update abhaengigkeit

1_data_science/simulationsstudie/yann_ahlgrim_simulationsstudie.ipynb

@@ -45,7 +45,7 @@
     "   Anzahl starker Bremsvorgänge mit hoher Verzögerung (>0,3 g). Modellierung z.B. als Poisson-verteilte Zufallsvariable mit geringem Mittelwert (wenige Ereignisse pro 100 km). Harte Bremsmanöver korrelieren mit aggressiver Fahrweise und sind prädiktiv für Fahrerwechsel.  \n",
     "   → Quelle: [Tesla Safety Score Definition](https://www.findmyelectric.com/blog/tesla-safety-score-beta-explained)\n",
     "\n",
-    "4. **Geschwindigkeitsüberschreitungen (ordinal):**  \n",
+    "4. **Geschwindigkeitsüberschreitungen (ordinal, 3 Kategorien):**  \n",
     "   Häufigkeit bzw. Ausmaß, mit dem Tempolimits überschritten werden. Kategorisierung z.B. in:  \n",
     "   - *selten*,  \n",
     "   - *manchmal*,  \n",
@@ -58,24 +58,26 @@
     "\n",
     "#### Nicht erklärende Variablen:\n",
     "\n",
-    "5. **Straßentyp (nominal, 3 Kategorien):**  \n",
-    "   - *Autobahn* (~30–33 %)  \n",
-    "   - *Außerorts* (~43 %)  \n",
-    "   - *Innerorts* (~24–27 %)  \n",
-    "   → Modelliert als Multinomialverteilung. Kontextvariable ohne direkte Prädiktionswirkung.  \n",
-    "   → Quelle: [Klimaschutzinstrumente im Verkehr](https://openumwelt.de/server/api/core/bitstreams/07bd23f9-ff0a-41e5-b89b-8d7baf0a5c36/content)\n",
     "\n",
-    "6. **Wetterbedingungen (nominal, 3 Kategorien):**  \n",
+    "5. **Wetterbedingungen (nominal, 3 Kategorien):**  \n",
     "   - *trocken* (~70–75 %)  \n",
     "   - *nass* (~20–25 %)  \n",
     "   - *winterlich* (<5 %)  \n",
     "   → Modelliert als Multinomial. Kontextvariable.  \n",
     " Die Einteilung basiert auf Daten des Statistischen Bundesamtes: Etwa 70–75 % aller Fahrten finden unter trockenen Bedingungen statt, 20–25 % bei Nässe und unter 5 % bei Schnee oder Glätte.\n",
     "\n",
-    "7. **Fahrstrecke (metrisch):**  \n",
+    "6. **Fahrstrecke (metrisch):**  \n",
     "   Länge der Fahrt (z.B. lognormalverteilt um 12 km). Kontextvariable, nicht direkt erklärend.  \n",
     "   → Quelle: [Mobilität in Deutschland 2017 – Ergebnisbericht](https://www.bmv.de/SharedDocs/DE/Anlage/G/mid-ergebnisbericht.pdf)\n",
     "\n",
+    "   \n",
+    "7. **Straßentyp (nominal, 3 Kategorien):**  \n",
+    "   - *Autobahn* (~30–33 %)  \n",
+    "   - *Außerorts* (~43 %)  \n",
+    "   - *Innerorts* (~24–27 %)  \n",
+    "   → Modelliert als Multinomialverteilung. Kontextvariable ohne direkte Prädiktionswirkung.  \n",
+    "   → Quelle: [Klimaschutzinstrumente im Verkehr](https://openumwelt.de/server/api/core/bitstreams/07bd23f9-ff0a-41e5-b89b-8d7baf0a5c36/content)\n",
+    "\n",
     "8. **Wochentag (nominal, 2–3 Kategorien):**  \n",
     "   Z.B. *Werktag* vs *Wochenende* oder *Mo–Fr*, *Sa*, *So*. Modellierung als kategorische Variable. Kontextvariable.  \n",
     "   → Quelle: [Mobilität in Deutschland 2017 – Ergebnisbericht](https://www.bmv.de/SharedDocs/DE/Anlage/G/mid-ergebnisbericht.pdf)\n"
@@ -91,7 +93,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 50,
    "id": "97ba29a9",
    "metadata": {},
    "outputs": [],
@@ -102,6 +104,8 @@
     "import matplotlib.pyplot as plt\n",
     "import seaborn as sns\n",
     "from scipy.stats import norm, multinomial, poisson, lognorm, bernoulli\n",
+    "import statsmodels.api as sm\n",
+    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
     "\n",
     "np.random.seed(11)\n",
     "N = 1_000_000"
@@ -117,7 +121,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 51,
    "id": "61247da5",
    "metadata": {},
    "outputs": [],
@@ -131,21 +135,40 @@
