diff --git a/notebooks/statsmodels_cours.ipynb b/notebooks/statsmodels_cours.ipynb
index 7c043b6b2905bbe5272ad11ca5eaff22579b67de..8bf5f2a7aefdf169f491956149501d5ee899abc5 100644
--- a/notebooks/statsmodels_cours.ipynb
+++ b/notebooks/statsmodels_cours.ipynb
@@ -8,7 +8,6 @@
"jupyter": {
"source_hidden": true
},
- "scrolled": false,
"tags": []
},
"outputs": [
@@ -17,12 +16,12 @@
"output_type": "stream",
"text": [
"Requirement already satisfied: statsmodels in /home/flaurent/.local/lib/python3.8/site-packages (0.12.2)\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: 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: 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 +425,8 @@
"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: Wed, 22 Sep 2021 Prob (F-statistic): 0.114\n",
- "Time: 08:49:55 Log-Likelihood: -96.604\n",
+ "Date: Thu, 23 Sep 2021 Prob (F-statistic): 0.114\n",
+ "Time: 14:56:51 Log-Likelihood: -96.604\n",
"No. Observations: 30 AIC: 199.2\n",
"Df Residuals: 27 BIC: 203.4\n",
"Df Model: 2 \n",
@@ -986,12 +985,12 @@
"output_type": "stream",
"text": [
"Requirement already satisfied: formulaic in /home/flaurent/.local/lib/python3.8/site-packages (0.2.4)\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: numpy in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.21.1)\n",
+ "Requirement already satisfied: astor in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (0.8.1)\n",
"Requirement already satisfied: wrapt in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.12.1)\n",
"Requirement already satisfied: scipy in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.7.1)\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: interface-meta>=1.2 in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.2.4)\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 +1322,10 @@
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 2.358</td>\n",
"</tr>\n",
"<tr>\n",
- " <th>Date:</th> <td>Wed, 22 Sep 2021</td> <th> Prob (F-statistic):</th> <td> 0.114</td> \n",
+ " <th>Date:</th> <td>Thu, 23 Sep 2021</td> <th> Prob (F-statistic):</th> <td> 0.114</td> \n",
"</tr>\n",
"<tr>\n",
- " <th>Time:</th> <td>08:49:58</td> <th> Log-Likelihood: </th> <td> -96.604</td>\n",
+ " <th>Time:</th> <td>14:56:54</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 +1380,8 @@
"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: Wed, 22 Sep 2021 Prob (F-statistic): 0.114\n",
- "Time: 08:49:58 Log-Likelihood: -96.604\n",
+ "Date: Thu, 23 Sep 2021 Prob (F-statistic): 0.114\n",
+ "Time: 14:56:54 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 +1478,8 @@
"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: Wed, 22 Sep 2021 Prob (F-statistic): 0.114\n",
- "Time: 08:49:59 Log-Likelihood: -96.604\n",
+ "Date: Thu, 23 Sep 2021 Prob (F-statistic): 0.114\n",
+ "Time: 14:56:54 Log-Likelihood: -96.604\n",
"No. Observations: 30 AIC: 199.2\n",
"Df Residuals: 27 BIC: 203.4\n",
"Df Model: 2 \n",
@@ -2178,7 +2177,7 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/plain": [
"<Figure size 957.6x295.2 with 2 Axes>"
]
@@ -2489,58 +2488,34 @@
},
{
"cell_type": "markdown",
- "id": "1d8f929c-fdd7-419d-8495-22080ea87926",
- "metadata": {
- "tags": []
- },
- "source": [
- "## Hierarchical models"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "b1936ef3",
+ "id": "f8cd7dd0-9c93-427f-b254-8098bd95e3c3",
"metadata": {},
"source": [
- "The notion of hierarchy in an analysis of variance arises when not all factors or dependent variables have equal importance in the analysis.\n",
- "\n",
- "* explicit hierarchies (student < class < school);\n",
- "* repeated measurements on the same sample;\n",
- "* sources of variation we cannot avoid but are not interested in."
+ "## Regression"
]
},
{
"cell_type": "markdown",
- "id": "42e71e2c-bf98-45e5-aa97-30475b0b10a4",
- "metadata": {},
+ "id": "929d319e",
+ "metadata": {
+ "tags": []
+ },
"source": [
- "### Repeated measures ANOVA and sphericity"
+ "What if -- instead of factors -- our independent variables are continuous variables?"
]
},
{
"cell_type": "markdown",
- "id": "1c1575be-558d-4ec2-bd32-d69762b25ceb",
+ "id": "a8bf953c",
"metadata": {},
"source": [
- "Example (one-way): each animal observed multiple times, *e.g.* at different ages; and we are not interested in the putative differences between animals.\n",
- "\n",
- "$$\n",
- "SS_{\\textrm{total}} = SS_{\\textrm{treatment}} + (SS_{\\textrm{subject}} + SS_{\\textrm{error}})\n",
- "$$\n",
- "\n",
- "$$\n",
- "F^* = \\frac{\\frac{SS_{\\textrm{treatment}}}{k - 1}}{\\frac{SS_{\\textrm{error}}}{(k-1)(n-1)}}\n",
- "$$\n",
- "\n",
- "Designs are balanced.\n",
- "\n",
- "Let us borrow an example from `pingouin` documentation:"
+ "### Ordinary Least Squares"
]
},
{
"cell_type": "code",
"execution_count": 48,
- "id": "5bbe2b04",
+ "id": "b350dec1",
"metadata": {},
"outputs": [
{
@@ -2564,83 +2539,178 @@
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
- " <th>Subject</th>\n",
- " <th>Time</th>\n",
- " <th>Metric</th>\n",
- " <th>Performance</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>1</td>\n",
- " <td>Pre</td>\n",
- " <td>Product</td>\n",
- " <td>13</td>\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>2</td>\n",
- " <td>Pre</td>\n",
- " <td>Product</td>\n",
- " <td>12</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>10</th>\n",
- " <td>1</td>\n",
- " <td>Pre</td>\n",
- " <td>Client</td>\n",
- " <td>12</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>11</th>\n",
- " <td>2</td>\n",
- " <td>Pre</td>\n",
- " <td>Client</td>\n",
- " <td>19</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>20</th>\n",
- " <td>1</td>\n",
- " <td>Pre</td>\n",
- " <td>Action</td>\n",
- " <td>17</td>\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>21</th>\n",
- " <td>2</td>\n",
- " <td>Pre</td>\n",
- " <td>Action</td>\n",
- " <td>18</td>\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>30</th>\n",
- " <td>1</td>\n",
- " <td>Post</td>\n",
- " <td>Product</td>\n",
- " <td>18</td>\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>31</th>\n",
- " <td>2</td>\n",
- " <td>Post</td>\n",
- " <td>Product</td>\n",
- " <td>6</td>\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": [
