion: the residuals should be normally distributed."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3ad9d670",
+   "metadata": {},
+   "source": [
+    "### QQ plot\n",
+    "\n",
+    "Complete OLS output:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 178,
+   "id": "5492f4e8-2ac8-4ba7-9a6c-241f33994998",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "                            OLS Regression Results                            \n",
+      "==============================================================================\n",
+      "Dep. Variable:               Response   R-squared:                       0.642\n",
+      "Model:                            OLS   Adj. R-squared:                  0.640\n",
+      "Method:                 Least Squares   F-statistic:                     354.9\n",
+      "Date:                Wed, 22 Sep 2021   Prob (F-statistic):           4.97e-46\n",
+      "Time:                        12:33:34   Log-Likelihood:                -103.52\n",
+      "No. Observations:                 200   AIC:                             211.0\n",
+      "Df Residuals:                     198   BIC:                             217.6\n",
+      "Df Model:                           1                                         \n",
+      "Covariance Type:            nonrobust                                         \n",
+      "==============================================================================\n",
+      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
+      "------------------------------------------------------------------------------\n",
+      "Intercept    -11.2792      0.599    -18.838      0.000     -12.460     -10.098\n",
+      "CHUK           0.9727      0.052     18.839      0.000       0.871       1.075\n",
+      "==============================================================================\n",
+      "Omnibus:                       11.549   Durbin-Watson:                   2.042\n",
+      "Prob(Omnibus):                  0.003   Jarque-Bera (JB):               11.949\n",
+      "Skew:                           0.586   Prob(JB):                      0.00254\n",
+      "Kurtosis:                       3.245   Cond. No.                         242.\n",
+      "==============================================================================\n",
+      "\n",
+      "Notes:\n",
+      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(model.summary())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "973f809c",
+   "metadata": {},
+   "source": [
+    "The hypothesis of normality of the residuals is rejected. This can be confirmed with a qqplot:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 213,
+   "id": "0d7780a9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sm.graphics.qqplot(model.resid, fit=True, line='45', fmt='b', marker='+');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "59367b93",
+   "metadata": {},
+   "source": [
+    "Note: `statsmodels`'s `qqplot` compares with R's qqplot as long as `fit=True` to standardize the residuals.\n",
+    "\n",
+    "Deviations at the distribution tails are common and not as informative (in terms of normality) as smaller but consistent deviations from the midline at or near the mode.\n",
+    "Here, the deviation around the theoretical median ($x=0$) is indicative of a departure from normality.\n",
+    "\n",
+    "However, the points at the tails are of interest, because they may be outliers."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7e8cf02d",
+   "metadata": {},
+   "source": [
+    "### Influence plots"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "345ad8a8",
+   "metadata": {},
+   "source": [
+    "To identify outliers and influential points, `statsmodels` features more [diagnostic measures and plots](https://www.statsmodels.org/stable/generated/statsmodels.stats.outliers_influence.OLSInfluence.html):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 180,
+   "id": "e79b930e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from statsmodels.stats.outliers_influence import OLSInfluence\n",
+    "diagnostics = OLSInfluence(model)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "id": "3cab691b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>dfb_Intercept</th>\n",
+       "      <th>dfb_CHUK</th>\n",
+       "      <th>cooks_d</th>\n",
+       "      <th>standard_resid</th>\n",
+       "      <th>hat_diag</th>\n",
