Multiple imputation with mice.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 使用mice进行缺失值处理\n",
    "\n",
    "##### 黄荣贵（复旦大学社会学系）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: lattice\n",
      "\n",
      "Attaching package: ‘mice’\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    cbind, rbind\n",
      "\n"
     ]
    }
   ],
   "source": [
    "################\n",
    "# use mice packge to do multiple imputations\n",
    "################\n",
    "\n",
    "library(mice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   age  bmi hyp chl\n",
      "1    1   NA  NA  NA\n",
      "2    2 22.7   1 187\n",
      "3    1   NA   1 187\n",
      "4    3   NA  NA  NA\n",
      "5    1 20.4   1 113\n",
      "6    3   NA  NA 184\n",
      "7    1 22.5   1 118\n",
      "8    1 30.1   1 187\n",
      "9    2 22.0   1 238\n",
      "10   2   NA  NA  NA\n",
      "11   1   NA  NA  NA\n",
      "12   2   NA  NA  NA\n",
      "13   3 21.7   1 206\n",
      "14   2 28.7   2 204\n",
      "15   1 29.6   1  NA\n",
      "16   1   NA  NA  NA\n",
      "17   3 27.2   2 284\n",
      "18   2 26.3   2 199\n",
      "19   1 35.3   1 218\n",
      "20   3 25.5   2  NA\n",
      "21   1   NA  NA  NA\n",
      "22   1 33.2   1 229\n",
      "23   1 27.5   1 131\n",
      "24   3 24.9   1  NA\n",
      "25   2 27.4   1 186\n"
     ]
    }
   ],
   "source": [
    "print(nhanes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$rr</dt>\n",
       "\t\t<dd><table>\n",
       "<thead><tr><th></th><th scope=col>age</th><th scope=col>bmi</th><th scope=col>hyp</th><th scope=col>chl</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>age</th><td>25</td><td>16</td><td>17</td><td>15</td></tr>\n",
       "\t<tr><th scope=row>bmi</th><td>16</td><td>16</td><td>16</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>hyp</th><td>17</td><td>16</td><td>17</td><td>14</td></tr>\n",
       "\t<tr><th scope=row>chl</th><td>15</td><td>13</td><td>14</td><td>15</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$rm</dt>\n",
       "\t\t<dd><table>\n",
       "<thead><tr><th></th><th scope=col>age</th><th scope=col>bmi</th><th scope=col>hyp</th><th scope=col>chl</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>age</th><td>0 </td><td>9 </td><td>8 </td><td>10</td></tr>\n",
       "\t<tr><th scope=row>bmi</th><td>0 </td><td>0 </td><td>0 </td><td> 3</td></tr>\n",
       "\t<tr><th scope=row>hyp</th><td>0 </td><td>1 </td><td>0 </td><td> 3</td></tr>\n",
       "\t<tr><th scope=row>chl</th><td>0 </td><td>2 </td><td>1 </td><td> 0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$mr</dt>\n",