- " Subject Time Metric Performance\n",
- "0 1 Pre Product 13\n",
- "1 2 Pre Product 12\n",
- "10 1 Pre Client 12\n",
- "11 2 Pre Client 19\n",
- "20 1 Pre Action 17\n",
- "21 2 Pre Action 18\n",
- "30 1 Post Product 18\n",
- "31 2 Post Product 6"
+ " 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": 48,
@@ -2649,1048 +2719,37 @@
}
],
"source": [
- "import pingouin as pg\n",
- "\n",
- "data = pg.read_dataset('rm_anova2')\n",
- "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):"
+ "patients = pd.read_csv('../data/patients.csv')\n",
+ "patients.head()"
]
},
{
"cell_type": "code",
"execution_count": 49,
- "id": "4a695145",
+ "id": "67e86aec",
"metadata": {},
"outputs": [
{
"data": {
+ "image/png": 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\n",
"text/plain": [
- "SpherResults(spher=True, W=0.6247989838343564, chi2=3.762602454747652, dof=2, pval=0.15239168046050933)"
+ "<Figure size 432x288 with 1 Axes>"
]
},
- "execution_count": 49,
- "metadata": {},
- "output_type": "execute_result"
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
}
],
"source": [
- "pg.sphericity(data, dv='Performance', subject='Subject', within=['Time', 'Metric'])"
+ "sns.scatterplot(data=patients, x='CHUK', y='Response', label='Patient');"
]
},
{
"cell_type": "code",
"execution_count": 50,
- "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 > 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": 50,
- "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": "5c4e709f",
- "metadata": {},
- "source": [
- "In contrast, [rm_anova](https://pingouin-stats.org/generated/pingouin.rm_anova.html) from `pingouin` does implement Greenhouse-Geiser correction."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 51,
- "id": "e523e3da",
- "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>Source</th>\n",
- " <th>SS</th>\n",
- " <th>ddof1</th>\n",
- " <th>ddof2</th>\n",
- " <th>MS</th>\n",
- " <th>F</th>\n",
- " <th>p-unc</th>\n",
- " <th>p-GG-corr</th>\n",
- " <th>np2</th>\n",
- " <th>eps</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>0</th>\n",
- " <td>Time</td>\n",
- " <td>828.816667</td>\n",
- " <td>1</td>\n",
- " <td>9</td>\n",
- " <td>828.816667</td>\n",
- " <td>33.85228</td>\n",
- " <td>0.000254</td>\n",
- " <td>0.000254</td>\n",
- " <td>0.789976</td>\n",
- " <td>1.000000</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>1</th>\n",
- " <td>Metric</td>\n",
- " <td>1365.233333</td>\n",
- " <td>2</td>\n",
- " <td>18</td>\n",
- " <td>682.616667</td>\n",
- " <td>26.95919</td>\n",
- " <td>0.000004</td>\n",
- " <td>0.000005</td>\n",
- " <td>0.749716</td>\n",
- " <td>0.969103</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>2</th>\n",
- " <td>Time * Metric</td>\n",
- " <td>224.433333</td>\n",
- " <td>2</td>\n",
- " <td>18</td>\n",
- " <td>112.216667</td>\n",
- " <td>12.63227</td>\n",
- " <td>0.000373</td>\n",
- " <td>0.001708</td>\n",
- " <td>0.583955</td>\n",
- " <td>0.727166</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " Source SS ddof1 ddof2 MS F p-unc \\\n",
- "0 Time 828.816667 1 9 828.816667 33.85228 0.000254 \n",
- "1 Metric 1365.233333 2 18 682.616667 26.95919 0.000004 \n",
- "2 Time * Metric 224.433333 2 18 112.216667 12.63227 0.000373 \n",
- "\n",
- " p-GG-corr np2 eps \n",
- "0 0.000254 0.789976 1.000000 \n",
- "1 0.000005 0.749716 0.969103 \n",
- "2 0.001708 0.583955 0.727166 "
- ]
- },
- "execution_count": 51,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "pg.rm_anova(data, dv='Performance', subject='Subject', within=['Time', 'Metric'])"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "6a895941",
- "metadata": {},
- "source": [
- "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."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "1ca9ce9c",
- "metadata": {},
- "source": [
- "### Mixed effects models"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "d14b605d-5737-4d22-9a37-4bd6df7dffb0",
- "metadata": {},
- "source": [
- "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": 52,
- "id": "c368c19e",
- "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>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",
- "<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: 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",
- "\"\"\""
- ]
- },
- "execution_count": 52,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "random_intercept_model = smf.mixedlm(\"Performance ~ Time * Metric\", data, groups=\"Subject\").fit()\n",
- "random_intercept_model.summary()"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "0c8455ee",
- "metadata": {},
- "source": [
- "For comparison with a fixed effect model without grouping:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 53,
- "id": "1d278355",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<table class=\"simpletable\">\n",
- "<tr>\n",
- " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[0.025</th> <th>0.975]</th> \n",
- "</tr>\n",
- "<tr>\n",
- " <th>Intercept</th> <td> 33.0000</td> <td> 2.123</td> <td> 15.543</td> <td> 0.000</td> <td> 28.743</td> <td> 37.257</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Time[T.Pre]</th> <td> -10.7000</td> <td> 3.003</td> <td> -3.564</td> <td> 0.001</td> <td> -16.720</td> <td> -4.680</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Metric[T.Client]</th> <td> -3.1000</td> <td> 3.003</td> <td> -1.032</td> <td> 0.306</td> <td> -9.120</td> <td> 2.920</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Metric[T.Product]</th> <td> -15.5000</td> <td> 3.003</td> <td> -5.162</td> <td> 0.000</td> <td> -21.520</td> <td> -9.480</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Time[T.Pre]:Metric[T.Client]</th> <td> 1.1000</td> <td> 4.246</td> <td> 0.259</td> <td> 0.797</td> <td> -7.413</td> <td> 9.613</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Time[T.Pre]:Metric[T.Product]</th> <td> 8.7000</td> <td> 4.246</td> <td> 2.049</td> <td> 0.045</td> <td> 0.187</td> <td> 17.213</td>\n",
- "</tr>\n",
- "</table>"
- ],
- "text/plain": [
- "<class 'statsmodels.iolib.table.SimpleTable'>"
- ]
- },
- "execution_count": 53,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "fe_nogrouping_model = ols(\"Performance ~ Time * Metric\", data).fit()\n",