+       "      <th>dffits_internal</th>\n",
+       "      <th>student_resid</th>\n",
+       "      <th>dffits</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>-0.001274</td>\n",
+       "      <td>0.001379</td>\n",
+       "      <td>0.000003</td>\n",
+       "      <td>0.030294</td>\n",
+       "      <td>0.007067</td>\n",
+       "      <td>0.002556</td>\n",
+       "      <td>0.030218</td>\n",
+       "      <td>0.002549</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0.001223</td>\n",
+       "      <td>-0.001576</td>\n",
+       "      <td>0.000028</td>\n",
+       "      <td>-0.102972</td>\n",
+       "      <td>0.005234</td>\n",
+       "      <td>-0.007469</td>\n",
+       "      <td>-0.102714</td>\n",
+       "      <td>-0.007451</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>0.021748</td>\n",
+       "      <td>-0.025056</td>\n",
+       "      <td>0.002629</td>\n",
+       "      <td>-0.959589</td>\n",
+       "      <td>0.005678</td>\n",
+       "      <td>-0.072515</td>\n",
+       "      <td>-0.959396</td>\n",
+       "      <td>-0.072500</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>-0.019622</td>\n",
+       "      <td>0.033215</td>\n",
+       "      <td>0.037323</td>\n",
+       "      <td>3.827412</td>\n",
+       "      <td>0.005070</td>\n",
+       "      <td>0.273213</td>\n",
+       "      <td>3.967316</td>\n",
+       "      <td>0.283200</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>-0.014066</td>\n",
+       "      <td>0.017275</td>\n",
+       "      <td>0.002340</td>\n",
+       "      <td>0.933618</td>\n",
+       "      <td>0.005341</td>\n",
+       "      <td>0.068412</td>\n",
+       "      <td>0.933314</td>\n",
+       "      <td>0.068390</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>195</th>\n",
+       "      <td>0.049498</td>\n",
+       "      <td>-0.052442</td>\n",
+       "      <td>0.003169</td>\n",
+       "      <td>-0.842874</td>\n",
+       "      <td>0.008843</td>\n",
+       "      <td>-0.079612</td>\n",
+       "      <td>-0.842255</td>\n",
+       "      <td>-0.079554</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>196</th>\n",
+       "      <td>-0.002152</td>\n",
+       "      <td>0.000169</td>\n",
+       "      <td>0.000850</td>\n",
+       "      <td>-0.581587</td>\n",
+       "      <td>0.005000</td>\n",
+       "      <td>-0.041228</td>\n",
+       "      <td>-0.580613</td>\n",
+       "      <td>-0.041159</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>197</th>\n",
+       "      <td>0.002771</td>\n",
+       "      <td>-0.001967</td>\n",
+       "      <td>0.000143</td>\n",
+       "      <td>0.236635</td>\n",
+       "      <td>0.005069</td>\n",
+       "      <td>0.016891</td>\n",
+       "      <td>0.236070</td>\n",
+       "      <td>0.016850</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>198</th>\n",
+       "      <td>-0.043672</td>\n",
+       "      <td>0.042665</td>\n",
+       "      <td>0.001156</td>\n",
+       "      <td>-0.306910</td>\n",
+       "      <td>0.023949</td>\n",
+       "      <td>-0.048075</td>\n",
+       "      <td>-0.306207</td>\n",
+       "      <td>-0.047965</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>199</th>\n",
+       "      <td>-0.090400</td>\n",
+       "      <td>0.095454</td>\n",
+       "      <td>0.009763</td>\n",
+       "      <td>1.439930</td>\n",
+       "      <td>0.009330</td>\n",
+       "      <td>0.139737</td>\n",
+       "      <td>1.443869</td>\n",
+       "      <td>0.140119</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>200 rows × 8 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "     dfb_Intercept  dfb_CHUK   cooks_d  standard_resid  hat_diag  \\\n",
+       "0        -0.001274  0.001379  0.000003        0.030294  0.007067   \n",
+       "1         0.001223 -0.001576  0.000028       -0.102972  0.005234   \n",
+       "2         0.021748 -0.025056  0.002629       -0.959589  0.005678   \n",
+       "3        -0.019622  0.033215  0.037323        3.827412  0.005070   \n",
+       "4        -0.014066  0.017275  0.002340        0.933618  0.005341   \n",
+       "..             ...       ...       ...             ...       ...   \n",
+       "195       0.049498 -0.052442  0.003169       -0.842874  0.008843   \n",
+       "196      -0.002152  0.000169  0.000850       -0.581587  0.005000   \n",
+       "197       0.002771 -0.001967  0.000143        0.236635  0.005069   \n",
