PyData_2017_pt5.ipynb

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   },
   "source": [
    "# Credit risk modeling in Python - part 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Commands to get to same point for data in part 1 and 2 notebooks\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image\n",
    "import seaborn as sns\n",
    "sns.set(style=\"white\")\n",
    "sns.set(style=\"whitegrid\", color_codes=True)\n",
    "\n",
    "data = pd.read_csv(\"creditrisk_pydata_nas.csv\", index_col = 0)\n",
    "data = data[data.age < 100]\n",
    "data = data[data.children < 30]\n",
    "data = data[data.address < (data.age + 2)]\n",
    "data[(data.employer > (data.age - 14))]\n",
    "data = data[(data.employer < (data.age - 14)) | data.employer.isnull()]\n",
    "data.amount.fillna(data.amount.median(), inplace = True)\n",
    "\n",
    "bins = [0, 10, 20 ,30, 40, 50]\n",
    "bins_emp1 = pd.cut(data['employer'], bins)\n",
    "\n",
    "bins = [0, 2, 5 ,10, 15, 50, 70]\n",
    "bins_emp2 = pd.cut(data['employer'], bins)\n",
    "bins_emp2.fillna(\"(50, 70]\", inplace = True)\n",
    "bins_emp2 = bins_emp2.cat.rename_categories([\"(0, 2]\",\"(2, 5]\",\"(5, 10]\",\"(10, 15]\",\"(15, 50]\", \"unknown\"])\n",
    "bins_emp2 = bins_emp2.cat.as_unordered()\n",
    "\n",
    "data['employer']= bins_emp2\n",
    "\n",
    "data['payfreq'] = data['payfreq'].astype('category')\n",
    "data['marstat'] = data['marstat'].astype('category')\n",
    "data['home'] = data['home'].astype('category')\n",
    "\n",
    "data['payfreq'] = data['payfreq'].cat.rename_categories([\"quarter\",\"bimon\",\"monthly\",\"biweek\"])\n",
    "data['marstat'] = data['marstat'].cat.rename_categories([\"single\",\"married\",\"divorced\",\"widowed\"])\n",
    "data['home'] = data['home'].cat.rename_categories([\"yes\", \"no\"])\n",
    "\n",
    "data.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Create these for our newly \"binned\" categorical variable `employer`:\n",
    "- A crosstable (value counts) --> store it in crosstab_employer\n",
    "- A stacked chart\n",
    "- A normalized crosstable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>default</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>employer</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>(0, 2]</th>\n",
       "      <td>782</td>\n",
       "      <td>119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(2, 5]</th>\n",
       "      <td>734</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5, 10]</th>\n",
       "      <td>813</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10, 15]</th>\n",
       "      <td>387</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15, 50]</th>\n",
       "      <td>573</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unknown</th>\n",
       "      <td>365</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "default     0    1\n",
       "employer          \n",
       "(0, 2]    782  119\n",
       "(2, 5]    734   71\n",
       "(5, 10]   813   56\n",
       "(10, 15]  387   16\n",
       "(15, 50]  573   12\n",
       "unknown   365   31"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Crosstable\n",
    "crosstab_employer = pd.crosstab(data[\"employer\"], data[\"default\"])\n",
    "crosstab_employer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x116a44e48>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Stacked chart\n",
    "crosstab_employer.div(crosstab_employer.sum(1), axis=0).plot(kind='bar', stacked = True)\n",
    "plt.title('Default for employment length')\n",
    "plt.xlabel('Employment length')\n",
    "plt.ylabel('Proportion of defaults')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbpresent": {
     "id": "4b729520-9f97-42f6-94b1-ab5b915d5841"
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     "slide_type": "slide"
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>default</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>employer</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>(0, 2]</th>\n",
       "      <td>0.867925</td>\n",
       "      <td>0.132075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(2, 5]</th>\n",
       "      <td>0.911801</td>\n",
       "      <td>0.088199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(5, 10]</th>\n",
       "      <td>0.935558</td>\n",
       "      <td>0.064442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(10, 15]</th>\n",
       "      <td>0.960298</td>\n",
       "      <td>0.039702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(15, 50]</th>\n",