- "fe_nogrouping_model.summary().tables[1]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ad998bc8",
- "metadata": {},
- "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": [
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- ],
- "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",
+ "id": "8bd68586",
"metadata": {},
"outputs": [
{
@@ -3702,8 +2761,8 @@
"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",
+ "Date: Thu, 23 Sep 2021 Prob (F-statistic): 4.97e-46\n",
+ "Time: 14:56:58 Log-Likelihood: -103.52\n",
"No. Observations: 200 AIC: 211.0\n",
"Df Residuals: 198 BIC: 217.6\n",
"Df Model: 1 \n",
@@ -3742,7 +2801,7 @@
},
{
"cell_type": "code",
- "execution_count": 196,
+ "execution_count": 51,
"id": "50155198",
"metadata": {},
"outputs": [
@@ -3804,7 +2863,7 @@
},
{
"cell_type": "code",
- "execution_count": 197,
+ "execution_count": 52,
"id": "bc471543",
"metadata": {},
"outputs": [
@@ -3857,7 +2916,7 @@
},
{
"cell_type": "code",
- "execution_count": 178,
+ "execution_count": 53,
"id": "5492f4e8-2ac8-4ba7-9a6c-241f33994998",
"metadata": {},
"outputs": [
@@ -3870,8 +2929,8 @@
"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",
+ "Date: Thu, 23 Sep 2021 Prob (F-statistic): 4.97e-46\n",
+ "Time: 14:56:58 Log-Likelihood: -103.52\n",
"No. Observations: 200 AIC: 211.0\n",
"Df Residuals: 198 BIC: 217.6\n",
"Df Model: 1 \n",
@@ -3907,7 +2966,7 @@
},
{
"cell_type": "code",
- "execution_count": 213,
+ "execution_count": 54,
"id": "0d7780a9",
"metadata": {},
"outputs": [
@@ -3959,7 +3018,7 @@
},
{
"cell_type": "code",
- "execution_count": 180,
+ "execution_count": 55,
"id": "e79b930e",
"metadata": {},
"outputs": [],
@@ -3970,7 +3029,7 @@
},
{
"cell_type": "code",
- "execution_count": 66,
+ "execution_count": 56,
"id": "3cab691b",
"metadata": {},
"outputs": [
@@ -4162,7 +3221,7 @@
"[200 rows x 8 columns]"
]
},
- "execution_count": 66,
+ "execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
@@ -4173,7 +3232,7 @@
},
{
"cell_type": "code",
- "execution_count": 182,
+ "execution_count": 57,
"id": "7f143230",
"metadata": {},
"outputs": [
@@ -4218,7 +3277,7 @@
},
{
"cell_type": "code",
- "execution_count": 237,
+ "execution_count": 58,
"id": "bc655fc0",
"metadata": {},
"outputs": [],
@@ -4230,7 +3289,7 @@
},
{
"cell_type": "code",
- "execution_count": 186,
+ "execution_count": 59,
"id": "b5b46df6",
"metadata": {},
"outputs": [
@@ -4255,7 +3314,7 @@
},
{
"cell_type": "code",
- "execution_count": 187,
+ "execution_count": 60,
"id": "a0b5ffc9",
"metadata": {},
"outputs": [],
@@ -4265,7 +3324,7 @@
},
{
"cell_type": "code",
- "execution_count": 248,
+ "execution_count": 61,
"id": "7bb8d264",
"metadata": {},
"outputs": [],
@@ -4277,7 +3336,7 @@
},
{
"cell_type": "code",
- "execution_count": 189,
+ "execution_count": 62,
"id": "1ddf4e63",
"metadata": {},
"outputs": [
@@ -4305,7 +3364,7 @@
},
{
"cell_type": "code",
- "execution_count": 191,
+ "execution_count": 63,
"id": "7a441682",
"metadata": {},
"outputs": [],
@@ -4316,13 +3375,13 @@
},
{
"cell_type": "code",
- "execution_count": 192,
+ "execution_count": 64,
"id": "0d8019bc",
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
"<Figure size 957.6x295.2 with 2 Axes>"
]
@@ -4385,7 +3444,7 @@
},
{
"cell_type": "code",
- "execution_count": 245,
+ "execution_count": 65,
"id": "b5b96410",
"metadata": {
"scrolled": true
@@ -4393,7 +3452,7 @@
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
@@ -4420,13 +3479,13 @@
},
{
"cell_type": "code",
- "execution_count": 265,
+ "execution_count": 66,
"id": "709f2da0",
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
"<Figure size 1080x576 with 6 Axes>"
]
@@ -4478,7 +3537,7 @@
},
{
"cell_type": "code",
- "execution_count": 404,
+ "execution_count": 68,
"id": "02debff3",
"metadata": {},
"outputs": [
@@ -4496,10 +3555,14 @@
}
],
"source": [
+ "def get_sample(n=100):\n",
+ " x = np.sort(stats.uniform.rvs(0, 2, size=n))\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",
+ " return x, y, y_th\n",
+ "\n",
"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",
+ "x, y, y_th = get_sample()\n",
"\n",
"df = pd.DataFrame({'x': x, 'y': y})\n",
"\n",
@@ -4520,13 +3583,13 @@
},
{
"cell_type": "code",
- "execution_count": 405,
+ "execution_count": 69,
"id": "32746edb",
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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BtVdBxtIFjXytt4cfPfxHjr92lFPrJ7D8EhckjBRALJo3lduBVZv3crCtmxkN1Sxvnj1Qf3Hw4EAHqO3bXbrTokXwF3/hViwaGjx5vjKyUkz81TFIhhO0Hc1lfDLWetM/2RjzZ8Aya+0tye//HFhsrf1fmW7T3NxsN2/eXKohiohHbl658aR0pK6+GI31Vdy7YnFe95n3ikg06jbCa2/PuF/Fpl1HMgcQwzlxAh580K1UbNrkUqIWLnQrFddfDzNm5PUcR2POPHOLtba5KHceQPkeU0o18W851MF1dz9+Ur79/eoYJCI+YIzJeEzxMol3D7DYGFODS5G6ElD0IGXJb+k+fpepoHrfsa687i/nFRFrXUBx4gR0jf6Yi+ZNHb0jVE8PrF/vgor16yEapefUWax/27t56Iy3Ys9ocoHJjALujyFFUapWoeoYJCJB5WUNxiZjzM+Bp4EY8Ayw0qvxyPhWzADAj+k+fpepoHrW5Jq87i9Ti9l7NrQMfg96eqCtzQUXiUSGe8tBLOZWKNauHegANW0a3HwzfzxvCf93XwWRipBLrersLcz+GJmEQoW/z3GqVBN/dQwSkdH4tU7L0zYk1tqvAl/1cgxBoTPgxVPsACDrya30G1RQHQnTHXV1Dbcuacrr/kZcEYnHXUDR1ub2mRgra+G551xNxQMPwOHDUFfn6iluvNHVV4TDfPcnW4lUFGh/jEwmTHDdp2proXqErlWSk1JN/NUxSERG4uc6LfU5DACdAS+uYgcAhU73GQ+WLmjkTtx7s+9YF7PGGFQPtyKS6OzkrIqY69xUiFq0XbsGOkDt2eM6QF1+uaureNvbTuoANeb9MYZjjAskUkHFhAn535dkVKqJvzoGiUgmiYRl22vHfbuzuwKMANAZ8OIqdgBQ6HSf8WLpgsaCfb5TKyJ9Xd1MjfcQ6mgnEY3x4Svmjym4eHrTDvb+6Gec/czjNLW+ijUGs3ix21n76qth4sSMt81rf4zhVFQMBBQ1NUqFKoFSTvzVMUhEhkqtXOw4cGLUdE2vUqgUYASAzoAXV7EDgEKn+0iO4nGWzpzA15sb+OnvXuZgWzfTG6pZftkZ+aUitbXBQw9x4qe/5NznnuF8LK+c0sSPrngfv3vjIj500wVZ3W9O+2MMlb5KUVmZ+3OQMdPEX0S8kmo08bHLmkZM1/QyhUoBRgDoDHhxFTsAKHS6j2TBWujsdF2gOjvBWi6aVcdF7z03v/vr7obHHnPpTxs2uA5QU0/h0Uv+hKfPuYTWqacA0BPNvoZi1P0x0oXDg1cpwuGTryMiIuNCqtHEL7bs47Yr5nP3up3Dpmtm6nj35tsvI2Ep6qqGAowA0Bnw4ipFAFDIdB8ZQaoLVEeHK94ei1gMnnxyoANUVxdMnw7vfz/ceCO3/+4E9dUTMGl/k3OtoRixvW1V1UBQoR28A8Gv3VxEpLykGk3sb+vhvze+yi2XNhEOwZULGjn7tEn9f3eG63g3uWYCT+85zpd/ta2oqxoKMAJAZ8CLTwGANwrSHS2RcCsVhegCZS1s3eqCivvvh6NHob4err3WdYC68ML+1YOZ27cWpoYiJbVKUVPjvmqVIlD83M1FRMpLeqOJ/W09fPeJFr7xnnMHBRcwfMe7P2ue1R9cQPEKwxVgBIQmwFJuxtwdrbcXjh8vzJ4VL7/s2squXQv79rnuS5df7oKKJUuGrXMYUw1FilYpykapNt8TEcm20cRwHe/e2Fhfkn18FGCIiCfy6o6W2mH7+HGXDgVs2nWEVZv3cqCtm5kj1TEMtX8/3HefCypeeMF1X7r4YvjkJ+Gqq9zKxQhyqqFICYcHVii0SlFWtOu2iJRSNo0mhgtErKUk+/gowBART+TUHa2vj989tZOfPfY8B4939QcSAHet20kkbKivinB0tN2wjx+HBx90QcVTT7mA5S1vga98xaVBTZ+e03MYsYYipbJSm92VgDFmNvBfwAzAAiuttXeV6vG167YUmmp6pBCGBiKJhC3JPj4KMEQCqBx2dh+1O5q1rlj7+HE2/XEf3x4mkKiJhImEzci7YXd1uQ5Qa9bAE09ANApnnOFWKm68EU4/vbBPLBQa3PGpQn9mSyQGfNZa+7Qxph7YYox52Fr7fCkeXLtuSyGppkeKpVT7+OjIJxIwdz/yEt9ev4tYIkFlOEQ8kQjkzu6ZuqN9/KLZcPiwK9pOdoJatXnvsIHE3mNdnD5kAldZEebw0Xb47W9dUPHooy7IaGyED37QBRVvehOD2j+NVfoqRVVVTvddDsGiH1hr9wP7k/9vN8a8AJwGlCTA0K7bUkiq6ZFiKsU+PgowRAJk/Y5Wvr1+FwlriYRDxC0c6YgytY6Tahf8PnEd1B3taCfzagy3vnUKF1V2wtHOQdc90NZNfdXgdKrKChds9MbiLuCwlqZ9O3nrc0+w+MU/QFe720n7hhvcv+bmwtU8hEKDaynyXKUYc6G7DMsYMxc4D9hUysfV5ntSKKrpkaBTgCESIPdsaCGesFSEDAaDMZDA0tYVZV9ooHYhKBPXpfMms3TaG1yb2Vgs4/VmNlQP2xJ21qRqpu7fw2UvbuSiFzYyre0QfRUR2i9aQt3yd7kOUBMmFGawFRWu8DtVS1GAFZC8Ct1lRMaYOuAXwF9Za08M8/MVwAqAOXPmlHh0kk41Bpmppmf8KpffCwUYIgGy91gXlRUhYnHbP781BnrjiUE7u/t64hqPu9qKEyfcDtlZGNoStu7IQZZu38hN+56m9pWXSRjDH+cs5KEr/ow3vv+dNJ9doIljRQXU1bnAoggF2jkVusuojDERXHDxI2vtL4e7jrV2JbASoLm52ZZweJJGNQYjK3ZNTyJh2XO0k4Mneunsi3H6lFrOmBbMiWw5KaffCwUYIgEye3INsXiCI519kHDBRdxaKkKhQTu7+3LimgoqOjtdAXcOFs2bymfbjtPy419y9tMbWPDaS+4H554Lf/M3hJYt45xp0zhnyO3yamEbDg8EFTU1I193jNIL3U90Rznc0UtvLEHNhDDrd7R6HwwGiDHGAN8FXrDWfsPr8cjIVGMwsmLW9CQSlnUvHmTnwQ7uenRn4CeyheblCkI5/V4owJCC8Hu+f6kU+3VIFUZPrZ1Ae0+M3liCcMjwiaXzBj3OqB2aSiUadcXao6RAZdTVBevWwZo1vPWJJ3hrLAbz5sHtt7ti7dmZN7XbtOtI9i1sPdrwLvV+HmrvcUEjYIDayrAvU9p87hLgg8A2Y8zW5GVfttbe792QJBPVGIyuWDU9u4908ty+NlZuaCmLiWwheb2CUE6/FwowZMyCku9fbKV4HQYVRh/rYlaGICZTh6b0VY6isdatUhw/7gKEXEWj8LvfDXSA6u6GmTPhwx92QcWZZ2ZV/5Cp81R/C9uqKrdKUV/vWSvZ1Pt526pnSFhLVUWY6fWV1FdF/JPSFhDW2idw8ZkEgGoMvHPwRA8JS9lMZAvJ6xWEcvq9UIAhY+brfP8SKtXrsHRB46j3l20gUlC9vW6l4sSJ/vayo0mlMB083snitr2898BWZvzuMRecTJoEN93kgoq3vtV1bsrB0M5TFgM1NeyIR6CpqaRBxUgrW0sXNDKxOsKcKTWYtMDJ85Q2kSLSviHemTGxirApzW7OQeP1CkI2vxdBKQJXgCFj5st8fw/47XXIJhAZs3gc2ttdGlRvb0433bTrCL/8yTqufHEji1/YyLS2w/RWTODwJUuYtvzdcOmlY+oANbOhmkPdMUxtHT2VVfRGquiMJdwBtMTBxWgrW75JaRMpEe0b4p25U2s5e1YDt185/6QajPEe4Hm9gjDa74XXKVy58DTAMMZMAr4DnAVY4KPW2ie9HJPkTpMjZ1y9Dl1dLqjo6Mi5YJt9++C++5j9w5/x9da9xE2I5+edw6+XvodNTedSO7mBb15xbv5jq6yEujreedNi/vrBXUTCpvRpYmmyWdnyNKVNxCOl2jckKGd8SyUUMlxx5gzeML2O8+dMpqsvxhx1kQL8sbI20u+F1ylcufB6BeMu4DfW2j81xkwAynAmVv40OXLK/nWIRgdSoKLR3G579Cg88ICrq3jmGQBOnDqf9dd8iC1vXkxH7UR3PQsH27JrXdvPGNdCtq7OFWlH3CrSkqlTubOyqmhpYtkW9GezsuVJSptIGUsFFUc6e3n9eA9f+MVzvj/jW0qhkGHutDrmTht5Uhqk4KwQY/X7yprXKVy58CzAMMY0AEuADwNYa/uAPq/GI/nT5Mgpy9chkXApUDnsWdGvsxMeeQTWrnVF2/E4zJ8Pn/403HAD9/zu8LCb51VHwnz6J1tHbi1rjAsmUhvfZajPKFaaWC4F/dmubJUkpU1kHEhPI7nl0ia++4S6JeUjSOk4hRxrqVbW8uF1ClcuvFzBOAM4BPynMeYtwBbgdmttp4djkjxpcuSUzevQ1eWCivb23FKg+voGd4Dq6YFTT4VbboEbbnAdoJKWN1cP2jyvNxanvSeGAWLWntxadv50t0qRWqkowE7a+cqloL/sV7ZEiiifs9LpaSTGqFtSvoKUjhOksY6FH1K4suVlgFEBnA98ylq7yRhzF/BF4G/Sr2SMWQGsAJgzp0C784rIyfJNgUokYMsWF1Q8+OBAB6h3vtMFFeefP+wKw6J5U7kd1072YFs3MxqqiYRCRBOJ/lWNSFUlHUT4/3b1smjZPE+DinS5FPSX5crWGBljLgG2Wms7jTEfwB0L7rLWvurx0MRH8j0rPTSNJChnfP0mSOk4QRrrWPg9hSudlwHGPmCftXZT8vuf4wKMQay1K4GVAM3NzTlWk4pIyrA1A2dOH0iBymXPCmvhxRddUHHffbB/v6uDuPJKF1RccklWHaAWzZs6KP3p5pVPUlVXQ3tVDd2VNcQqIlhrae2M+ia4gNwL+stmZatw/g14S3L1+rO4Zh//BbzN01F5JEh57qWU71np9DSSX2zZx21XzOfudeqWlKsgpeMEaaxj5ecUrnSeBRjW2gPGmL3GmDOttS8CVwLPezUekXI2tGbg2LETfOPHT1B9yWksOmNy9ne0d68LKNasgZdfdu1eL7kEPvtZF1zU5NmnobIS6usJNzWxpzvu+05cSnsas5i11hpj3gF8y1r7XWPMLV4PygtBynMvtXzPSqenkexv6+Enm/ew8oPNRMKm5AFckIPHIKXjBGms44XXXaQ+Bfwo2UGqBfiIx+MR8VS2nYlydc+GFipNgqmxPmo6OonE+uiJxln1h1dHDzCOHHEdoNau7e8ARXMzfPWrsGwZTJmS36BSnZ/q6vo7P33sijMDMXFX2tOYtRtjvgR8AFhijAkBkVFuU5bGS+54PvI9K+2XNJKgB49+eR2zEaSxjheeBhjW2q1As5djEPGLXDoTZc1a6Oyk69U9nGFig7KMKivCmVvCdnS4DlBr1sCTT7oOUGee6VYqrr8eTjst97Gk2snW17ugIhw+6SpBmrgr7WlM3gu8D7gluZo9B/hHj8eUlUKfkR4vueP5GMtZaT+kkZRD8OiH1zFbQRrreOD1CoaIJOXSmWhUfX1uI7wTJyAep6kKjnbGT2oJO6OhevBtNmxwKxXr1rmduU87Df7iL1xdxfz5uT8pY1zaVKqd7DBBxVClnrgXa9VIMrPWHgC+kfb9HlwNhq8V44z0eModz1XQz0oreJTxTAGGiE/k0ploWKk9K9raXHvYNMubZ5/UEjYatyw//zT4wx8GOkC1tcHkyRx4+w38ZOZb2DhxNjMn1bA8NIVF2T6RcHiglazH7WRHU5RVI8nIGNMODNeswwDWWjuxxEPKSTHOSCt3fGRBPiut4FHGMwUYIj6Ra2ciwKVApfas6OjIuGfFoJawx7s4v/sg72t9jlP/+1E4eNCtMlx1FdxwA3+YuYB/2fAKkbChviI8eC+KoRvepYTDA6lP+RZ6e6Cgq0YyKmttvddjGItinJEO+ll6yUzB4/gU5ML+QlKAIeITOXUm6ukZ2AgvHj/px5t2HWHV5r2Dd8OOdLLo8O9cClRLi+sAddll8PnPwxVX9AcG9/5kK5Gw6U+ncl/jrNq8d3CAkVqpqK8PVFCRbsyrRjImxphGoP90bjJVyreKdUY6yGfpJTMvg8dynuT6+bkFvbC/kBRgiPjEqAXOPT1ulaKjw9VLZLBp1xHuWreTSNhwWqyTc3/7CFP+7UnYv8td4YIL4EMfgmuugcknd5A60NZNfdXgSXd/QXgoNDioKEL6UylrIvJaNZIxM8bcBPwzcCrQCpwOvAAs9HJco9EZacnVSMFjsSbK5TzJLdVzy/e9KYfC/kJRgCGS5Idi35MKnLu6oLXVBRWxWFb38asnXmTp87/nkh0bedMrfyRkLa82zmHN29/HjV9ZAaecMuztUqseRzv7ONbZx7T6Smor3Z+ItlCE6jkzYV5xd9MudU2E9rPwzN8Bi4FHrLXnGWMux7Ws9TWlM0mhFHOiXM6T3FI8t7G8NyrsH6AAQwSfFft2dbnUp46OYdOfhpXqALV6NXc+uo4JsSiHJk3ngUvewVMLL+L1abPo6Ily4wjBRWrVY1rdBA6e6GNvR5yJ1fX01E6klxB3Xr2w6AXbpa6JCFJb3DITtdYeMcaEjDEha+1jxph/8XpQ2Si3dCY/p5uUs2JOlMt5kluK5zaW9yZTGuXMiVW0HOoYV79nCjBE8EGxb2+vCypOnMh6pYJ43HWAWrvWdYBqb4cpU9j01it4bP4iXjv9jf0BQW90SEvaIVZt3kskbIhUVRKbUA2TJ3CwO8GBOJw/qbZkk24vaiK0n4Unjhtj6oANuM1WW4FOj8c0LqQHFKc0VPH8/vayTKXxu2JOlMu5e1UpnttY3pvh0ii/9b7zxuXvmQIMEbKb2BY8hSoVVIxSUzGItbB9uwsq7rvPpU/V1MDVV7u9Ki66iAmvtrFj3U4iscTglrTNs0++P2OgqoodsUoqG6cRj0xwzx14Q52lrTvKvSsW5/8cc6SaiHHjHUAP8Gng/UADcKenIxoHhqZ+3HblG1i5oaUsU2n8rpgT5XKuFSrFcxvLezNcGqW1cP2/Pj7ufs8UYIgw+sS2IClU1kJ390ChdrYrFQC7d7ugYu1aeOUViERgyRIXVFx+udshO2lQS9q2bmakukilOkClCrVT+1SEQkw67TX3/NMe0ouJvWoixgdrbfpqxQ88G8g4MzT1I2HxPJVmvKZoFXOiXM61QqV4bmN9b4amUT656/CIv2fl+jugAEOE0Se2eadQJRLQ2TnwL9uaCnCrE/ff74KKbdvcasOFF8JHP+o6QDU0ZLzponlTh28pm9qnYkgthV8m9qqJGB+GbLg3AYgAnX7faC/ohkv98DKVppy7HY2m2BPlYtQK+WUiXOw6qEK/NyOtiJTz74ACDBFGn9jmVBtgrVuhaG93QUWGze+G1d4ODz3kgoqNG12AsnCh26vi+uth5szs76uy0q1Q1NVB1cgTBj9N7DPVRPihy5cURvqGe8YYg0uZKl0u3jg1dKLziy37uP3K+dz16E5PUmnKudtRNoLUMKCcJ8LDKeR7M9KKSDn/DoyLAEMTE8nGSMW+o9YGxGIDqxRdXS4wyFZvL/z2ty6oeOwxV48xezZ8/OMuBWrevOzvq6pqYJ+KSGT066fxc7Gzr7p8SUFZay3wP8aYrwJf9Ho85WzoROdYVx/zZ9Rx36cu41BH6VNpSt3tKJcz8H45W+8XQZwI++U9HGlFpJw7fpV9gKGJif8FIQAcLoUo0RfjE2+ZAnv2uE3wcpHqALV6tVux6OiAadNg+XK48UY4++zsW8JWVrqAIo+gIig87/IlBWWMeVfatyGgGVf0LUU00kRnXmPpJzOl7HaUyxn48Xa2PhtBmwhneg+vftMM9hzrKnnQkWlFpJw7fo0aYBhjPgX80Fp7rATjKThNTPwtKAFgKoXoO4+9xJEDR1hQDX9+biOLJpN9cGGtq6VYu9bVVhw65FKYrrnGrVQsWgQVWcb8qaCirg4mTMj3afleKvj8w+6jVIYNjROr+ncZL3b7WimqG9P+HwN249KkpMj8lJZTym5HuZyBD+LZ+mIL2kR4uPfw6795gWg8wRd+8ZxvAsdy7viVzWxmBvCUMeZp4HvAg8klbV8Y7ey3F331ZWTp79mJ7ii1lWEaqt0fKV8GgLEYnDjB0upull7ZCOQ4rldegbVr6f7lr6l+fS/RcAUvvPE8qj92O/OX3zhqfUS/CRNg4sSyXqlIlx58VlWE6IsneP14D6dOgvqqiNrXBpi19iNej0G8V8puR7mcgQ/a2fpSCNpEeLj38IZzTusPLsAfgWM5d/waNcCw1v61MeZvgKuBjwDfMsb8FPiutXZXsQc4kmzOfquvvr8Mfc8OtPXQ3RensiLsrzPTicTAxnfd3bnf/uBBeOABlwK1fTvWGHbNfhOblt3CcwsXcbyiimjUcvtrnSyaN0KAUVExEFRUVub/fAIoffVxWl0lr7d1Y7G0nughHDJqXxtAxph/ZaB71EmstbeVcDjiA6VaUcnlDHzQztaXQtAmwsO9h+GQ922Zh+OnVcVCCmVzpeSKxYHkvxgwGfi5Meb/LeLYRpU+ATHGfY2EDfdsaOm/zq1LmojGLV19Max1XzUx8c7Q96yyIgQGDrX39l/H0wCwqwsOHIBdu1yQkEtwceIE/Oxn8KEPwdveBn//9+7yL36Rv/3s/8c/3vxF/tB8BT3VtVRFwkTChlWb9558P6GQCyhmzYKmJlebMc6CC3Crj9WRMAATqyOc2lDNhHCI3rilsb6KO29a6J9VLsnWZmALUAWcD+xM/jsX1652TIwxy4wxLxpjXjbGqGBc+qXOwFdF3LRnpDPwuVy3nCUSlpZDHTy56zAthzoAaJpex+KmaTRNr/NtcAHDv4cXnD6l//uU8R44FlM2NRi3A38OHAa+A3zOWhs1xoRwB4bPF3eImWWT/uSn9ptBUOyC66HvWerMdE8sjrXWm/0XenrcakV7e26b36Vuu369q6tYvx6iUZg7Fz7xCddWtsk9j5dWPkl9RXjQTSsrwhxsSwYwxrh6jFRdRbYF3mVs6OrjxOoIFWFDY31VSXcXl8Kx1v4AwBjzl8Cl1tpY8vt/Bx4fy30bY8LAt4G3A/twqb2rrbXPj23UUg5yOQM/3HXnTK7xRUeiUgl6oXum9zBIaV5Bl00NxhTgXdbaV9MvtNYmjDE3jHUAyYPCZuA1a21O95dt+pOf22/6SSkKroebNPbG4nT1xWnrjpYuAOzrcysO7e0uKMhFLAabNsGaNa4DVGcnTJ8O73uf6wB11lknBQgzG6o52tlLVWQgyOiNxZkyrQEaG11gEQ4PfaRxzS+b/0lRTAYmAkeT39clLxuLC4GXrbUtAMaYVbjCcQUYAuSWipJ+3aBPtvPh10L3XFrPDvd+lzrNyy+tcr0waoqUtfarQ4OLtJ+9UIAx3A7kdT+5pj+t39HKzSs3cunX13Hzyo2s39E6lnGXnWxSzsZquPdsQkWYu5efx+NfuIJ7VywuXnARi8HRo/Dqq7B7t/t/tsGFtfDss/C1r7n0p49+FB5+GJYtg+9/3+1j8eUvZ2wvu7x5NtG4pScaJ2bCtEZq2TtxBn/6JxfDpEkKLoaxdEEjd960kMb6Ktq6o0qLKi//ADxjjPm+MeYHwNPA/x3jfZ4GpOcc7kteNogxZoUxZrMxZvMrB47yzYdfAuDyf1pPy6EOtu1r44Z/dYspX1v7PP+R/Pt34f95hIMnenhy1xHee8+TAHzpl8/x4017AFh4x2/o6I3xyPMHueX7TwFw273P8OutrwEw94v3AfDrra9x273PAHDL95/ikecP0tEbY+EdvwHgx5v28KVfPgfAe+95kid3HeHgiR4u/D+PAPAfG1r42loXM93wr4+zbV8bLYc6uPyf1gPwzYdf0nMq8HN633c2cvuqZwZNtm9b9QyfSv48iM9ptPfpEz9+eth6hX9+6EXPntOnfvw0f7f2ea67+3Fu/o9NXHf34/zd2uf51I+fzuo5vfeeJ9n0ylFqKyu47d6tNE2v47tPvFK09ymRsHzwe5u4+l82cPN/bOKKf/4t/7P1NR7efqBsfp9GYrxsCGWMmQX8APg/wGdGW8E486xz7fm3/fug9B3ILv0p/ex8+tlQTVgGXPr1dUyqjmDSJsjWWtq6ozz+hSsK9jipNKySpKzF4wPpT/kUa+/a5dKf1q51+11MmACXX+7Sn5Yuzb42IhTi9693s/LZw+zqskrVE08YY7ZYa5u9HgeAMWYmsCj57SZr7YEx3t+fAsustR9Lfv9BYJG19pOZbtPc3Gw3b948loeVceDJXYe5+T82nXT5qhWLWNw0zYMRFf/MeMuhDq67+/GTCt3v93AFw49jGslYxhuUlY+Rjileb7T3L7gajvpsrvz68W5mtfcMTt+5aWFW+djaD2N0uXTcGkutRtFT1lK7are3u6LtXB04APfd54KK5593RdeLF7udta++2qUzZau21nWBqq3l4jeEuHhJ7sMRKRfGmAXW2h3GmPOTF6VWHE41xpxqrX16DHf/GjA77ftZyctE8pZIWGJx66uuUqVI2fJjW9qgtQ/Od7zlkpLnWYCRrN9otdZuMcYsHeF6K4AVAJWTZ+QdIGg/jNFlm/Puy83xenvdbtidnbnvqg3Q1ubqKVavhqeecilRZ58NX/4yT795Mf/d0s2BI93MvH8Xy5tns2je1Mz3VVk50Fo2243zRMaHz+D+nv/zMD+zwFiWSp8C5htjzsAFFsuB943h/kTYfaSTv/71Nm67Yj53r9vZP+H7+rvPyXuyPdaz06WojxhLW9pinX0PWvvgfMfr1/qXXHk5+7kEuMkYcx2uZeFEY8wPrbUfSL+StXYlsBJg0pwFg/K5cgkQtB/G6LLtuOWX1aANz+7hh49s51jrUWbVRUaf+A/V3Q2PPeZWKjZsGOgA9clPup21585l064j3LVuJ5Gwob4qwtHOXu5at5PbYfBjpVrLNjRkv3GeyDhjrV2R/Hp5Ee47Zoz5JPAgEAa+Z63dXujHkfHl4IkeXj3SzX9vfJVbLm3CGHf+6bRJVXlNmgtxdrpUZ/Lz2Z+hmGff/biqMpJ8xxu0lZpMPAswrLVfAr4EkFzB+H+GBhdDJYbUi+QSIOTbkabYbVv9Jpv0Jc9Wg6x1KU8dHWx89lX+/eEdRMKGyZFw5on/ULEYPPmkCyoeesjdX2MjfOADLqhYuHBQkfaqzXvdTtLJ7k/ua5xVm/e6x6mpGVitUGtZkawYY/4M+I21tt0Y89e4PTH+zlr7zFju11p7P3B/IcYoAgNnofe39fDtx14G3Fnod59/Uv+ArBTi7LSfz+QX8+x7sTf7K/TKS77j9fP7m4tA5W9YS94tK/PZD8OXqUA+UNLVIGsH6ik6O90O28BPNu0eeeI/9D62bnVBxQMPwJEjLii4/noXVFxwQcYuTgfauvt3GE+pqJzAS9EInHEGRCLD3k5ERvQ31tqfGWMuBa4C/hH4dwaKvkV8odBnzQtxdtqPZ/JTk/OXDrYX9ez7cKsqhQgMirXyks8qkB/f33z4IsCw1q4H1o92vVMnVdNYX5V396Fci4v9kgrkN0XfnyCRcMFEqqYikTjpKsNN/Csrwrx6uINP/2QrB9q6eUvvET546DlO+92jsG+fq424/HIXVLztba4j1ChS+1dUTojQXVlDV1Utxwm7MwkKLkTyFU9+vR5Yaa29zxjzNS8HJDKcQp81L8TZ6WKfyc9V+uT8Y5c1lfTse6ECAz/VPfjt/c2XLwKMbNVXVZR0B18Vhg+vKLujJxI8/vQr3LvueY4eOsYpE6tGrKkYbuO6Y1191Bw9xKLnHuLiFzYy5+CrJIzh+HkXMOkTn3AdoOpy+0PxnovncecTrxOtqaWqMhLYzd7GW6qf+N5rxph7cLtuf90YU0kW+zKJeCGfs9CZFOrsdCHHNFbpk/NfbNl3UkF8Mc++Fyow8Fvdg5/e33wFKsAoNRWGZ1aQVrPRaP9KxaY/7uPfHn2JSNgwsbJi1JqK5c2zuWvdTiDO5Gg3b9m+kbc+9wTn7N8JwCunzmPV1R/k9/MvIDxjBt9817nZjyscdjUVEydy0Rur+MJps0u3b0cRKNVPfOg9wDLgn6y1x40xpwCf83hMgROUXvml5ufXpVzOTqdLn5zvb+vpL4g/57SJzJ9RX9TnV6jAoFzqHvxEAcYIip4KNB6l2sl2dLj/J616ak/2NRXAolNr+N/h3fT+z2oW7NxKRSLOnkkz+c/mm3j8zEX0nTqL2soKrIWOtiw32EvtWVFXN6hgu+j7dhSZUv3Eb6y1XcaYVuBSYCcQS34d97KdHJdLr/xCC8LrUg5np9MNnZzvb+vhu0+0lGQDvEIFBuVS9+AnCjBGUJRUoPHGWtcONlVTEY0Oe7VMNRUH04ODaBR+/3tXrP3II8zv6oIZM3j9ne/lX2sW8EztDBLWuDaCJ3ppnAjhkGFGQ3Xm8aX2rJg4MWOhd9Ap1U/8xhjzVaAZOBP4TyAC/BDXvnzcymVy7KeccT/R61J6Xk7OC5lyVm4rS15TgDGKoJ+99kRqJ+2uroxF2kMNV1PRG4szY2IVPP00rFnjOkAdO+aCgRtucP+am/nHn2/jaGcvU+OW1vZeTLKb8eH2XqbUVbK8efbgB0ulQDU0uACjzCnVT3zoncB5wNMA1trXjTH13g7Je7lMjv2WM+4Xfnld/JymVWheTs4L+djltrLkNQUYUhg9PQOpT319Od88vaaisiLMtP2vsmj777lm9xY4uN8FAldc4YKKJUsGdYBKrX6kFkCOdfURjVsscPsV8wdSrKqrXVCRtmfFeCh+Vqqf+FCftdYa404HGGOUh0Buk2PljA/P69clkbDsOdrJ03uO8+VfbfNtmlaheTk5V2DgTwowJH/JTe/o6HCrFmOwaN5UPndwP/t+/Ave8swG5hzehw2FMZdcDJ/5K7jqqowdoNJXP+qqKqirqqAnGmdKbSWL5k93Kx5DVivW72jlHx54gZ2HOoiEQsyYWFm2xc9K9RM/McYYYG2yi9QkY8xfAB8F/sPbkXkvl8mxcsaHV+jXJZeViFSK244DJ1i5oUVpWjKuKcCQ7KU2vUvtTxGPj36b0Rw9Cg8+CGvWcN6WLZwHcO658JcfwVx7LUwdYVfupKGrH72xOF2mgo8tOx+amiA0uPtlqqtSa3sPYWOwwP62Xk6dVEUkbPqLn8tpdUOpfuIXyZWLPwM+A5zA1WHcYa192NuReS+XybFyxodXyNcl14LxVIrbxy5r8kWaloiXAhVgtPfEuHnlxrKY8PlZ+sR6TkMlf9k8k8tOrXZBhbVjf4CuLnj0UVes/cQTbvVj3jz4q79yKVCzZ496F+kWzZvK7cCqzfto6TU0zJ7OJ658E5dl+GykuirFE5awMRhjSGA51N7LGdNq2XesS61dRYrraeC4tVatadPkOjlWasjwCvW65Fownp7ipvQ1Ge8CFWC8frybWe09mvAV0fodrfzvXz1HfbyHeYle7O5u/m3XLiak1zLkIxqF3/3OFWs/+qjrLHXKKfDhD8ONN8KZZw5qDZuTSIRFixew6OoLs+oEleqqNCEcIha3GAOJRIKuGOw40E7NhDBf/82OwLR2HW2lpZxWYqRsLALeb4x5FehMXWitPce7IfmDggb/yLVgPJXiVurN5kT8KFABhjEEYsIXSMki7V/86nfMaesY6OYUCdGDzbgfxYgSiYEOUL/5DRw/DpMmwU03uX/nn39S+lJOamvd/dXm9kc71VVpWl0lr7d1E48liCUXZgxQWxnmpdYOZk0afLap2K1d8wkERltp0UqM+NQ1Xg9AZDS5Foynp7j998ZX+cxV81lwykRiccvpyeBiPHWXkvEtUAFGaMgZbvXyH4NEYqCNbGdnf5H24SMnRt+PYjQvvuiCivvug9dfh6oquPJKl/506aWDOkDlLBRyBduTJkEkMurVh5PqqhQJG05tqGLvMffcqipCzGyoor4qwrGuKAdP9DKxemCsxWztmm8gMNometpkT/zIWvuq12MoJU0qgynXgvH0FLejnb28dryHFf+9pf+233rfefTFrK83ARQplEAFGIkh+f/q5Z+jaHSgSLu7e9h6ioz7UYy0WR3Avn0uoFi7Fl56yaUqXXqpq6u46qqcVxlOUlnpgoqJE09Kpcr1zP/QrkqRcIiZEysHBRMz6ivZd7y7ZK1d8w0ERttET5vsiXgrCDtL+41fArJ8CsZTKW4AH/juHwbVbzy3r03dpYrAL5+XYgjycwtUgGEtw074lGM+gvRdtLPYn2K4jkzRuD15szpwHaAeeMCtVjzzjLvsvPPgjjvg2mthypSxjd0Y15p20iS3h8Uw8j3zn95V6eaVG2lt7xn084pwiPnT65hcW1mS1q75BgKjbaKnTfZEvFXqnaWDPCEB/wVk+dbEDFe/kbCou1SB+e3zUkhBf26BCjBOnVRNY33VoAkfoBzzdInEQNpTHq1kBzoy7eVgWzczGqpZ3jx7oP6is9MVaa9Z44q243F44xvhs5+F666DWbPG/hwqKlxQ0dAwatF2IVKAMm1E9zfXv7lkn6F8A4HRNtHTJnsi3irlztJBn5BA6QOyYhmufiNs1F2q0Mrl8zKcoD+3QAUY9VUV3Lti8aDLbl65UTnm0ejA3hQZUp9ysWje1MEF3X19sG6dS3969FFXEH7qqXDLLa6u4swzx/gEkmprXVCRYUO94RQiBcgPG9HlGwiMNnY/PDeR8ayUO0sHfUICpQ3Iimm4+o2zZzVoc8QCK5fPy3CC/twCFWAMZ9zmmCe7PmWb+pSzRAK2bHErFQ8+ONAB6p3vdEFFnh2gNu06wqrNeznQ1s3Mhmreu2gui887wwUWeRR/FyoFKJuN6IqZijeWQGC0sWuTPRHvlHLH7aBPSKC0AVkxZarfALQ5YgGVy+dlOEF/boEPMMZNjnkxdtEe7jHSO0Dt3+9qH6680u1VcckleXduAhdc3LVuJ5Gwoaqull2mis8/08GdcyxLp+fXWapUKUClaPeqQECk/JRyx+2gT0igtAFZsWWq39A+J4Xj98/LWGqi0p/b5JoJ/FnzLN7YWI+17n79HpgaW4idmUukubnZbt68edBl6RO/9AnmnTctDP5kLVVP0d7uWsomEqPfJh9797r0p7Vr4eWXXQ3EpZe6lYorr4SawgRrf/XTZ9kbqyAxsYFYxAUUXX0xGuurTkp9y0VqZaGYKUCpQvD0QLYQYxcpJWPMFmtts9fj8IvhjilBVg41GDAwKdNZfsmGXz8vufw+ZgpEEgnLnqOdPL3nOF/+1Tbf/V6PdEzxbAXDGDMb+C9gBmCBldbau3K9n3LJMU9Nkl8/3M4bauBj507notNqx1xPkdGRI64D1Nq1Ax2g3vpW+Nu/hWuuGXsHqHRVVTBpEpsr9jJp4gRMWpvZQqSzleLM/7hNxRORwCjlakkxaTdzyYVfPy/Z1kSNFogkLP3BxUj34zdepkjFgM9aa582xtQDW4wxD1trn8/1joKeWrLh2T388y+fpi7Ww5kmQe+JOP96335CV8zPfffskXR0wCOPuBSoJ58c3AHqhhtc4XahGAP19a5uo8otz8+eUhvYdLZxk4onIoHm18mWSJDlk+qUbU3UaIFIUGurPAswrLX7gf3J/7cbY14ATgNyDjCCZv0LB/n+I89z5OARmqoNnZ09TEkk+je3c1/jrNq8d+wBRl8fPP64CyrWrYPeXjjtNPiLv4Drr3cBRiFFIq5ge5gWs0FumRrksYtIeQj6HhciQZRv6mG2NVGjBRBBra3yRZG3MWYucB6waZifrQBWAMyZM6e0Ayuk5C7av3/2VVbe9xyREJxSEeZ4e5x9x3qYOXECpO2eXVkR5mBbd36PlUjAU0+59KcHH4S2Npg8Gf70T91KxXnnnbQb9pjV1rrVihF27A5yOluQx17OtMmmjBd+ra9Q0CPlLt/2z9kWoI8WQPi9kD0TzwMMY0wd8Avgr6y1J4b+3Fq7ElgJriCv0I9ftAmKta4wO7XhXTQKwM82vEgkxKDVikgYjnT0UVc1kOPfG4szo2H43aszPt4LLwx0gDp40BVnX3WVCyouvnhMHaCGFQ4PrFZked9BSWfL9LkIwtjHi1J09hLxCz/uceHXoCcoFJwFQ74pStnWRI0WQAS1tsrTAMMYE8EFFz+y1v6y1I9f8AlKLDZ4F+1hCrQPtHVTXzV4Mj61dgIHTvTSE41TWRGmN+bSb5Y3zx79MffsGegAtWuXm+hfdhl84QtwxRWuzWyh1dQMbIhX6JUQH9DENRgKsYu7SFD4MQ/bj0FPUAQtOBvPwdBYUpSyqYnKJoAIYm2Vl12kDPBd4AVr7Te8GENBJih9fQMb3vX0jHr1mQ3VHO3s7V/BAKgIh5g7pYaJNRM42NbNjIZqljfPzlx/cejQQAeoZ591l11wAXzoQ3D11S4dqtAiEZg40f0r9EqIz2jiGgzq7CUpxph/BG4E+oBdwEestcc9HVSBlSoPO5eJpB+DnrEq1UQ6SMFZ0IKhlEK9l6VIUQpiADEaL1cwLgE+CGwzxmxNXvZla+39pRpA3hOU7u6BoCKZ+pSt5c2zuWvdTmDwasX/uuINIxd0d3TAww8PdIBKJGDBAvjc51yx9imn5DSOrBjjVikaGgq2F0YQaOIaDOrsJWkeBr5krY0ZY74OfAn4gsdjKqhSTHKGm0h+633nccbUOlrbT56kBbX4NJNSTqSLGZwVOkgKWjC0+0gnRzp7ef14D1/4xXNjfi+DmqLkNS+7SD0BePruZD1BSSRcPUUBdtFeNG8qtwOrNu8dfbWirw82bIDVq2H9etcBatYsWLHC7az9hjfkPY4RTZjggoqJE0/qBDUeaOIaDOrsJSnW2ofSvt0I/KlXYymWUkxyhk4kJ9dMYOfBDj7542eGnaQFtfg0k1JOpIsVnBUjSArKSlX6c7/l0ia++0RLwd7LclxhKDbPi7y9NOIEJVVP0dHhgosCbni3aN7UzKsV8Tj84Q8DHaDa22HqVHjPe9xKxbnnFq/uoa7OdYLy+WpFsTsHaeIaDOrsJRl8FPiJ14MohmJPcoZOJN91/izuenRnxklauZ3ZLeVEuljBWTGCpKCsVKU/d2MIRFBUzsZ1gDF0gjK3roJb3zqDS2t6oKWldAOxFrZvd0HFffdBa6ub5F99tQsqLr4YKor0VqU6QU2aVLzHKKBSFGBr4hoc6uw1fhhjHgFmDvOjr1hrf528zldwm7j+aIT7KY/W50UwdCKZzSStnM7slnIiXazgrBhBUlBWqoY+9yAEReXM/zPKYrKWpbNrWfonTYNayWZTrF0Qu3e7oGLNGvf/SASWLHFtZS+/vDgdoFKqq11QkUMnKD/sOVCqAmxNXEX8xVp71Ug/N8Z8GLgBuNLazEvOxW59HmRDJ5JhM74macWeSA9XG1Ho4KwYQVJQVqrSn/svtuzjtivmc/e6nb4OisrZ+Aswipj6lJXWVtcBas0a2LbNTe4vuAA+9jG3YtHQULzHDoddXUVDg6uzyIFfWreqAFtEhjLGLAM+D7zNWqs/BnkaOpGcObGKM2dO9P2Z60Ip5kS6VAXk+QZJoxWGB2GlKv2572/r4Seb97Dyg81Ewmbctdb1AzPCiR7faW5utps3b879hr29A0FFqVYn0rW3w0MPudWKjRtd0fib3+wKta+7DmYOt+pfQNXVLqior8+7fuPmlRtPKnzu6ovRWF/FvSsWF2qkgRmHSBAZY7ZYa5u9HkehGWNeBiqBI8mLNlprPz7a7fI+powjqYmnn89cj8YPezi0HOrgursfP2ll4f4iFJDn+p4FtQ3tcMrh8xokIx1TArWCseNAOzev3Jhdak5qF+08WskWRG8v/Pa3bqVi/XrXEWrOHPj4x10K1Lx5xX18Y9xqxaRJUFk55rvzy8qBCrBFZChrbZFa6kkQzlyPJBZLcN8f9xekXelYlLKAPNf3LEhtaEcT9M9rOQlUgFERMplTcwrYSjZv8Ths2uSCiocecmOZNg2WL3dBxTnnFH/n61SL2YYGCIUKdrd+ad2qAmwREclGImH5fcuR/uACvJs8+7kTU1Da0EqwBCrAgCFFvfOnDmx450U9BbjH3LbNpT/df7/bZbu2Fq65xnWAWry4+N2ZjHGPWcQWs35aOShWAbYfithFRKQwdh/pZPOrR30xefZzJyY/Bz8SXIELMCpiUab3ddH3ygHYNcW7gbS0uJaya9cOdIBautStVCxdClUl+MWsqBhYrShyEFPuKwd+KWIXEZHCOHiih4T1RycsP3diGi348UMNiwRPoAKMSCxK49H99ETjnFI79rqCnB086FYp1qxx+1YYAxde6DpAXXONq3kohZoat1pRW1v8lKs05dy6tVTtb0VEpDRmTKxizbOvndSu9OvvPoe5U2tLPnH2a33ASMFPORWAS2kFKsDAWnqSqTnLm2eX5jFPnHA7aq9d6+orrIWFC+FLX4Jrr4UZM0ozjlBoYLUixxazfueH1CS/FLGLiEhhzJ1ayxeWvYmv/+YFbrm0iXAImk+fwsVNUwE0cU6TKfgppwJwKa1ABRgJa5lSW8ny5tksmje1eA/U0+M6P61d675Go3D66fCJT7gUqDPOKN5jDxWJuNWKAhdt+8Xdj7zEt9fvIpZIUBkOEU8k+lOTgJIFHn4pYhcRGY1SVrLTf2Z+Zv1JZ+ZbDnVo4pwFFYBLvgIVYJwxrZZvvvfc4tx5LOb2qFi71nWA6uyE6dPh/e93xdpnn126dCRj3A7bEye6NKgytX5HK99ev4uEtUTCIeIWjnREmVoH//DAC3RFEyWrifBTEbuISCZKWclNpjPzmjhnRwXgkq9ABRgFZy0895yrqXjgATh82E3sly1zm+BdeKHb/bpUUqsVEyeW9nE9cs+GFuIJS0XIYDAYAwksbV1RjnZGmTW5umQ1EeVexC4i5UEpK4WhiXN2/Nz9SvxtfAYYu3a5lYq1a2HPHlfTcPnlbqVi6dKCbEyXk7q6oraY9au9x7qorAgRi9v+xSFjoDeeoCIUojoyOMgqdk1EORexi0h50Jn3wtDEOTt+7n4l/jZ+AowDBwY6QD3/vKtnWLwY/vIv4e1vh/r6nO9y064jrNq8lwNt3cxsqM6tNiQUcisVkye7lYtxaPbkGmLxBEc6+yDhgou4tVSEQjRNq6U7GldNhIhIGp15LwxNnLPn1+5X4m/lHWAcP+7qKdasgaeecilRZ53lOkBddx005n+2etOuI9y1bieRsKG+KsLRzl7uWreT22HkICO10/Y4SYMaSaruYWrtBNp7YvTGEoRDhk8sncc5syapJkJEZAideS8cTZxFiqf8AoyeHli3zqU/bdjgOkCdcQZ88pOuA9TcuQV5mFWb9xIJG6qSaTzua5xVm/eeHGAY41ZIGhqgurogj18ORqt7UE2EiMhgOvMeLOr4JeNVeQQYsRg8+eRAB6iuLrc68YEPuKBi4cKCd4A60NZNfdXg1KbKijAH27oHLijxaoUf9pPI1Uh1D6qJEBE5mc68B4M6fsl45mmAYYxZBtwFhIHvWGv/IesbWwvPPuvSn+6/H44edasE113ngooid4Ca2VDN0c7e/hUMgN5YnBkNNS6gKPFqxfodrdyxenvJ2rqKiIhIZur4JeOZZwGGMSYMfBt4O7APeMoYs9pa+/yIN3z5ZRdU3Hcf7N3rOj5dfrkLKt72tjHtcp1L0fby5tnctW4nEKeyIkyHDXG8qo6PvOsCmDkz7zHk654NLUTCpmRtXUVERCQzdfyS8czLFYwLgZettS0AxphVwDuAzAHGrl2ulWwoBBdd5HbWfvvbXZvXMcq1aHvRvKncbgz/ue0IO3tDNDZO5vMepiTtPdbFpOrBKVvFbusqIiIiw1PHLxnPvAwwTgP2pn2/D1g09ErGmBXACoBzIhH467+Ga6+FadMKOpiciraTtRWL5s1j0bKT07C8qIWYPbmG1vYetXUVERHxAXX8kvHM90Xe1tqVwEqA5rPOsnzwg0V5nFGLtrPsBOVVLUSq5avauoqIiHhPHb9kPPMywHgNmJ32/azkZZ7IVLQ9dcpEmD49605QxayFGGllZLSWryIiIlJa6vgl45WXAcZTwHxjzBm4wGI58D6vBjO0aPtYuJLjdTV85F1vdbttZ6lQtRBDg4mLmqbw86dfG3FlRG1dRURERMRrngUY1tqYMeaTwIO4NrXfs9Zu92o8i+ZN5bZIBd/ZdpSXukOcMq2er+SxAlCIWojh0qy+vX4XU2ojNFS74jB1iQrmvh8iIiIi5c7TGgxr7f3A/V6OAYDaWpg0icVvfCOLrxrbXRWiFmK4NKt4wtLWFWVa3UD3ifHcJUr7foiI5C7fnaW1I7WI5ML3Rd5FEw67gu2GBohERr9+lgpRCzFcmlVlRYieWHzQZeO5S5T2/RARyU2+O0trR2oRydX4CzCqqmDSJNcRyhTnD+NYayGGS7Oqr6og1mXHXZeoTGlQ2vdDRCQ3+e4srR2pRSRXIa8HUBLGuJWK00+HOXNcR6giBReFcOuSJqJxF0xY675OqAjziaXzaKyvoq07SmN9FXfetLCsz9an0qBa23sGpUGt39HK7Mk1dEe1oiMikq2RdpYuxu1EZPwq6xWMjXtP8B/bjvFSt2HW1LrAFAGPlGZ1m9eDK6GR0qC074eISG7y3VlaO1KLSK7KL8AwBurq2HCgl7/e0k4kHKGhNjzmIuBSdyxSy9mRW/5q3w8Rkdzku7N0ue5IPVLhuoraRcamfAKMioqBou2KCv5tzcaCFQGrY5E3Rmv5qyBMRCR7+e4sXY47Uo9UuA6oqF1kjIJfg1FTA6eeCk1NMHWqCzRwZ7+rI4N33s63CDg9VccY9zUSNtyzoaUgT0GGN1wtitKgRCQTY8xnjTHWGDPN67H4VWpn6cVN02iaXpf1hDnf2/lVpsL13Uc6R/yZiGQnmCsY4bAr1J40KWOL2UJseJeijkXeUBqUiGTLGDMbuBrY4/VYxP9GKly3low/U9cskewEK8AIhWDmzKxazBayCLiQwYrkRmlQIpKlbwKfB37t9UDE/0YrXFdRu8jYBCtFasKErFvMLl3QyJ03LSxIW1el6oiI+Jcx5h3Aa9baZ7O47gpjzGZjzOZDhw6VYHTiR6nC9aqImwalF66P9DMRyY6x1no9hqw1NzfbzZs3e/LYqS5SStURkaAyxmyx1jZ7PY58GGMeAWYO86OvAF8GrrbWthljdgPN1trDo92nl8cU8V6qU9Rwhesj/UxEnJGOKcFKkfKQUnVERLxjrb1quMuNMWcDZwDPGre6PQt42hhzobX2QAmHKAGTKlwfrq5ipJ+JyOgUYIiISGBZa7cB/Wd/clnBEBGR4ghWDYaIiIiIiPiaVjBERKRsWGvnej0GEZHxTisYIiIiIiJSMFrByEOqo9TeY13MVkcpEREREZF+WsHI0fodrdyxejut7T1Mqo7Q2t7DHau3s35Hq9dDExERERHxnFYwcnTPhhYiYdO/q3fNhAq6+mLcs6GlZKsYWkEREREREb/yZAXDGPOPxpgdxpjnjDG/MsZM8mIc+dh7rIvqSHjQZdWRMPuOdZXk8bWCIiIiIiJ+5lWK1MPAWdbac4CXgC95NI6czZ5cQ3c0Puiy7micWZNrSvL46SsoxrivkbDhng0tJXl8EREREZGReBJgWGsfstbGkt9uxO28Ggi3LmkiGrd09cWw1n2Nxi23LmkqyeN7vYIiIiIiEjSJhKXlUAdP7jpMy6EOEgnr9ZDKmh9qMD4K/CTTD40xK4AVAHPmzCnVmDJauqCRO3ErCfuOdTGrxDUQsyfX0Nre018DAqVdQREREREJkkTC8pvtB/jMT7fSE01QFQnxjfecy7KFMwmFjNfDK0tFCzCMMY8AM4f50Vestb9OXucrQAz4Uab7sdauBFYCNDc3+yLcXLqgcUwBxViKtG9d0sQdq7fT1RejOhKmOxov6QqKiIiISJDsPtLZH1wA9EQTfOanW1lw22U0Ta/zeHTlqWgBhrX2qpF+boz5MHADcKW11heBQymkirQjYTOoSPtOyCrI8HoFRURERCRIDp7o6Q8uUnqiCVrbexRgFIknKVLGmGXA54G3WWvHVfFAIdrcjnUFRURERGS8mDGxiqpIaFCQURUJ0Vhf5eGoyptXXaS+BdQDDxtjthpj/t2jcZScirRFRERESmfu1Fq+8Z5zqYq4aW+qBmPu1FqPR1a+PFnBsNa+wYvH9QMVaYuIiIiUTihkWLZwJgtuu4zW9h4a66uYO7VWBd5F5NUKxrjldZtbERERkfEmFDI0Ta9jcdM0mqbXKbgoMgUYJbZ0QSN33rSQxvoq2rqjNNZXcedNC1VTISIiIiJlwQ/7YIw7QS/SHkubXRERkWwkEpbdRzo5eKKHGROV0iISJAowJCdjbbMrIiIyGm2MJhJsSpGSnKS32TXGfY2EDfdsaPF6aCIiUiYybYy2+0inxyMTkWwowJCcqM2uiIgU20gbo4mI/ynAkJzMnlxDdzQ+6DK12RURkUJKbYyWThujiQSHAgzJidrsiohIsWljNJFgU5G35GTpgkbuxNVi7DvWxSx1kRIRkQLTxmgiwaYAQ3IW9Da7IiLif6mN0Zqm13k9FBHJkVKkRERERESkYBRgiIiIiIhIwSjAEBERERGRglGAISIiIiIiBaMAQ0RERERECsZYa70eQ9aMMYeAV70exzCmAYe9HkSWNNbi0FiLQ2MtrNOttdO9HoRf5HBM8fN76+exgb/Hp7HlR2PLTzmOLeMxJVABhl8ZYzZba5u9Hkc2NNbi0FiLQ2MVP/Dze+vnsYG/x6ex5Udjy894G5tSpEREREREpGAUYIiIiIiISMEowCiMlV4PIAcaa3ForMWhsYof+Pm99fPYwN/j09jyo7HlZ1yNTTUYIiIiIiJSMFrBEBERERGRglGAMQJjzDJjzIvGmJeNMV8c5uefMcY8b4x5zhjzqDHm9LSfxY0xW5P/VvtgrB82xhxKG9PH0n72IWPMzuS/D/lgrN9MG+dLxpjjaT8r9ev6PWNMqzHmjxl+bowxdyefy3PGmPPTflbq13W0sb4/OcZtxpjfG2Pekvaz3cnLtxpjNvtgrEuNMW1p7/UdaT8b8fPjwVg/lzbOPyY/o1OSPyvp6yq5y+LvUaUx5ifJn28yxsxN+9mXkpe/aIy5xoOxeXYM8vMxx8/HGD8fU/x8DPHzMcPPxwhjzGxjzGPJvxPbjTG3D3Od4nzmrLX6N8w/IAzsApqACcCzwJuHXOdyoCb5/78EfpL2sw6fjfXDwLeGue0UoCX5dXLy/5O9HOuQ638K+J4Xr2vy8ZYA5wN/zPDz64AHAAMsBjZ58bpmOdaLU2MArk2NNfn9bmCaj17XpcDasX5+SjHWIde9EVjn1euqfzm/t9n87fxfwL8n/7889XceeHPy+pXAGcn7CZd4bJ4cg/x8zPH7McbPxxQ/H0P8fMzw8zECOAU4P/n/euClYX5Xi/KZ0wpGZhcCL1trW6y1fcAq4B3pV7DWPmat7Up+uxGYVeIxpow61hFcAzxsrT1qrT0GPAwsK9I4Ifex3gzcW8TxjMhauwE4OsJV3gH8l3U2ApOMMadQ+td11LFaa3+fHAt4+3nN5nXNZCyf9bzkOFZPP6+Ss2w+T+8AfpD8/8+BK40xJnn5Kmttr7X2FeDl5P2VbGweHoP8fMzx9THGz8cUPx9D/HzM8PMxwlq731r7dPL/7cALwGlDrlaUz5wCjMxOA/amfb+Pk9+UdLfgIsCUKmPMZmPMRmPMnxRhfOmyHeu7k8tfPzfGzM7xtoWS9eMll/vPANalXVzK1zUbmZ5PqV/XXA39vFrgIWPMFmPMCo/GNNRFxphnjTEPGGMWJi/z7etqjKnB/fH9RdrFfnxdZUA2n6f+61hrY0AbMDXL2xZ7bOlKeQzy8zEn6MeYoBxT/HgM8fUxw+tjhHHpnecBm4b8qCifuYq8RimDGGM+ADQDb0u7+HRr7WvGmCZgnTFmm7V2lzcjBGANcK+1ttcYcyvujNwVHo4nG8uBn1tr42mX+e11DRxjzOW4g8OlaRdfmnxdG4GHjTE7kmdlvPI07r3uMMZcB/wPMN/D8WTjRuB31tr0M1l+e12lDPn0GBSEY46OMXnw6TEkCMcMz44Rxpg6XGDzV9baE4W+/+FoBSOz14DZad/PSl42iDHmKuArwE3W2t7U5dba15JfW4D1uKjRs7Faa4+kje87wFuzvW2B5fJ4yxmylFji1zUbmZ5PqV/XrBhjzsG9/++w1h5JXZ72urYCv6KwqR45s9aesNZ2JP9/PxAxxkzDp69r0kifV1+8rnKSbD5P/dcxxlQADcCRLG9b7LF5dQzy8zEn6McYXx9T/HoMCcgxw5NjhDEmggsufmSt/eUwVynOZ84WqbAk6P9wqzstuOXTVGHQwiHXOQ9XPDR/yOWTgcrk/6cBOyliIWqWYz0l7f/vBDbagSKeV5Jjnpz8/xQvx5q83gJc8ZPx6nVNe9y5ZC4su57BxVF/8OJ1zXKsc3B54hcPubwWqE/7/++BZR6PdWbqvcf9wd2TfI2z+vyUcqzJnzfgcnBrvX5d9S+n9zWbv52fYHCR90+T/1/I4CLvFgpb5O3bY1CWY/PkmJPt3wg8PMaM8rfP02PKKGPz9Bgyytg8PWaMNLbkzz05RiRfg/8C/mWE6xTlM1fQF7jc/uEq61/C/QH/SvKyO3FnigAeAQ4CW5P/VicvvxjYlvwgbwNu8cFY/x7YnhzTY8CCtNt+NPlH42XgI16PNfn93wL/MOR2Xryu9wL7gSgu//AW4OPAx5M/N8C3k89lG9Ds4es62li/AxxL+7xuTl7elHxNn01+Rr7ig7F+Mu3zupG0A9pwnx8vx5q8zodxBb/ptyv566p/eb2/o/3trAJ+lvw9/gPQlHbbryRv9yJwrQdj8+wYlMXYPDvmjDa25Pd/iwfHmCz+9nl2TMlibJ4dQ7IYm2fHjNHGlrzOh/HgGIFLY7PAc2nv23Wl+MxpJ28RERERESkY1WCIiIiIiEjBKMAQEREREZGCUYAhIiIiIiIFowBDREREREQKRgGGiIiIiIgUjAIMEREREREpGAUYIiIiIiJSMAowRMbIGHOBMeY5Y0yVMabWGLPdGHOW1+MSEZHg0TFFyoE22hMpAGPM13A7/lYD+6y1f+/xkEREJKB0TJGgU4AhUgDGmAnAU0APcLG1Nu7xkEREJKB0TJGgU4qUSGFMBeqAetxZJxERkXzpmCKBphUMkQIwxqwGVgFnAKdYaz/p8ZBERCSgdEyRoKvwegAiQWeM+XMgaq39sTEmDPzeGHOFtXad12MTEZFg0TFFyoFWMEREREREpGBUgyEiIiIiIgWjAENERERERApGAYaIiIiIiBSMAgwRERERESkYBRgiIiIiIlIwCjBERERERKRgFGCIiIiIiEjBKMAQEREREZGC+f8BpY+kChPTLoUAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 957.6x295.2 with 2 Axes>"
]
@@ -4564,7 +3627,7 @@
},
{
"cell_type": "code",
- "execution_count": 406,
+ "execution_count": 70,
"id": "9a3edfab",
"metadata": {},
"outputs": [
@@ -4638,7 +3701,7 @@
"4 2.486747 0.075106 0.005641"
]
},
- "execution_count": 406,
+ "execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
@@ -4650,7 +3713,7 @@
},
{
"cell_type": "code",
- "execution_count": 407,
+ "execution_count": 71,
"id": "24c100a8",
"metadata": {},
"outputs": [],
@@ -4670,7 +3733,7 @@
},
{
"cell_type": "code",
- "execution_count": 408,
+ "execution_count": 72,
"id": "d6ac4ac8",
"metadata": {},
"outputs": [],
@@ -4681,7 +3744,7 @@
},
{
"cell_type": "code",
- "execution_count": 409,
+ "execution_count": 73,
"id": "078047e2",
"metadata": {},
"outputs": [
@@ -4717,7 +3780,7 @@
"source": [
"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",
- "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)."