+       "198      -0.043672  0.042665  0.001156       -0.306910  0.023949   \n",
+       "199      -0.090400  0.095454  0.009763        1.439930  0.009330   \n",
+       "\n",
+       "     dffits_internal  student_resid    dffits  \n",
+       "0           0.002556       0.030218  0.002549  \n",
+       "1          -0.007469      -0.102714 -0.007451  \n",
+       "2          -0.072515      -0.959396 -0.072500  \n",
+       "3           0.273213       3.967316  0.283200  \n",
+       "4           0.068412       0.933314  0.068390  \n",
+       "..               ...            ...       ...  \n",
+       "195        -0.079612      -0.842255 -0.079554  \n",
+       "196        -0.041228      -0.580613 -0.041159  \n",
+       "197         0.016891       0.236070  0.016850  \n",
+       "198        -0.048075      -0.306207 -0.047965  \n",
+       "199         0.139737       1.443869  0.140119  \n",
+       "\n",
+       "[200 rows x 8 columns]"
+      ]
+     },
+     "execution_count": 66,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "diagnostics.summary_frame()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 182,
+   "id": "7f143230",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 957.6x295.2 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "_, axes = plt.subplots(1, 2, figsize=(13.3,4.1))\n",
+    "\n",
+    "diagnostics.plot_influence(ax=axes[0])\n",
+    "axes[0].axhline(0, linestyle=':', linewidth=1)\n",
+    "\n",
+    "diagnostics.plot_index(threshold=0.02, ax=axes[1])\n",
+    "axes[1].axhline(0, linestyle=':', linewidth=1);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "91d44448",
+   "metadata": {},
+   "source": [
+    "### Leverage and Cook's distance"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "37a8f174",
+   "metadata": {},
+   "source": [
+    "Let us consider a smaller data sample:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 237,
+   "id": "bc655fc0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "np.random.seed(237598)\n",
+    "x = stats.lognorm.rvs(1, size=30)\n",
+    "y = np.log(4 + x + stats.norm.rvs(size=x.size))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 186,
+   "id": "b5b46df6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ax = sns.scatterplot(x=x, y=y)\n",
+    "ax.set_xlabel('x')\n",
+    "ax.set_ylabel('y');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 187,
+   "id": "a0b5ffc9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#sns.regplot(x=x, y=y);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 248,
+   "id": "7bb8d264",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X = np.stack((np.ones_like(x), x), axis=1)\n",
+    "model = sm.OLS(y, X).fit()\n",
+    "diagnostics = OLSInfluence(model)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 189,
+   "id": "1ddf4e63",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 957.6x295.2 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "_, axes = plt.subplots(1, 2, figsize=(13.3,4.1))\n",
+    "\n",
+    "diagnostics.plot_influence(ax=axes[0])\n",
+    "axes[0].axhline(0, linestyle=':', linewidth=1)\n",
+    "diagnostics.plot_index(threshold=0.02, ax=axes[1]);\n",
+    "axes[1].axhline(0, linestyle=':', linewidth=1);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 191,
+   "id": "7a441682",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "high_leverage_point = np.argmax(diagnostics.hat_matrix_diag)\n",
+    "cooks_distant_point = np.argmax(diagnostics.cooks_distance[0])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 192,
+   "id": "0d8019bc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 957.6x295.2 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "_, axes = plt.subplots(1, 2, figsize=(13.3,4.1))\n",
+    "for ax, influential_point in zip(axes, set([high_leverage_point, cooks_distant_point])):\n",
+    "    sns.scatterplot(x=x, y=y, ax=ax)\n",
+    "    sns.regplot(x=x, y=y, ax=ax, scatter=False, label=f'{influential_point:d} included')\n",
+    "    selection = np.ones(len(x), dtype=bool)\n",
+    "    selection[influential_point] = False\n",
+    "    sns.regplot(x=x[selection], y=y[selection], scatter=False, ax=ax, label=f'{influential_point:d} excluded')\n",
+    "    xi, yi = x[influential_point], y[influential_point]\n",
+    "    ax.plot(xi, yi, 'r.', markersize=14)\n",
+    "    ax.text(xi, yi, f'{influential_point:d}')\n",
