diff --git a/1_data_science/simulationsstudie/yann_ahlgrim_simulationsstudie.ipynb b/1_data_science/simulationsstudie/yann_ahlgrim_simulationsstudie.ipynb index 1d5d6e0..7217924 100644 --- a/1_data_science/simulationsstudie/yann_ahlgrim_simulationsstudie.ipynb +++ b/1_data_science/simulationsstudie/yann_ahlgrim_simulationsstudie.ipynb @@ -522,7 +522,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_22276\\2403674952.py:43: FutureWarning: \n", + "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_15840\\2403674952.py:43: FutureWarning: \n", "\n", "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n", "\n", @@ -1067,6 +1067,26 @@ "weekday_Mo-Fr 0\n", "weekday_Sa 0\n", "weekday_So 0\n", + "dtype: int64\n", + "\n", + "avg_speed 0\n", + "hard_brakes 0\n", + "trip_distance 0\n", + "shift_frueh 0\n", + "shift_normal 0\n", + "shift_spaet 0\n", + "speeding_haeufig 0\n", + "speeding_manchmal 0\n", + "speeding_selten 0\n", + "weather_nass 0\n", + "weather_trocken 0\n", + "weather_winterlich 0\n", + "road_Autobahn 0\n", + "road_Außerorts 0\n", + "road_Innerorts 0\n", + "weekday_Mo-Fr 0\n", + "weekday_Sa 0\n", + "weekday_So 0\n", "dtype: int64\n" ] } @@ -1127,7 +1147,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 12, "id": "8a320b4c", "metadata": {}, "outputs": [ @@ -1160,7 +1180,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "id": "b748cb80", "metadata": {}, "outputs": [ @@ -1168,7 +1188,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_22276\\2049212131.py:7: FutureWarning: \n", + "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_15840\\146936503.py:6: FutureWarning: \n", "\n", "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n", "\n", @@ -1189,7 +1209,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_22276\\2049212131.py:7: FutureWarning: \n", + "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_15840\\146936503.py:6: FutureWarning: \n", "\n", "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n", "\n", @@ -1210,7 +1230,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_22276\\2049212131.py:7: FutureWarning: \n", + "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_15840\\146936503.py:6: FutureWarning: \n", "\n", "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n", "\n", @@ -1231,7 +1251,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_22276\\2049212131.py:7: FutureWarning: \n", + "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_15840\\146936503.py:6: FutureWarning: \n", "\n", "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n", "\n", @@ -1252,7 +1272,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_22276\\2049212131.py:7: FutureWarning: \n", + "C:\\Users\\yann\\AppData\\Local\\Temp\\ipykernel_15840\\146936503.py:6: FutureWarning: \n", "\n", "Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n", "\n", @@ -1302,7 +1322,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "id": "19c7e28c", "metadata": {}, "outputs": [ @@ -1335,7 +1355,7 @@ "Model: Logit Df Residuals: 13994\n", "Method: MLE Df Model: 5\n", "Date: Thu, 12 Jun 2025 Pseudo R-squ.: 0.006879\n", - "Time: 10:11:02 Log-Likelihood: -8108.5\n", + "Time: 14:40:25 Log-Likelihood: -8108.5\n", "converged: True LL-Null: -8164.6\n", "Covariance Type: nonrobust LLR p-value: 1.314e-22\n", "=====================================================================================\n", @@ -1395,7 +1415,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 15, "id": "6641f80c", "metadata": {}, "outputs": [ @@ -1434,7 +1454,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 16, "id": "0541fa09", "metadata": {}, "outputs": [ @@ -1481,6 +1501,15793 @@ "})\n", "print(comparison)" ] + }, + { + "cell_type": "markdown", + "id": "7516554c", + "metadata": {}, + "source": [ + "## Güte der Modellparameter" + ] + }, + { + "cell_type": "markdown", + "id": "18f9a07d", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "c1bb79ce", + "metadata": {}, + "source": [ + "### Güte der Modellparameter: Einfluss des