+ "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 the following examples in `statsmodels` documentation: [1](https://www.statsmodels.org/stable/examples/notebooks/generated/predict.html) [2](https://www.statsmodels.org/stable/examples/notebooks/generated/ols.html)."
]
},
{
@@ -4725,7 +3788,7 @@
"id": "5e8e27d4",
"metadata": {},
"source": [
- "### Model selection"
+ "### Overfitting"
]
},
{
@@ -4738,7 +3801,7 @@
},
{
"cell_type": "code",
- "execution_count": 410,
+ "execution_count": 74,
"id": "fba76906",
"metadata": {},
"outputs": [],
@@ -4749,7 +3812,7 @@
},
{
"cell_type": "code",
- "execution_count": 411,
+ "execution_count": 75,
"id": "424e6080",
"metadata": {},
"outputs": [
@@ -4776,40 +3839,17 @@
"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": [
- "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": "63c07909",
"metadata": {},
"source": [
- "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."
+ "If we compare the various models, we can observe that more complex models tend to perform better on the training data."
]
},
{
"cell_type": "code",
- "execution_count": 413,
+ "execution_count": 76,
"id": "74c19b10",
"metadata": {},
"outputs": [
@@ -4890,7 +3930,7 @@
"6 445.311406 "
]
},
- "execution_count": 413,
+ "execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
@@ -4904,12 +3944,123 @@
"scores"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 105,
+ "id": "d52c5826",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# we need a few helpers to automate the parameter search\n",
+ "\n",
+ "def poly(x, order):\n",
+ " return np.stack([x**k for k in range(order+1)], axis=1)\n",
+ "\n",
+ "def fit(x, y, order):\n",
+ " return sm.OLS(y, poly(x, order)).fit()\n",
+ "\n",
+ "models = {k: fit(x, y, k) for k in range(1, 7)}\n",
+ "\n",
+ "def predict(model, x, order):\n",
+ " X = poly(x, order)\n",
+ " beta = model.params\n",
+ " y_pred = np.dot(X, beta)\n",
+ " return y_pred\n",
+ "\n",
+ "def sum_of_squares(y_predicted, y_expected=None):\n",
+ " y_ = np.mean(y_predicted) if y_expected is None else y_expected\n",
+ " y_ = y_predicted - y_\n",
+ " return np.dot(y_, y_)\n",
+ "\n",
+ "def R2(y_predicted, y_expected):\n",
+ " residual_ss = sum_of_squares(y_predicted, y_expected)\n",
+ " total_ss = sum_of_squares(y_expected)\n",
+ " return 1 - residual_ss / total_ss"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ddca584a",
+ "metadata": {},
+ "source": [
+ "Now if we get a new sample from the same population, and compute the coefficient of determination:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 112,
+ "id": "a7c3be8a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x_test, y_test, _ = get_sample()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 113,
+ "id": "4b0254fb",
+ "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": [
+ "R2_train_data = {}\n",
+ "R2_test_data = {}\n",
+ "for order in models:\n",
+ " trained_model = models[order]\n",
+ " y_pred = predict(trained_model, x_test, order)\n",
+ " R2_train_data[order] = trained_model.rsquared\n",
+ " R2_test_data[order] = R2(y_pred, y_test)\n",
+ " \n",
+ "ax = plt.gca()\n",
+ "ax.plot(list(R2_train_data.keys()), list(R2_train_data.values()), 'b-', label='train')\n",
+ "ax.plot(list(R2_test_data.keys()), list(R2_test_data.values()), 'g-', label='test')\n",
+ "ax.set_xlabel('polynomial order')\n",
+ "ax.set_ylabel('$R^2$')\n",
+ "ax.axvline(3, color='r', linestyle=':', linewidth=1, label='true')\n",
+ "ax.legend();"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c49be8f1",
+ "metadata": {},
+ "source": [
+ "...the over-complex models perform poorly."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "34e0a478",
+ "metadata": {},
+ "source": [
+ "### Model selection"
+ ]
+ },
{
"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."
+ "Choosing among models should not rely on data fitness only, especially if we only consider the data used to fit the model.\n",
+ "\n",
+ "To choose between models, two strategies:\n",
+ "\n",
+ "* model evaluation on test data, *i.e.* a second (sub-)sample drawn from the same population as the data used to fit the model,\n",
+ " * => `scikit-learn`\n",
+ "* heuristics; for example, model complexity is to be controlled, so that simpler models are favored over complex models."
]
},
{
@@ -4925,7 +4076,175 @@
"id": "b31a31c9",
"metadata": {},
"source": [
- "Akaike (AIC) and Bayes (BIC) information criteria combine model fitness with the notion of model complexity."
+ "[Akaike (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) and [Bayesian (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion) information criteria combine model fitness with the notion of model complexity."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 116,
+ "id": "d9da7ebb",
+ "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>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": 116,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "scores"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1f9e1fa4",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "AIC = 2k - 2\\log{L}\n",
+ "$$\n",
+ "$$\n",
+ "BIC = k\\log{n} - 2\\log{L}\n",
+ "$$\n",
+ "\n",
+ "with $\\log{L}$ the maximum log-likelihood we also met in the OLS summary, and quantifies the goodness-of-fitness.\n",
+ "\n",
+ "$k$ is the number of estimated parameters in the model, and $n$ the number of observations.\n",
+ "For $p$ predictors (explaining variables), a linear model's $k=p+2$ because we also estimate an intercept and the error variance.\n",
+ "\n",
+ "The likelihood is the probability that the data are generated by the model: $L=P\\left(X,y|\\mathcal{M}(\\theta)\\right)$, denoting $\\mathcal{M}(\\theta)$ the model with parameters $\\theta$ (estimated coefficients).\n",
+ "\n",
+ "In the case of a linear regression with normally-distributed residuals: $\\log{L}\\propto \\frac{\\sum_i(y_i - \\textbf{x}_i^\\top\\beta)^2}{\\sigma^2}$ with $\\beta$ are the regression coefficients."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 127,
+ "id": "29b6d783",
+ "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": [
+ "AIC = {}\n",
+ "BIC = {}\n",
+ "for order in models:\n",
+ " trained_model = models[order]\n",
+ " AIC[order] = trained_model.aic\n",
+ " BIC[order] = trained_model.bic\n",
+ "\n",
+ "ax = plt.gca()\n",
+ "\n",
+ "orders, criteria = list(AIC.keys()), list(AIC.values())\n",
+ "ax.plot(orders, criteria, 'b-', label='AIC')\n",
+ "k = np.argmin(criteria)\n",
+ "ax.plot(orders[k], criteria[k], 'ro', markerfacecolor='none')\n",
+ "ax.annotate('AIC best candidate',\n",
+ " xy=(orders[k], criteria[k]),\n",
+ " xytext=(orders[k]-.2, criteria[k]+6),\n",
+ " arrowprops=dict(arrowstyle=\"->\"),\n",
+ ")\n",
+ "\n",
+ "orders, criteria = list(BIC.keys()), list(BIC.values())\n",
+ "ax.plot(orders, criteria, 'g-', label='BIC')\n",
+ "k = np.argmin(criteria)\n",
+ "ax.plot(orders[k], criteria[k], 'ro', markerfacecolor='none')\n",
+ "ax.annotate('BIC best candidate',\n",
+ " xy=(orders[k], criteria[k]),\n",
+ " xytext=(orders[k]-.6, criteria[k]+7),\n",
+ " arrowprops=dict(arrowstyle=\"->\"),\n",
+ ")\n",
+ "\n",
+ "ax.set_xlabel('polynomial order')\n",
+ "ax.axvline(3, color='r', linestyle=':', linewidth=1, label='true')\n",
+ "ax.legend();"
]
},
{
@@ -4953,6 +4272,29 @@
"metadata": {},
"outputs": [],
"source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4d16690d-a3b2-4903-b746-04ce95030288",
+ "metadata": {},
+ "source": [
+ "### Hierarchical models"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e9847067-50f5-4271-a3ef-440ca555ee82",
+ "metadata": {},
+ "source": [
+ "The notion of hierarchy in an analysis of variance arises when not all factors or dependent variables have equal importance in the analysis.\n",
+ "\n",
+ "* repeated measurements on the same sample;\n",
+ "* nested designs (student < class < school);\n",
+ "* crossed designs;\n",
+ "* etc.\n",
+ "\n",
+ "We cannot cover all cases and variations; just be careful whether your observations are independent and were sampled randomly ([good read](https://online.stat.psu.edu/onlinecourses/sites/stat503/files/lesson14/recognize_split_plot_experiment.pdf))."
+ ]
}
],
"metadata": {