+    "    ax.legend()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "29b9eb6d",
+   "metadata": {},
+   "source": [
+    "The leverage for a point tells how much the model would change if we move the response value of that point, while Cook's distance reflects how much the model changes if we omit the point.\n",
+    "\n",
+    "Therefore, Cook's distance is an «effect size» for outliers. Influential points that fall above $1$ are undesirable and should preferably be removed or trimmed (see also [robust linear models](https://www.statsmodels.org/stable/generated/statsmodels.robust.robust_linear_model.RLM.html)). A Cook's distance between $0.5$ and $1$ signals a point (=an observation) to be examined.\n",
+    "\n",
+    "Note: compared to other implementations of influence plots, `statsmodels`' influence plot lacks the Cook's distance isocurves."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "57e0be6f",
+   "metadata": {},
+   "source": [
+    "## Non-linear regression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "73598e37",
+   "metadata": {},
+   "source": [
+    "### Data transformation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b229d5e0",
+   "metadata": {},
+   "source": [
+    "In the previous simulated data example, the relationship between the explanatory and response variables is actually not linear. The true model is:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 245,
+   "id": "b5b96410",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.regplot(x=np.log(x), y=y);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "433fbffe",
+   "metadata": {},
+   "source": [
+    "Such simple non-linear relationships are common and a useful trick consists in transforming the explanatory variables using monotonous functions.\n",
+    "\n",
+    "Examples (heavily inspired by the RS3 session about linear models on [Institut Pasteur's Moodle](https://moodle01.hosting.pasteur.fr)):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 265,
+   "id": "709f2da0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1080x576 with 6 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "_, axes = plt.subplots(2, 3, figsize=(15, 8))\n",
+    "\n",
+    "for ax, tr in zip(axes.T, (lambda x: 1./x, np.log, lambda x: x*x)):\n",
+    "    x = np.linspace(1, 50, 30)\n",
+    "    y = tr(x)\n",
+    "    scale = y.max() - y.min()\n",
+    "    y += .05 * scale * stats.norm.rvs(size=x.size)\n",
+    "    x_grid = np.linspace(1, 50, 100)\n",
+    "    ax[0].plot(x, y, 'b+')\n",
+    "    ax[0].plot(x_grid, tr(x_grid), 'r-')\n",
+    "    ax[1].plot(tr(x), y, 'b+')\n",
+    "    ax[1].plot(tr(x_grid), tr(x_grid), 'r-')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a8c3ba5c",
+   "metadata": {},
+   "source": [
+    "Generic standardization functions exist, such as the [Box-Cox transform](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.boxcox.html) in `scipy`, but they often require the explanatory variable to take positive values and the interpretation of the relationship becomes less straight-forward."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5150655f",
+   "metadata": {},
+   "source": [
+    "### Polynomial regression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9cd56cd7",
+   "metadata": {},
+   "source": [
+    "Let us consider some almost-linearly related data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 404,
+   "id": "02debff3",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "np.random.seed(237598)\n",
+    "x = np.sort(stats.uniform.rvs(0, 2, size=100))\n",
+    "y_th = 1 + 0.5 * x + 1.5 * x**2 + 0.3 * x**3\n",
+    "y = y_th + 2 * stats.norm().rvs(size=x.size)\n",
+    "\n",
+    "df = pd.DataFrame({'x': x, 'y': y})\n",
+    "\n",
+    "ax = sns.scatterplot(x='x', y='y', data=df, label='observations')\n",
+    "ax.plot(x, y_th, 'r-', label='true relationship')\n",
+    "ax.set_xlabel('$x$ (explanatory)')\n",
+    "ax.set_ylabel('$y$ (response)')\n",
+    "ax.legend();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "32cc46cf",
+   "metadata": {},
+   "source": [
+    "A linear model performs very well, but the structured errors leave no doubt the model is not flexible enough:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 405,
+   "id": "32746edb",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 957.6x295.2 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "df = pd.DataFrame({'x': x, 'y': y})\n",