       "\t\t<dd><table>\n",
       "<thead><tr><th></th><th scope=col>age</th><th scope=col>bmi</th><th scope=col>hyp</th><th scope=col>chl</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>age</th><td> 0</td><td>0 </td><td>0 </td><td>0 </td></tr>\n",
       "\t<tr><th scope=row>bmi</th><td> 9</td><td>0 </td><td>1 </td><td>2 </td></tr>\n",
       "\t<tr><th scope=row>hyp</th><td> 8</td><td>0 </td><td>0 </td><td>1 </td></tr>\n",
       "\t<tr><th scope=row>chl</th><td>10</td><td>3 </td><td>3 </td><td>0 </td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$mm</dt>\n",
       "\t\t<dd><table>\n",
       "<thead><tr><th></th><th scope=col>age</th><th scope=col>bmi</th><th scope=col>hyp</th><th scope=col>chl</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>age</th><td>0 </td><td>0 </td><td>0 </td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>bmi</th><td>0 </td><td>9 </td><td>8 </td><td> 7</td></tr>\n",
       "\t<tr><th scope=row>hyp</th><td>0 </td><td>8 </td><td>8 </td><td> 7</td></tr>\n",
       "\t<tr><th scope=row>chl</th><td>0 </td><td>7 </td><td>7 </td><td>10</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$rr] \\begin{tabular}{r|llll}\n",
       "  & age & bmi & hyp & chl\\\\\n",
       "\\hline\n",
       "\tage & 25 & 16 & 17 & 15\\\\\n",
       "\tbmi & 16 & 16 & 16 & 13\\\\\n",
       "\thyp & 17 & 16 & 17 & 14\\\\\n",
       "\tchl & 15 & 13 & 14 & 15\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$rm] \\begin{tabular}{r|llll}\n",
       "  & age & bmi & hyp & chl\\\\\n",
       "\\hline\n",
       "\tage & 0  & 9  & 8  & 10\\\\\n",
       "\tbmi & 0  & 0  & 0  &  3\\\\\n",
       "\thyp & 0  & 1  & 0  &  3\\\\\n",
       "\tchl & 0  & 2  & 1  &  0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$mr] \\begin{tabular}{r|llll}\n",
       "  & age & bmi & hyp & chl\\\\\n",
       "\\hline\n",
       "\tage &  0 & 0  & 0  & 0 \\\\\n",
       "\tbmi &  9 & 0  & 1  & 2 \\\\\n",
       "\thyp &  8 & 0  & 0  & 1 \\\\\n",
       "\tchl & 10 & 3  & 3  & 0 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$mm] \\begin{tabular}{r|llll}\n",
       "  & age & bmi & hyp & chl\\\\\n",
       "\\hline\n",
       "\tage & 0  & 0  & 0  &  0\\\\\n",
       "\tbmi & 0  & 9  & 8  &  7\\\\\n",
       "\thyp & 0  & 8  & 8  &  7\\\\\n",
       "\tchl & 0  & 7  & 7  & 10\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$rr\n",
       ":   \n",
       "| <!--/--> | age | bmi | hyp | chl | \n",
       "|---|---|---|---|\n",
       "| age | 25 | 16 | 17 | 15 | \n",
       "| bmi | 16 | 16 | 16 | 13 | \n",