     "# 3. Harte Bremsmanöver (metrisch, Poisson)\n",
     "hard_brakes = np.random.poisson(lam=2, size=N)\n",
     "\n",
-    "# 4. Geschwindigkeitsüberschreitungen (ordinal, 3 Kategorien)\n",
+    "# 4. Geschwindigkeitsüberschreitungen (ordinal, 3 Kategorien) – Abhängigkeit von avg_speed\n",
-    "speeding = np.random.choice(['selten', 'manchmal', 'häufig'], size=N, p=[0.6, 0.3, 0.1])\n",
+    "def softmax(x):\n",
+    "    e_x = np.exp(x - np.max(x, axis=1, keepdims=True))\n",
+    "    return e_x / e_x.sum(axis=1, keepdims=True)\n",
     "\n",
-    "# 5. Straßentyp (nominal, Kontext)\n",
+    "speed_scaled = (avg_speed - avg_speed.min()) / (avg_speed.max() - avg_speed.min())\n",
-    "road_type = np.random.choice(['Autobahn', 'Außerorts', 'Innerorts'], size=N, p=[0.32, 0.43, 0.25])\n",
+    "strength = 0.01\n",
+    "logits = np.zeros((N, 3))\n",
+    "logits[:, 0] = 1 - strength * speed_scaled   # selten\n",
+    "logits[:, 1] = 1                            # manchmal\n",
+    "logits[:, 2] = 1 + strength * speed_scaled   # häufig\n",
+    "probs = softmax(logits)\n",
+    "speeding = [np.random.choice(['selten', 'manchmal', 'häufig'], p=p) for p in probs]\n",
     "\n",
-    "# 6. Wetterbedingungen (nominal, Kontext)\n",
+    "# 5. Wetterbedingungen (nominal, Kontext)\n",
     "weather = np.random.choice(['trocken', 'nass', 'winterlich'], size=N, p=[0.75, 0.2, 0.05])\n",
     "\n",
-    "# 7. Fahrstrecke (metrisch, lognormal)\n",
+    "# 6. Fahrstrecke (metrisch, lognormal)\n",
     "mu, sigma = np.log(12), 0.7\n",
     "trip_distance = np.random.lognormal(mean=mu, sigma=sigma, size=N)\n",
     "\n",
+    "# 7. Straßentyp (nominal, Kontext) – schwächere Abhängigkeit von trip_distance\n",
+    "road_probs = []\n",
+    "for dist in trip_distance:\n",
+    "    if dist < 5:\n",
+    "        road_probs.append([0.5, 0.35, 0.15])\n",
+    "    elif dist < 20:\n",
+    "        road_probs.append([0.2, 0.5, 0.3])\n",
+    "    else:\n",
+    "        road_probs.append([0.1, 0.4, 0.5])\n",
+    "road_type = [np.random.choice(['Innerorts', 'Außerorts', 'Autobahn'], p=prob) for prob in road_probs]\n",
+    "\n",
     "# 8. Wochentag (nominal, Kontext)\n",
-    "weekday = np.random.choice(['Mo-Fr', 'Sa', 'So'], size=N, p=[0.7, 0.15, 0.15])\n"
+    "weekday = np.random.choice(['Mo-Fr', 'Sa', 'So'], size=N, p=[0.7, 0.15, 0.15])"
    ]
   },
   {
@@ -158,29 +181,183 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 52,
    "id": "f8e0efb0",
    "metadata": {},
-   "outputs": [],
+   "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>avg_speed</th>\n",
+       "      <th>shift_behavior</th>\n",
+       "      <th>hard_brakes</th>\n",
+       "      <th>speeding</th>\n",
+       "      <th>weather</th>\n",
+       "      <th>trip_distance</th>\n",
+       "      <th>road_type</th>\n",
+       "      <th>weekday</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>64.494547</td>\n",
+       "      <td>früh</td>\n",
+       "      <td>2</td>\n",
+       "      <td>manchmal</td>\n",
+       "      <td>trocken</td>\n",
+       "      <td>30.449962</td>\n",
+       "      <td>Außerorts</td>\n",
+       "      <td>Mo-Fr</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>44.139270</td>\n",
+       "      <td>früh</td>\n",
+       "      <td>3</td>\n",
+       "      <td>häufig</td>\n",
+       "      <td>trocken</td>\n",
+       "      <td>11.911103</td>\n",
+       "      <td>Autobahn</td>\n",
+       "      <td>Mo-Fr</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>42.154349</td>\n",
+       "      <td>spät</td>\n",
+       "      <td>2</td>\n",