+    "linear_model = sm.OLS.from_formula('y ~ x', df).fit()\n",
+    "\n",
+    "_, axes = plt.subplots(1, 2, figsize=(13.3,4.1))\n",
+    "sns.regplot(x='x', y='y', data=df, ax=axes[0], line_kws=dict(color='r', linewidth=1.5))\n",
+    "sns.scatterplot(x='x', y='residuals', data=df.assign(residuals=linear_model.resid), ax=axes[1])\n",
+    "axes[1].axhline(0, linestyle=':', linewidth=1);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2a8c0e8",
+   "metadata": {},
+   "source": [
+    "A flexible approach consists of introducing powers of the explanatory variable, in the shape of multiple data columns.\n",
+    "\n",
+    "$$\n",
+    "Y = \\left[ X^0, X^1, X^2, ... \\right]\\beta + \\epsilon\n",
+    "$$\n",
+    "or similarly $y_i = \\beta_0 + \\beta_1 x_i +\\beta_2 x_i^2 +... +\\epsilon_i$ for all observation $i$.\n",
+    "\n",
+    "For example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 406,
+   "id": "9a3edfab",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
        "    .dataframe tbody tr th {\n",
        "        vertical-align: top;\n",
        "    }\n",
@@ -3115,140 +4589,344 @@
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
-       "      <th>df</th>\n",
-       "      <th>sum_sq</th>\n",
-       "      <th>mean_sq</th>\n",
-       "      <th>F</th>\n",
-       "      <th>PR(&gt;F)</th>\n",
+       "      <th>y</th>\n",
+       "      <th>x</th>\n",
+       "      <th>x2</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
-       "      <th>Time</th>\n",
-       "      <td>1.0</td>\n",
-       "      <td>828.816667</td>\n",
-       "      <td>828.816667</td>\n",
-       "      <td>18.387125</td>\n",
-       "      <td>0.000075</td>\n",
+       "      <th>0</th>\n",
+       "      <td>1.010651</td>\n",
+       "      <td>0.030349</td>\n",
+       "      <td>0.000921</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>Metric</th>\n",
-       "      <td>2.0</td>\n",
-       "      <td>1365.233333</td>\n",
-       "      <td>682.616667</td>\n",
-       "      <td>15.143708</td>\n",
-       "      <td>0.000006</td>\n",
+       "      <th>1</th>\n",
+       "      <td>3.869300</td>\n",
+       "      <td>0.042248</td>\n",
+       "      <td>0.001785</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>Time:Metric</th>\n",
-       "      <td>2.0</td>\n",
-       "      <td>224.433333</td>\n",
-       "      <td>112.216667</td>\n",
-       "      <td>2.489503</td>\n",
-       "      <td>0.092427</td>\n",
+       "      <th>2</th>\n",
+       "      <td>2.815199</td>\n",
+       "      <td>0.044500</td>\n",
+       "      <td>0.001980</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4.360370</td>\n",
+       "      <td>0.069110</td>\n",
+       "      <td>0.004776</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>Residual</th>\n",
-       "      <td>54.0</td>\n",
-       "      <td>2434.100000</td>\n",
-       "      <td>45.075926</td>\n",
-       "      <td>NaN</td>\n",
-       "      <td>NaN</td>\n",
+       "      <th>4</th>\n",
+       "      <td>2.486747</td>\n",
+       "      <td>0.075106</td>\n",
+       "      <td>0.005641</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "text/plain": [
-       "               df       sum_sq     mean_sq          F    PR(>F)\n",
-       "Time          1.0   828.816667  828.816667  18.387125  0.000075\n",
-       "Metric        2.0  1365.233333  682.616667  15.143708  0.000006\n",
-       "Time:Metric   2.0   224.433333  112.216667   2.489503  0.092427\n",
-       "Residual     54.0  2434.100000   45.075926        NaN       NaN"
+       "          y         x        x2\n",
+       "0  1.010651  0.030349  0.000921\n",
+       "1  3.869300  0.042248  0.001785\n",
+       "2  2.815199  0.044500  0.001980\n",
+       "3  4.360370  0.069110  0.004776\n",
+       "4  2.486747  0.075106  0.005641"
       ]
      },
-     "execution_count": 75,
+     "execution_count": 406,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "sm.stats.anova_lm(fe_nogrouping_model)"
+    "augmented_df = df.assign(x2 = x**2)[['y', 'x', 'x2']]\n",
+    "augmented_df.head()"
    ]
   },
   {
-   "cell_type": "markdown",
-   "id": "7ddee4e7-319b-460a-b577-9f299e8bd555",
+   "cell_type": "code",
+   "execution_count": 407,
+   "id": "24c100a8",
    "metadata": {},
+   "outputs": [],
    "source": [
-    "Rule of thumb: a random effect factor should exhibit at least 5 levels."