       "| hyp | 17 | 16 | 17 | 14 | \n",
       "| chl | 15 | 13 | 14 | 15 | \n",
       "\n",
       "\n",
       "\n",
       "$rm\n",
       ":   \n",
       "| <!--/--> | age | bmi | hyp | chl | \n",
       "|---|---|---|---|\n",
       "| age | 0  | 9  | 8  | 10 | \n",
       "| bmi | 0  | 0  | 0  |  3 | \n",
       "| hyp | 0  | 1  | 0  |  3 | \n",
       "| chl | 0  | 2  | 1  |  0 | \n",
       "\n",
       "\n",
       "\n",
       "$mr\n",
       ":   \n",
       "| <!--/--> | age | bmi | hyp | chl | \n",
       "|---|---|---|---|\n",
       "| age |  0 | 0  | 0  | 0  | \n",
       "| bmi |  9 | 0  | 1  | 2  | \n",
       "| hyp |  8 | 0  | 0  | 1  | \n",
       "| chl | 10 | 3  | 3  | 0  | \n",
       "\n",
       "\n",
       "\n",
       "$mm\n",
       ":   \n",
       "| <!--/--> | age | bmi | hyp | chl | \n",
       "|---|---|---|---|\n",
       "| age | 0  | 0  | 0  |  0 | \n",
       "| bmi | 0  | 9  | 8  |  7 | \n",
       "| hyp | 0  | 8  | 8  |  7 | \n",
       "| chl | 0  | 7  | 7  | 10 | \n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$rr\n",
       "    age bmi hyp chl\n",
       "age  25  16  17  15\n",
       "bmi  16  16  16  13\n",
       "hyp  17  16  17  14\n",
       "chl  15  13  14  15\n",
       "\n",
       "$rm\n",
       "    age bmi hyp chl\n",
       "age   0   9   8  10\n",
       "bmi   0   0   0   3\n",
       "hyp   0   1   0   3\n",
       "chl   0   2   1   0\n",
       "\n",
       "$mr\n",
       "    age bmi hyp chl\n",
       "age   0   0   0   0\n",
       "bmi   9   0   1   2\n",
       "hyp   8   0   0   1\n",
       "chl  10   3   3   0\n",
       "\n",
       "$mm\n",
       "    age bmi hyp chl\n",
       "age   0   0   0   0\n",
       "bmi   0   9   8   7\n",
       "hyp   0   8   8   7\n",
       "chl   0   7   7  10\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p <- md.pairs(nhanes)\n",
    "\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* rr行列都观察到\n",
    "* rm行观察到，列缺失"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>age</th><th scope=col>hyp</th><th scope=col>bmi</th><th scope=col>chl</th><th scope=col></th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>13</th><td>1 </td><td>1 </td><td>1 </td><td> 1</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>1 </td><td>1 </td><td>1 </td><td> 0</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>1</th><td>1 </td><td>1 </td><td>0 </td><td> 1</td><td> 1</td></tr>\n",
       "\t<tr><th scope=row>1</th><td>1 </td><td>0 </td><td>0 </td><td> 1</td><td> 2</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1 </td><td>0 </td><td>0 </td><td> 0</td><td> 3</td></tr>\n",