+       "      <td>selten</td>\n",
+       "      <td>trocken</td>\n",
+       "      <td>6.086055</td>\n",
+       "      <td>Autobahn</td>\n",
+       "      <td>Mo-Fr</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>20.466814</td>\n",
+       "      <td>normal</td>\n",
+       "      <td>5</td>\n",
+       "      <td>häufig</td>\n",
+       "      <td>trocken</td>\n",
+       "      <td>5.732684</td>\n",
+       "      <td>Außerorts</td>\n",
+       "      <td>Mo-Fr</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>46.917154</td>\n",
+       "      <td>spät</td>\n",
+       "      <td>2</td>\n",
+       "      <td>selten</td>\n",
+       "      <td>trocken</td>\n",
+       "      <td>7.256758</td>\n",
+       "      <td>Außerorts</td>\n",
+       "      <td>Mo-Fr</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   avg_speed shift_behavior  hard_brakes  speeding  weather  trip_distance  \\\n",
+       "0  64.494547           früh            2  manchmal  trocken      30.449962   \n",
+       "1  44.139270           früh            3    häufig  trocken      11.911103   \n",
+       "2  42.154349           spät            2    selten  trocken       6.086055   \n",
+       "3  20.466814         normal            5    häufig  trocken       5.732684   \n",
+       "4  46.917154           spät            2    selten  trocken       7.256758   \n",
+       "\n",
+       "   road_type weekday  \n",
+       "0  Außerorts   Mo-Fr  \n",
+       "1   Autobahn   Mo-Fr  \n",
+       "2   Autobahn   Mo-Fr  \n",
+       "3  Außerorts   Mo-Fr  \n",
+       "4  Außerorts   Mo-Fr  "
+      ]
+     },
+     "execution_count": 52,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "df = pd.DataFrame({\n",
     "    'avg_speed': avg_speed,\n",
     "    'shift_behavior': shift_behavior,\n",
     "    'hard_brakes': hard_brakes,\n",
     "    'speeding': speeding,\n",
-    "    'road_type': road_type,\n",
     "    'weather': weather,\n",
     "    'trip_distance': trip_distance,\n",
+    "    'road_type': road_type,\n",
     "    'weekday': weekday\n",
     "})\n",
     "\n",
     "df.head()\n"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f06e7c4d",
+   "metadata": {},
+   "source": [
+    "### VIF der Abhängigkeiten prüfen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "id": "6bfb199a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Variance Inflation Factor (VIF) für ausgewählte Variabeln:\n",
+      "              features  VIF Factor\n",
+      "0            avg_speed    5.768491\n",
+      "1        trip_distance    2.469313\n",
+      "2  road_type_Außerorts    2.238422\n",
+      "3    speeding_manchmal    1.900947\n",
+      "4      speeding_selten    1.893981\n",
+      "5  road_type_Innerorts    1.587059\n"
+     ]
+    }
+   ],
+   "source": [
+    "vif = pd.DataFrame()\n",
+    "columns = ['avg_speed', 'speeding', 'trip_distance', 'road_type']\n",
+    "vif_df = pd.get_dummies(df[columns], drop_first=True)\n",
+    "vif_df = vif_df.astype(float)\n",
+    "vif['features'] = vif_df.columns\n",
+    "vif['VIF Factor'] = [variance_inflation_factor(vif_df.values, i) for i in range(vif_df.shape[1])]\n",
+    "vif = vif.sort_values('VIF Factor', ascending=False).reset_index(drop=True)\n",
+    "print(\"\\nVariance Inflation Factor (VIF) für ausgewählte Variabeln:\")\n",
+    "print(vif)"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "base",
+   "display_name": "hft_ml",
    "language": "python",
    "name": "python3"
   },
@@ -194,7 +371,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.9"
+   "version": "3.11.10"
   }
  },
  "nbformat": 4,