+    "poly2_model = ols('y ~ 1 + x + x2', augmented_df).fit()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a5f2e5a4-1119-4379-8b02-abde4828eb02",
+   "id": "761ebbca",
    "metadata": {},
    "source": [
-    "### Nested designs"
+    "As the predictors we plug into the model are synthetic, we do not need to model any interaction between them.\n",
+    "\n",
+    "Similarly, we can manually define the `exog` matrix:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 408,
+   "id": "d6ac4ac8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X_poly2 = np.stack((np.ones_like(x), x, x*x), axis=1)\n",
+    "poly2_model_bis = sm.OLS(y, X_poly2).fit()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 409,
+   "id": "078047e2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x_grid = np.linspace(x.min(), x.max(), 100)\n",
+    "X_grid = np.stack((np.ones_like(x_grid), x_grid, x_grid**2), axis=1)\n",
+    "# y_grid = poly2_model.predict(X_grid) # bug?\n",
+    "beta = poly2_model.params\n",
+    "y_grid = np.dot(X_grid, beta)\n",
+    "ax = sns.scatterplot(x='x', y='y', data=df, label='observations')\n",
+    "ax.plot(x, y_th, 'r-', label='true')\n",
+    "ax.plot(x_grid, y_grid, 'g-', label='predicted')\n",
+    "ax.legend();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f999ae16",
+   "id": "97671b61",
    "metadata": {},
    "source": [
-    "\"Sometimes, constraints prevent us from crossing every level of one factor with every level of the other factor. In these cases we are forced into what is known as a nested layout. We say we have a nested layout when fewer than all levels of one factor occur within each level of the other factor.\"\n",
-    "[Engineering Statistics Handbook](https://www.itl.nist.gov/div898/handbook/ppc/section2/ppc233.htm)\n",
-    "\n",
-    "Examples: Students in classrooms in schools; mice in breeding cages\n",
-    "\n",
-    "Terminology: the `student` factor is nested in `classroom`, that in turn is nested in `school`. `classroom` is a grouping factor for `student`, and `school` is a grouping factor for `classroom`.\n",
-    "\n",
-    "Again, it is possible to treat these factors as *fixed effect* factors in the model, introducing the grouping factors in interaction terms only. For example:\n",
-    "\n",
-    "`test_score ~ student_age + student_age:C(classroom) + C(classroom):C(school)`\n",
+    "Polynomial models are flexible enough to closely approximate any function in the neighborhood of a point (think of Taylor series expansions) but, of course, may not be adequate enough as we are modelling a function across an entire domain.\n",
     "\n",
-    "However, it becomes more common to treat the grouping factors as *random effect* factors instead.\n",
-    "Models with both fixed and random effects are called [linear *mixed effects* models](https://www.statsmodels.org/stable/mixed_linear.html)."
+    "It is also possible to introduce any other non-linear transformation of the explanatory variable as additional terms in the modelling equation or columns in the design matrix. See for example the documentation for the broken [predict function](https://www.statsmodels.org/stable/examples/notebooks/generated/predict.html)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5e8e27d4",
+   "metadata": {},
+   "source": [
+    "### Model selection"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "41ccd181",
+   "metadata": {},
+   "source": [
+    "Let us introduce higher order terms:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "id": "8001e35b",
+   "execution_count": 410,
+   "id": "fba76906",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "augmented_again_df = augmented_df.assign(x3=x**3, x4=x**4, x5=x**5, x6=x**6) # yippee!\n",
+    "poly6_model = ols('y ~ 1 + x + x2 + x3 + x4 + x5 + x6', augmented_again_df).fit()"
+   ]
   },
   {
-   "cell_type": "markdown",
-   "id": "f8cd7dd0-9c93-427f-b254-8098bd95e3c3",
+   "cell_type": "code",
+   "execution_count": 411,
+   "id": "424e6080",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "beta6 = poly6_model.params\n",
+    "X6_grid = np.stack([x_grid**p for p in range(7)], axis=1)\n",
+    "y6_grid = np.dot(X6_grid, beta6)\n",
+    "ax = sns.scatterplot(x='x', y='y', data=df, label='observations')\n",