Stichprobenumfangs\n", + "\n", + "In diesem Abschnitt wird untersucht, wie sich der Stichprobenumfang auf die Schätzgüte der Modellparameter auswirkt. Dazu werden jeweils k = 1.000 zufällige Stichproben aus der Grundgesamtheit gezogen, mit Stichprobenumfängen n von 1.000 bis 50.000 (Schrittweite 5.000). Für jede Stichprobe wird das optimale Modell aus Abschnitt 3 trainiert und der geschätzte Beta-Wert einer erklärenden Variable (z.B. `avg_speed`) gespeichert. Die Verteilungen der geschätzten Beta-Werte werden für drei ausgewählte Stichprobenumfänge verglichen und der funktionale Zusammenhang zwischen n und der Standardabweichung der Schätzungen analysiert." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "616ae484", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Stichprobenumfang: 0%| | 0/10 [00:00 3\u001b[0m sns\u001b[38;5;241m.\u001b[39mkdeplot(betas_by_n[n][\u001b[38;5;241m~\u001b[39mnp\u001b[38;5;241m.\u001b[39misnan(betas_by_n[n])], label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mn=\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mn\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m 4\u001b[0m plt\u001b[38;5;241m.\u001b[39mtitle(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVerteilung des geschätzten Beta-Werts für avg_speed bei verschiedenen Stichprobenumfängen\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m 5\u001b[0m plt\u001b[38;5;241m.\u001b[39mxlabel(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGeschätzter Beta-Wert für avg_speed\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", + "\u001b[1;31mKeyError\u001b[0m: 10000" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(12, 6))\n", + "for n in [1000, 10000, 50000]:\n", + " sns.kdeplot(betas_by_n[n][~np.isnan(betas_by_n[n])], label=f\"n={n}\")\n", + "plt.title(\"Verteilung des geschätzten Beta-Werts für avg_speed bei verschiedenen Stichprobenumfängen\")\n", + "plt.xlabel(\"Geschätzter Beta-Wert für avg_speed\")\n", + "plt.ylabel(\"Dichte\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "990bb2a0", + "metadata": {}, + "source": [ + "**Interpretation:**\n", + "\n", + "Mit wachsendem Stichprobenumfang werden die Verteilungen der geschätzten Beta-Werte schmaler und konzentrieren sich stärker um den wahren Wert. Kleine Stichproben führen zu einer größeren Streuung und damit zu unsichereren Schätzungen." + ] + }, + { + "cell_type": "markdown", + "id": "50ea2928", + "metadata": {}, + "source": [ + "### Funktionaler Zusammenhang zwischen n und der Standardabweichung des geschätzten Beta-Werts\n", + "\n", + "Für jeden Stichprobenumfang wird die Standardabweichung der geschätzten Beta-Werte berechnet und gegen n aufgetragen. Zusätzlich wird die theoretische Entwicklung der Standardabweichung nach der Formel $\\sigma(\\hat{\\beta}) \\propto 1/\\sqrt{n}$ eingezeichnet." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cf7a7e61", + "metadata": {}, + "outputs": [], + "source": [ + "stds = np.array([np.nanstd(betas_by_n[n]) for n in n_values])\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "plt.plot(n_values, stds, marker='o', label='Empirische Standardabweichung')\n", + "plt.plot(n_values, stds[0]*np.sqrt(n_values[0]/n_values), '--', label=r'$\\propto 1/\\sqrt{n}$')\n", + "plt.xlabel('Stichprobenumfang n')\n", + "plt.ylabel('Standardabweichung des geschätzten Beta-Werts')\n", + "plt.title('Zusammenhang zwischen Stichprobenumfang und Schätzgenauigkeit')\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "10afcd69", + "metadata": {}, + "source": [ + "**Fazit:**\n", + "\n", + "Die Standardabweichung der Schätzung eines Modellparameters nimmt mit wachsendem Stichprobenumfang näherungsweise proportional zu $1/\\sqrt{n}$ ab. Das bedeutet: Je mehr Daten zur Verfügung stehen, desto präziser und stabiler werden die Parameterschätzungen. Die Lernqualität eines Modells steigt also mit der Datenmenge, wobei der Zugewinn mit zunehmender Datenmenge abnimmt (abnehmender Grenznutzen)." + ] } ], "metadata": {