       "      <td>0.979487</td>\n",
       "      <td>0.020513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unknown</th>\n",
       "      <td>0.921717</td>\n",
       "      <td>0.078283</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "default          0         1\n",
       "employer                    \n",
       "(0, 2]    0.867925  0.132075\n",
       "(2, 5]    0.911801  0.088199\n",
       "(5, 10]   0.935558  0.064442\n",
       "(10, 15]  0.960298  0.039702\n",
       "(15, 50]  0.979487  0.020513\n",
       "unknown   0.921717  0.078283"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Crosstable with fractions\n",
    "pd.crosstab(data[\"employer\"], data[\"default\"],  normalize='index')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "d70e2a3a-4845-414b-be75-d559ae9c5a36"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 3. One estimate for loan default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "nbpresent": {
     "id": "24619971-15e1-44f0-bab6-633ad78da83a"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn import preprocessing\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "nbpresent": {
     "id": "ddd40255-6999-4407-b871-50dc2b195828"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "data_ML = data[((data[\"default\"] == 1) | (data[\"month\"] == 24))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "nbpresent": {
     "id": "061fb60f-2a68-4ce7-bfeb-a3a6b7ef7aaa"
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2155, 10)\n"
     ]
    }
   ],
   "source": [
    "print(data_ML.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What changed?\n",
    "- 2155 observations now. The default rate in this data set went up, from 7.7% to 14.15%\n",
    "- Important assumption: distribution of the variables does not change drastically when taking out censored cases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3207e440-bbe4-4614-bbc2-e4d615a006a3"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 3.1 Create dummies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbpresent": {
     "id": "f59b15a0-a6ef-4347-b12c-a2ec482f267c"
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from patsy import dmatrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "nbpresent": {
     "id": "a1f70247-9b23-4d97-b689-69cea5a34621"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Intercept', 'C(employer)[T.(2, 5]]', 'C(employer)[T.(5, 10]]',\n",
      "       'C(employer)[T.(10, 15]]', 'C(employer)[T.(15, 50]]',\n",
      "       'C(employer)[T.unknown]', 'C(payfreq)[T.bimon]',\n",
      "       'C(payfreq)[T.monthly]', 'C(payfreq)[T.biweek]',\n",
      "       'C(marstat)[T.married]', 'C(marstat)[T.divorced]',\n",
      "       'C(marstat)[T.widowed]', 'C(home)[T.no]', 'age', 'amount', 'address',\n",
      "       'children'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "# create dataframes with an intercept column and dummy variables\n",
    "y, X = dmatrices('default ~ age + amount + address + C(employer) + \\\n",
    "                  children + C(payfreq) + C(marstat) + C(home)',\n",
    "                  data_ML, return_type = \"dataframe\")\n",
    "print(X.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   default\n",
       "3      0.0\n",
       "4      0.0\n",
       "5      0.0\n",
       "7      0.0\n",
       "8      0.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Intercept</th>\n",
       "      <th>C(employer)[T.(2, 5]]</th>\n",
       "      <th>C(employer)[T.(5, 10]]</th>\n",
       "      <th>C(employer)[T.(10, 15]]</th>\n",
       "      <th>C(employer)[T.(15, 50]]</th>\n",
       "      <th>C(employer)[T.unknown]</th>\n",
       "      <th>C(payfreq)[T.bimon]</th>\n",
       "      <th>C(payfreq)[T.monthly]</th>\n",
       "      <th>C(payfreq)[T.biweek]</th>\n",
       "      <th>C(marstat)[T.married]</th>\n",
       "      <th>C(marstat)[T.divorced]</th>\n",
       "      <th>C(marstat)[T.widowed]</th>\n",
       "      <th>C(home)[T.no]</th>\n",
       "      <th>age</th>\n",
       "      <th>amount</th>\n",
       "      <th>address</th>\n",
       "      <th>children</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>8.7</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>21.5</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>62.0</td>\n",
       "      <td>1500.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>28.4</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>2.8</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Intercept  C(employer)[T.(2, 5]]  C(employer)[T.(5, 10]]  \\\n",