+    "ax.plot(x, y_th, 'r-', label='true')\n",
+    "ax.plot(x_grid, y6_grid, 'g-', label='predicted')\n",
+    "ax.legend();"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 414,
+   "id": "a5e7b1bf",
    "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4.1070453397608935"
+      ]
+     },
+     "execution_count": 414,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "## Regression"
+    "crazy_augmented_df = augmented_df.assign(**{ f'x{k}': x**k for k in range(3, 21) }) # yihaa!\n",
+    "crazy_poly_model = ols('y ~ 1 + x + ' + ' + '.join([ f'x{k}' for k in range(2, 21) ]), crazy_augmented_df).fit()\n",
+    "crazy_poly_model.scale"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3ad43587-7f54-4288-a775-ffc16a15c171",
-   "metadata": {
-    "tags": []
-   },
+   "id": "63c07909",
+   "metadata": {},
    "source": [
-    "What if -- instead of factors -- our independent variables are continuous variables?\n",
-    "\n",
-    "### Residuals and model selection\n",
-    "\n",
-    "### Diagnostic plots"
+    "If we compare the three models (linear, order-2 polynomial and order-6 polynomial), we can observe that more complex models tend to perform better on the training data."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "id": "5492f4e8-2ac8-4ba7-9a6c-241f33994998",
+   "execution_count": 413,
+   "id": "74c19b10",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>R2</th>\n",
+       "      <th>R2_adjusted</th>\n",
+       "      <th>F</th>\n",
+       "      <th>pvalue</th>\n",
+       "      <th>scale</th>\n",
+       "      <th>AIC</th>\n",
+       "      <th>BIC</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0.574957</td>\n",
+       "      <td>0.570619</td>\n",
+       "      <td>132.564667</td>\n",
+       "      <td>6.538526e-20</td>\n",
+       "      <td>4.691088</td>\n",
+       "      <td>440.333896</td>\n",
+       "      <td>445.544236</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>0.630454</td>\n",
+       "      <td>0.622834</td>\n",
+       "      <td>82.742084</td>\n",
+       "      <td>1.076287e-21</td>\n",
+       "      <td>4.120626</td>\n",
+       "      <td>428.342307</td>\n",
+       "      <td>436.157817</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>0.663161</td>\n",
+       "      <td>0.641430</td>\n",
+       "      <td>30.516072</td>\n",
+       "      <td>5.483515e-20</td>\n",
+       "      <td>3.917469</td>\n",
+       "      <td>427.075215</td>\n",
+       "      <td>445.311406</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "         R2  R2_adjusted           F        pvalue     scale         AIC  \\\n",
+       "1  0.574957     0.570619  132.564667  6.538526e-20  4.691088  440.333896   \n",
+       "2  0.630454     0.622834   82.742084  1.076287e-21  4.120626  428.342307   \n",
+       "6  0.663161     0.641430   30.516072  5.483515e-20  3.917469  427.075215   \n",
+       "\n",
+       "          BIC  \n",
+       "1  445.544236  \n",
+       "2  436.157817  \n",
+       "6  445.311406  "
+      ]
+     },
+     "execution_count": 413,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "scores = pd.DataFrame(np.array(\n",
+    "    [[model.rsquared, model.rsquared_adj, model.fvalue, model.f_pvalue, model.scale, model.aic, model.bic] \\\n",
+    "        for model in (linear_model, poly2_model, poly6_model)]),\n",
+    "    index=['1', '2', '6'],\n",
+    "    columns=['R2', 'R2_adjusted', 'F', 'pvalue', 'scale', 'AIC', 'BIC'])\n",
+    "scores"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "96e112ca",
+   "metadata": {},
+   "source": [
+    "Choosing among models should not rely on model fitness only. Model complexity is also to be controlled, so that simpler models are favored over complex models."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "55f85206",
+   "metadata": {},
+   "source": [
+    "### Information criteria"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b31a31c9",
+   "metadata": {},
+   "source": [
+    "Akaike (AIC) and Bayes (BIC) information criteria combine model fitness with the notion of model complexity."
+   ]
   },
   {
    "cell_type": "markdown",
-- 
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