       "3        1.0                    0.0                     0.0   \n",
       "4        1.0                    1.0                     0.0   \n",
       "5        1.0                    0.0                     0.0   \n",
       "7        1.0                    0.0                     1.0   \n",
       "8        1.0                    1.0                     0.0   \n",
       "\n",
       "   C(employer)[T.(10, 15]]  C(employer)[T.(15, 50]]  C(employer)[T.unknown]  \\\n",
       "3                      0.0                      0.0                     1.0   \n",
       "4                      0.0                      0.0                     0.0   \n",
       "5                      0.0                      0.0                     0.0   \n",
       "7                      0.0                      0.0                     0.0   \n",
       "8                      0.0                      0.0                     0.0   \n",
       "\n",
       "   C(payfreq)[T.bimon]  C(payfreq)[T.monthly]  C(payfreq)[T.biweek]  \\\n",
       "3                  0.0                    1.0                   0.0   \n",
       "4                  0.0                    1.0                   0.0   \n",
       "5                  0.0                    1.0                   0.0   \n",
       "7                  0.0                    1.0                   0.0   \n",
       "8                  0.0                    1.0                   0.0   \n",
       "\n",
       "   C(marstat)[T.married]  C(marstat)[T.divorced]  C(marstat)[T.widowed]  \\\n",
       "3                    0.0                     0.0                    0.0   \n",
       "4                    0.0                     0.0                    0.0   \n",
       "5                    0.0                     0.0                    0.0   \n",
       "7                    1.0                     0.0                    0.0   \n",
       "8                    0.0                     0.0                    0.0   \n",
       "\n",
       "   C(home)[T.no]   age  amount  address  children  \n",
       "3            1.0  21.0  1400.0      8.7       0.0  \n",
       "4            1.0  21.0  1200.0     21.5       0.0  \n",
       "5            1.0  62.0  1500.0      1.2       0.0  \n",
       "7            0.0  52.0  5000.0     28.4       0.0  \n",
       "8            1.0  32.0  1000.0      2.8       0.0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# fix column names of X\n",
    "X = X.rename(columns = {'C(employer)[T.(2, 5]]':'emp_(2, 5]',\n",
    "                        'C(employer)[T.(5, 10]]':'emp_(5, 10]',\n",
    "                        'C(employer)[T.(10, 15]]':'emp_(10, 15]',\n",
    "                        'C(employer)[T.(15, 50]]':'emp_(15, 50]',\n",
    "                        'C(employer)[T.unknown]':'emp_unknown',\n",
    "                        'C(payfreq)[T.bimon]':'freq_bimon',\n",
    "                        'C(payfreq)[T.monthly]':'freq_monthly',\n",
    "                        'C(payfreq)[T.biweek]':'freq_biweek',\n",
    "                        'C(marstat)[T.married]': 'ms_married',\n",
    "                        'C(marstat)[T.divorced]': 'ms_divorced',\n",
    "                        'C(marstat)[T.widowed]':'ms_widowed', \n",
    "                        'C(home)[T.no]': 'home_no'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "nbpresent": {
     "id": "0f7aac61-db5c-4aa2-90ad-a565e91db98c"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Intercept</th>\n",
       "      <th>emp_(2, 5]</th>\n",
       "      <th>emp_(5, 10]</th>\n",
       "      <th>emp_(10, 15]</th>\n",
       "      <th>emp_(15, 50]</th>\n",
       "      <th>emp_unknown</th>\n",
       "      <th>freq_bimon</th>\n",
       "      <th>freq_monthly</th>\n",
       "      <th>freq_biweek</th>\n",
       "      <th>ms_married</th>\n",
       "      <th>ms_divorced</th>\n",
       "      <th>ms_widowed</th>\n",
       "      <th>home_no</th>\n",
       "      <th>age</th>\n",
       "      <th>amount</th>\n",
       "      <th>address</th>\n",
       "      <th>children</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
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       "      <td>1.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1400.0</td>\n",
       "      <td>8.7</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>21.5</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>62.0</td>\n",
       "      <td>1500.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>28.4</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>2.8</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Intercept  emp_(2, 5]  emp_(5, 10]  emp_(10, 15]  emp_(15, 50]  \\\n",
       "3        1.0         0.0          0.0           0.0           0.0   \n",
       "4        1.0         1.0          0.0           0.0           0.0   \n",
       "5        1.0         0.0          0.0           0.0           0.0   \n",
       "7        1.0         0.0          1.0           0.0           0.0   \n",
       "8        1.0         1.0          0.0           0.0           0.0   \n",
       "\n",
       "   emp_unknown  freq_bimon  freq_monthly  freq_biweek  ms_married  \\\n",
       "3          1.0         0.0           1.0          0.0         0.0   \n",
       "4          0.0         0.0           1.0          0.0         0.0   \n",
       "5          0.0         0.0           1.0          0.0         0.0   \n",
       "7          0.0         0.0           1.0          0.0         1.0   \n",
       "8          0.0         0.0           1.0          0.0         0.0   \n",
       "\n",
       "   ms_divorced  ms_widowed  home_no   age  amount  address  children  \n",
       "3          0.0         0.0      1.0  21.0  1400.0      8.7       0.0  \n",
       "4          0.0         0.0      1.0  21.0  1200.0     21.5       0.0  \n",
       "5          0.0         0.0      1.0  62.0  1500.0      1.2       0.0  \n",
       "7          0.0         0.0      0.0  52.0  5000.0     28.4       0.0  \n",
       "8          0.0         0.0      1.0  32.0  1000.0      2.8       0.0  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "nbpresent": {
     "id": "9a6ece86-fab7-48e6-ade0-b6ba69041154"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# default (y) to array, for scikit-learn to properly understand it as a response\n",
    "y = np.ravel(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "6762b3c6-2647-468d-b379-5b3298a8088e"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 3.2 Logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "0bf6c630-634c-4b64-a412-58d65c4457e3"
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### 3.2.1 Fitting a logistic regression model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "8ddc92a3-0914-4f64-86ed-a90af5488eb5"
    }
   },
   "source": [
    "- `statsmodels.api` when we look at parameters.\n",
    "- scikit-learn afterwards."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.369322\n",
      "         Iterations 7\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "logit_model = sm.Logit(y, X)\n",
    "result = logit_model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>y</td>        <th>  No. Observations:  </th>  <td>  2155</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>  2138</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>    16</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 30 Nov 2017</td> <th>  Pseudo R-squ.:     </th>  <td>0.09421</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>04:00:44</td>     <th>  Log-Likelihood:    </th> <td> -795.89</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -878.67</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>6.472e-27</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>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>    <td>   -0.1000</td> <td>    0.317</td> <td>   -0.316</td> <td> 0.752</td> <td>   -0.720     0.520</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>emp_(2, 5]</th>   <td>   -0.4435</td> <td>    0.171</td> <td>   -2.596</td> <td> 0.009</td> <td>   -0.778    -0.109</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>emp_(5, 10]</th>  <td>   -0.6014</td> <td>    0.184</td> <td>   -3.263</td> <td> 0.001</td> <td>   -0.963    -0.240</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>emp_(10, 15]</th> <td>   -1.1479</td> <td>    0.290</td> <td>   -3.959</td> <td> 0.000</td> <td>   -1.716    -0.580</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>emp_(15, 50]</th> <td>   -1.6232</td> <td>    0.331</td> <td>   -4.903</td> <td> 0.000</td> <td>   -2.272    -0.974</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>emp_unknown</th>  <td>   -0.4880</td> <td>    0.230</td> <td>   -2.119</td> <td> 0.034</td> <td>   -0.939    -0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>freq_bimon</th>   <td>   -0.1897</td> <td>    0.385</td> <td>   -0.492</td> <td> 0.623</td> <td>   -0.945     0.566</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>freq_monthly</th> <td>   -0.5853</td> <td>    0.136</td> <td>   -4.299</td> <td> 0.000</td> <td>   -0.852    -0.318</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>freq_biweek</th>  <td>    0.7253</td> <td>    0.562</td> <td>    1.290</td> <td> 0.197</td> <td>   -0.377     1.828</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ms_married</th>   <td>   -0.0789</td> <td>    0.183</td> <td>   -0.430</td> <td> 0.667</td> <td>   -0.438     0.281</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ms_divorced</th>  <td>    0.5474</td> <td>    0.268</td> <td>    2.039</td> <td> 0.041</td> <td>    0.021     1.074</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ms_widowed</th>   <td>    0.5839</td> <td>    0.815</td> <td>    0.716</td> <td> 0.474</td> <td>   -1.014     2.182</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>home_no</th>      <td>    0.3001</td> <td>    0.146</td> <td>    2.062</td> <td> 0.039</td> <td>    0.015     0.585</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age</th>          <td>   -0.0187</td> <td>    0.008</td> <td>   -2.212</td> <td> 0.027</td> <td>   -0.035    -0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>amount</th>       <td>-4.717e-05</td> <td> 6.44e-05</td> <td>   -0.732</td> <td> 0.464</td> <td>   -0.000  7.91e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>address</th>      <td>   -0.0453</td> <td>    0.010</td> <td>   -4.407</td> <td> 0.000</td> <td>   -0.065    -0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>children</th>     <td>    0.0853</td> <td>    0.072</td> <td>    1.181</td> <td> 0.238</td> <td>   -0.056     0.227</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                 2155\n",
       "Model:                          Logit   Df Residuals:                     2138\n",
       "Method:                           MLE   Df Model:                           16\n",
       "Date:                Thu, 30 Nov 2017   Pseudo R-squ.:                 0.09421\n",
       "Time:                        04:00:44   Log-Likelihood:                -795.89\n",
       "converged:                       True   LL-Null:                       -878.67\n",
       "                                        LLR p-value:                 6.472e-27\n",
       "================================================================================\n",
       "                   coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
       "--------------------------------------------------------------------------------\n",
       "Intercept       -0.1000      0.317     -0.316      0.752        -0.720     0.520\n",
       "emp_(2, 5]      -0.4435      0.171     -2.596      0.009        -0.778    -0.109\n",
       "emp_(5, 10]     -0.6014      0.184     -3.263      0.001        -0.963    -0.240\n",
       "emp_(10, 15]    -1.1479      0.290     -3.959      0.000        -1.716    -0.580\n",
       "emp_(15, 50]    -1.6232      0.331     -4.903      0.000        -2.272    -0.974\n",
       "emp_unknown     -0.4880      0.230     -2.119      0.034        -0.939    -0.037\n",
       "freq_bimon      -0.1897      0.385     -0.492      0.623        -0.945     0.566\n",
       "freq_monthly    -0.5853      0.136     -4.299      0.000        -0.852    -0.318\n",
       "freq_biweek      0.7253      0.562      1.290      0.197        -0.377     1.828\n",
       "ms_married      -0.0789      0.183     -0.430      0.667        -0.438     0.281\n",
       "ms_divorced      0.5474      0.268      2.039      0.041         0.021     1.074\n",
       "ms_widowed       0.5839      0.815      0.716      0.474        -1.014     2.182\n",
       "home_no          0.3001      0.146      2.062      0.039         0.015     0.585\n",
       "age             -0.0187      0.008     -2.212      0.027        -0.035    -0.002\n",
       "amount       -4.717e-05   6.44e-05     -0.732      0.464        -0.000  7.91e-05\n",
       "address         -0.0453      0.010     -4.407      0.000        -0.065    -0.025\n",
       "children         0.0853      0.072      1.181      0.238        -0.056     0.227\n",
       "================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "How does a 1 unit increase/decrease affect the odds of default?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept       0.904877\n",
       "emp_(2, 5]      0.641781\n",
       "emp_(5, 10]     0.548017\n",
       "emp_(10, 15]    0.317298\n",
       "emp_(15, 50]    0.197275\n",
       "emp_unknown     0.613843\n",
       "freq_bimon      0.827194\n",
       "freq_monthly    0.556911\n",
       "freq_biweek     2.065345\n",
       "ms_married      0.924139\n",
       "ms_divorced     1.728750\n",
       "ms_widowed      1.793050\n",
       "home_no         1.349971\n",
       "age             0.981426\n",
       "amount          0.999953\n",
       "address         0.955713\n",
       "children        1.089003\n",
       "dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(result.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "f5c387c2-df51-40b5-925f-d30c2c65879f"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "You'll notice that the results are slightly different in SK-learn. https://stats.stackexchange.com/questions/203740/logistic-regression-scikit-learn-vs-statsmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Parameters through scikit learn:"
   ]
  },
  {
   "cell_type": "code",
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    "nbpresent": {
     "id": "691d824a-f35b-4567-b430-5f5711756c1f"
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     "data": {
      "text/plain": [
       "LogisticRegression(C=1000000000000.0, class_weight=None, dual=False,\n",
       "          fit_intercept=False, intercept_scaling=1, max_iter=100,\n",
       "          multi_class='ovr', n_jobs=1, penalty='l2', random_state=None,\n",
       "          solver='liblinear', tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# logistic regression model on all the data using scikit learn (C = inverse regularization strength)\n",
    "logreg = LogisticRegression(fit_intercept = False, C = 1e12)\n",
    "model_log = logreg.fit(X, y)\n",
    "model_log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "nbpresent": {
     "id": "79550a08-e855-4010-9716-0837e2bc2fe2"
    }
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    {
     "data": {
      "text/plain": [
       "array([[ -1.10398342e-01,  -4.38962462e-01,  -6.05328755e-01,\n",
       "         -1.14820612e+00,  -1.62173934e+00,  -4.89412887e-01,\n",
       "         -2.02408005e-01,  -5.84734962e-01,   4.29731327e-01,\n",
       "         -1.34366332e-01,   5.38176357e-01,   1.91702925e-01,\n",
       "          3.00616585e-01,  -1.73694244e-02,  -5.06806869e-05,\n",
       "         -4.55095478e-02,   9.55282520e-02]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_log.coef_"
   ]
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  {
   "cell_type": "markdown",
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     "id": "24fc40c9-4508-46f2-92aa-d3c6a2f375a1"
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   "source": [
    "#### 3.2.2 Using the model to predict the probability of loan default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict the probability of default for someone who\n",
    "Started a new job **last year**, repays **monthly**, is **widowed**, does **not own** a house, is **50 years old**, borrowed **4k USD**, has been living at the same **address for 24 years**, has **1 child**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "nbpresent": {
     "id": "07a0d936-97a4-4a8d-85c6-634402695619"
    }
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Intercept', 'emp_(2, 5]', 'emp_(5, 10]', 'emp_(10, 15]',\n",
      "       'emp_(15, 50]', 'emp_unknown', 'freq_bimon', 'freq_monthly',\n",
      "       'freq_biweek', 'ms_married', 'ms_divorced', 'ms_widowed', 'home_no',\n",
      "       'age', 'amount', 'address', 'children'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "print(X.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "nbpresent": {
     "id": "5bc8b3f5-3fb6-4255-bdf7-17a037eede0d"
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   "outputs": [],
   "source": [
    "predict_1= np.array([1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 50, 4000, 24, 1]).reshape(1, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "nbpresent": {
     "id": "c2b4f99b-0b99-4bc4-93ed-1243c9656315"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.90642191,  0.09357809]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_log.predict_proba(predict_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "**Do it yourself!**\n",
    "\n",
    "Predict the probability of default for someone who\n",
    "- is at the same job for 8 years now\n",
    "- Repays quarterly\n",
    "- is married\n",
    "- does not own a house\n",
    "- is 38 years old\n",
    "- borrowed 9k USD\n",
    "- moved 2 years ago\n",
    "- has 3 children"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "predict_2 = ___\n",
    "model_log.predict_proba(predict_2)"
   ]
  }
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