       "\t<tr><th scope=row></th><td>0 </td><td>8 </td><td>9 </td><td>10</td><td>27</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & age & hyp & bmi & chl & \\\\\n",
       "\\hline\n",
       "\t13 & 1  & 1  & 1  &  1 &  0\\\\\n",
       "\t3 & 1  & 1  & 1  &  0 &  1\\\\\n",
       "\t1 & 1  & 1  & 0  &  1 &  1\\\\\n",
       "\t1 & 1  & 0  & 0  &  1 &  2\\\\\n",
       "\t7 & 1  & 0  & 0  &  0 &  3\\\\\n",
       "\t & 0  & 8  & 9  & 10 & 27\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | age | hyp | bmi | chl |  | \n",
       "|---|---|---|---|---|---|\n",
       "| 13 | 1  | 1  | 1  |  1 |  0 | \n",
       "| 3 | 1  | 1  | 1  |  0 |  1 | \n",
       "| 1 | 1  | 1  | 0  |  1 |  1 | \n",
       "| 1 | 1  | 0  | 0  |  1 |  2 | \n",
       "| 7 | 1  | 0  | 0  |  0 |  3 | \n",
       "|  | 0  | 8  | 9  | 10 | 27 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   age hyp bmi chl   \n",
       "13 1   1   1    1   0\n",
       "3  1   1   1    0   1\n",
       "1  1   1   0    1   1\n",
       "1  1   0   0    1   2\n",
       "7  1   0   0    0   3\n",
       "   0   8   9   10  27"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mPT/JKnHKOfTbptjX8JFBCY9EtY4DCmJHA7ge/F0nUR+W01+Va7fCXT13cGgkGA\nAAECBHoqcM3wvHefcP7NulUTtllFYNEFNEiLTmrCLRTIzx7l/5J9aMR+W/izdidAgAABAgSW\nhsDmNEj5FeAGgeICGqTixA4QAjtG5GeNmq/0HkeZG65YPb7BMgECBAgQINALgf8YnmV+3ff4\naNY132Y3vt0ygUUV0CAtKqfJFhDIxidfFs87uMPH9jkylvN/yv5KRPMhzLFdLBIgQIAAAQJL\nXOCTcX5fj3haRPOFDXnKuwzX5eOET+UKg0BpAQ1SaWHzNwIvjCv5SlF+Y91rIx4ZkV/v/ZGI\nWyN+O8IgQIAAAQIE+ivwmjj1vSIuiHhyxFOG1+8Ul8+KyMcLBoHiAr7muzixAwwFPhOXj434\nm4hThhEXg89F/E7EV3PBIECAAAECBHor8L4483zy/g0Rpw0VfhKX+a23+Y23BoGpCGiQpsLc\nm4OcFWc6s5GzPS+23Ssi/6O3fSIujbgxwiBAgAABAgQIpMA/Rrw34sCIlRH5GeZ1EQaBqQlo\nkKZG7UAjAvktNL6JZgTEVQIECBAgQOC/BObjWjZGBoFWBHwGqRV2ByVAgAABAgQIECBAoIsC\nGqQuVkVOBAgQIECAAAECBAi0IqBBaoXdQQkQIECAAAECBAgQ6KKABqmLVZETAQIECBAgQIAA\nAQKtCGiQWmF3UAIECBAgQIAAAQIEuiigQepiVeREgAABAgQIECBAgEArAhqkVtgdlAABAgQI\nECBAgACBLgpokLpYFTkRIECAAAECBAgQINCKgAapFXYHJUCAAAECBAgQIECgiwIapC5WRU4E\nCBAgQIAAAQIECLQioEFqhd1BCRAgQIAAAQIECBDoooAGqYtVkRMBAgQIECBAgAABAq0IaJBa\nYXdQAgQIECBAgAABAgS6KKBB6mJV5ESAAAECBAgQIECAQCsCGqRW2B2UAAECBAgQIECAAIEu\nCmiQulgVOREgQIAAAQIECBAg0IqABqkVdgclQIAAAQIECBAgQKCLAhqkLlZFTgQIECBAgAAB\nAgQItCKgQWqF3UEJECBAgAABAgQIEOiigAapi1WREwECBAgQIECAAAECrQhokFphd1ACBAgQ\nIECAAAECBLoooEHqYlXkRIAAAQIECBAgQIBAKwIapFbYHZQAAQIECBAgQIAAgS4KaJC6WBU5\nESBAgAABAgQIECDQioAGqRV2ByVAgAABAgQIECBAoIsCGqQuVkVOBAgQIECAAAECBAi0IqBB\naoXdQQkQIECAAAECBAgQ6KKABqmLVZETAQIECBAgQIAAAQKtCGiQWmF3UAIECBAgQIAAAQIE\nuiigQepiVeREgAABAgQIECBAgEArAhqkVtgdlAABAgQIECBAgACBLgpokLpYFTkRIECAAAEC\nBAgQINCKgAapFXYHJUCAAAECBAgQIECgiwIapC5WRU4ECBAgQIAAAQIECLQioEFqhd1BCRAg\nQIAAAQIECBDoooAGqYtVkRMBAgQIECBAgAABAq0IaJBaYXdQAgQIECBAgAABAgS6KKBB6mJV\n5ESAAAECBAgQIECAQCsCGqRW2B2UAAECBAgQIECAAIEuCmiQulgVOREgQIAAAQIECBAg0IqA\nBqkVdgclQIAAAQIECBAgQKCLAhqkLlZFTgQIECBAgAABAgQItCKgQWqF3UEJECBAgAABAgQI\nEOiigAapi1WREwECBAgQIECAAAECrQhokFphd1ACBAgQIECAAAECBLoosLyLScmJQLsC89ts\nuPGKuwwuP3tlu3k4+hYLzG9YPr/mR9utv/zse27xz/qBdgVuXbtifu2qGbVrtwxbc/T5dau3\nm5mZWa52W6PX7s/E37pdB4P59e1m4egEuicw072UZESgZYGZZasH8/Pbt5yFw2+NwEzcpc3P\nb81P+pnWBbJu/iS1XoatSkDttoqtKz80M7NmMD+3Y1fSkQeBLgh4BakLVZBDxwRmr1txn6et\nXnHIiVd3LDHpbEJgzRlPOWZ234f8bOWDXnzhJna1uWMCaz78jEcs2+Vug20ffuoFHUtNOpsQ\nuPljJz9031U/2uG1gwedu4ldbe6YwBmDK/c7Y/6qHTd0LC/pEGhbwGeQ2q6A4xMgQIAAAQIE\nCBAg0BkBDVJnSiERAgQIECBAgAABAgTaFtAgtV0BxydAgAABAgQIECBAoDMCGqTOlEIiBAgQ\nIECAAAECBAi0LaBBarsCjk+AAAECBAgQIECAQGcENEidKYVECBAgQIAAAQIECBBoW0CD1HYF\nHJ8AAQIECBAgQIAAgc4IaJA6UwqJECBAgAABAgQIECDQtoAGqe0KOD4BAgQIECBAgAABAp0R\n0CB1phQSIUCAAAECBAgQIECgbQENUtsVcHwCBAgQIECAAAECBDojoEHqTCkkQoAAAQIECBAg\nQIBA2wIapLYr4PgECBAgQIAAAQIECHRGQIPUmVJIhAABAgQIECBAgACBtgU0SG1XwPEJECBA\ngAABAgQIEOiMgAapM6WQCAECBAgQIECAAAECbQtokNqugOMTIECAAAECBAgQINAZAQ1SZ0oh\nEQIECBAgQIAAAQIE2hbQILVdAccnQIAAAQIECBAgQKAzAhqkzpRCIgQIECBAgAABAgQItC2g\nQWq7Ao5PgAABAgQIECBAgEBnBDRInSmFRAgQIECAAAECBAgQaFtAg9R2BRyfAAECBAgQIECA\nAIHOCGiQOlMKiRAgQIAAAQIECBAg0LaABqntCjg+AQIECBAgQIAAAQKdEdAgdaYUEiFAgAAB\nAgQIECBAoG0BDVLbFXB8AgQIECBAgAABAgQ6I6BB6kwpJEKAAAECBAgQIECAQNsCGqS2K+D4\nBAgQIECAAAECBAh0RkCD1JlSSIQAAQIECBAgQIAAgbYFNEhtV8DxCRAgQIAAAQIECBDojIAG\nqTOlkAgBAgQIECBAgAABAm0LaJDaroDjEyBAgAABAgQIECDQGQENUmdKIRECBAgQIECAAAEC\nBNoW0CC1XQHHJ0CAAAECBAgQIECgMwIapM6UQiIECBAgQIAAAQIECLQtoEFquwKOT4AAAQIE\nCBAgQIBAZwQ0SJ0phUQIECBAgAABAgQIEGhbQIPUdgUcnwABAgQIECBAgACBzghokDpTCokQ\nIECAAAECBAgQINC2gAap7Qo4PgECBAgQIECAAAECnRHQIHWmFBIhQIAAAQIECBAgQKBtAQ1S\n2xVwfAIECBAgQIAAAQIEOiOgQepMKSRCgAABAgQIECBAgEDbAhqktivg+AQIECBAgAABAgQI\ndEZAg9SZUkiEAAECBAgQIECAAIG2BZa3nYDj905gpzjjIyJ2i/h8xLURBgECBAgQIECAAIFO\nCHgFqRNl6E0SJ8aZXhHxiYgzIq6JuDBizwiDAAECBAgQIDAqsH8sPH10hesEpiGgQZqGsmOk\nwMMj3h1xY8RzIu4b8YqIwyP+LWJlhEGAAAECBAgQSIGdI86JeFMuGASmKeAtdtPU7vexTonT\nn414UcTZQ4pvxOX+Ec+MyAbq3AiDAAECBAgQ6LdAvg3/fRH3jljdbwpn34aAV5DaUO/nMT8U\np/1nEfls0Og4f7iQd4IGAQIECBAg0G+BJ8XpXxzxmIhb+k3h7NsS0CC1Jd+/4741TvllEfMj\npz4T1/OOMMfHb7vwLwECBAgQINBTgcfGeZ8esU3EcRHZKBkEpi6gQZo6uQOGwCERr4r4UkTe\nAb40wp1gIBgECBAgQKDHArfGuZ8acVDEWT12cOotC/gMUssF6Onh83NIJw3P/bK4/GhPHZw2\nAQIECBAg8HOB/CyyzyP/3MO1lgS8gtQSfM8Pm68e7RXx3Ii1ERdF5DfbGQQIECBAgAABAgRa\nFdAgtcrf24N/L878uoi3RJwQka9kPj/CIECAAAECBAgQINCqgAapVX4HD4H87NHnIw6N2C/C\nIECAAAECBAgQINCagAapNfpeHXjHONv8rFHzld7jJz83XOH/OhiXsUyAAAECBAgQIDBVAQ3S\nVLl7e7BsfFZFHBVx+JjCkbH84IivRNwwts0iAQIECBAgQIAAgakKaJCmyt3rg70wzj5fKcpv\nrHttxCMj8uu9PxKRX+v52xEGAQIECBAgQIAAgVYFNEit8vfq4J+Js83/AC5fJTol4ryIP4u4\nJOJBEV+OMAgQIECAAAECBAi0KuD/QWqVv3cHz6boXhH7RuwTcWnEjREGAQIECBAgQIAAgU4I\naJA6UYbeJfH9OOMMgwABAgQIECCwkMARC22wnkBJAW+xK6lrbgIECBAgQIAAAQIEqhLQIFVV\nLskSIECAAAECBAgQIFBSQINUUtfcBAgQIECAAAECBAhUJaBBqqpckiVAgAABAgQIECBAoKSA\nBqmkrrkJECBAgAABAgQIEKhKQINUVbkkS4AAAQIECBAgQIBASQENUkldcxMgQIAAAQIECBAg\nUJWABqmqckmWAAECBAgQIECAAIGSAhqkkrrmJkCAAAECBAgQIECgKgENUlXlkiwBAgQIECBA\ngAABAiUFNEgldc1NgAABAgQIECBAgEBVAhqkqsolWQIECBAgQIAAAQIESgpokErqmpsAAQIE\nCBAgQIAAgaoENEhVlUuyBAgQIECAAAECBAiUFNAgldQ1NwECBAgQIECAAAECVQlokKoql2QJ\nECBAgAABAgQIECgpoEEqqWtuAgQIECBAgAABAgSqEtAgVVUuyRIgQIAAAQIECBAgUFJAg1RS\n19wECBAgQIAAAQIECFQloEGqqlySJUCAAAECBAgQIECgpIAGqaSuuQkQIECAAAECBAgQqEpA\ng1RVuSRLgAABAgQIECBAgEBJAQ1SSV1zEyBAgAABAgQIECBQlYAGqapySZYAAQIECBAgQIAA\ngZICGqSSuuYmQIAAAQIECBAgQKAqAQ1SVeWSLAECBAgQIECAAAECJQU0SCV1zU2AAAECBAgQ\nIECAQFUCGqSqyiVZAgQIECBAgAABAgRKCmiQSuqamwABAgQIECBAgACBqgQ0SFWVS7IECBAg\nQIAAAQIECJQU0CCV1DU3AQIECBAgQIAAAQJVCWiQqiqXZAkQIECAAAECBAgQKCmgQSqpa24C\nBAgQIECAAAECBKoS0CBVVS7JEiBAgAABAgQIECBQUkCDVFLX3AQIECBAgAABAgQIVCWgQaqq\nXJIlQIAAAQIECBAgQKCkgAappK65CRAgQIAAAQIECBCoSkCDVFW5JEuAAAECBAgQIECAQEkB\nDVJJXXMTIECAAAECBAgQIFCVgAapqnJJlgABAgQIECBAgACBkgIapJK65iZAgAABAgQIECBA\noCoBDVJV5ZIsAQIECBAgQIAAAQIlBTRIJXXNTYAAAQIECBAgQIBAVQIapKrKJVkCBAgQIECA\nAAECBEoKaJBK6pqbAAECBAgQIECAAIGqBJZXla1kCUxHYHZuzY92ufW6i/aazuEcZdEE5ueW\nza/76TZqt2ii05tobv3s4NY1A7WbHvliHWn+1nUrbhnMzX5t8GP3mYuFOqV5rh+s22VKh3IY\nAlUJzFSVrWQJTENgZtmawfzcdtM4lGMstkC+KD632JOajwABAktWYNlg5ua5wfz2S/YEnRiB\nrRDwCtJWoPmRJS4wP3Ptsns8Yd2KA4+9Zomf6ZI7vXXnvfhhy/Y6fM2KQ3/jS0vu5Jb4Ca07\n/w+PPHj9YP63Bgd9bomf6pI7vb8afP2IH+yw+w4rf/nln15yJ7fET2j95R/ZZ+6yc1YOBhuW\n+Jk6PQJbJqBB2jIve/dBYGbZYHblLutnd97/5j6c7pI6x5ll8zPLt5tTuwqrOjs7v836+cEv\nDHZwu6usfCsGs/Mzy5bPu91VVrhIdy7+1s3NLFs5mNcg1Vc9GZcU8CUNJXXNTYAAAQIECBAg\nQIBAVQIapKrKJVkCBAgQIECAAAECBEoKaJBK6pqbAAECBAgQIECAAIGqBDRIVZVLsgQIECBA\ngAABAgQIlBTQIJXUNTcBAgQIECBAgAABAlUJaJCqKpdkCRAgQIAAAQIECBAoKaBBKqlrbgIE\nCBAgQIAAAQIEqhLQIFVVLskSIECAAAECBAgQIFBSQINUUtfcBAgQIECAAAECBAhUJaBBqqpc\nkiVAgAABAgQIECBAoKSABqmkrrkJECBAgAABAgQIEKhKQINUVbkkS4AAAQIECBAgQIBASQEN\nUkldcxMgQIAAAQIECBAgUJWABqmqckmWAAECBAgQIECAAIGSAhqkkrrmJkCAAAECBAgQIECg\nKgENUlXlkiwBAgQIECBAgAABAiUFNEgldc1NgAABAgQIECBAgEBVAhqkqsolWQIECBAgQIAA\nAQIESgpokErqmpsAAQIECBAgQIAAgaoENEhVlUuyBAgQIECAAAECBAiUFNAgldQ1NwECBAgQ\nIECAAAECVQlokKoql2QJECBAgAABAgQIECgpoEEqqWtuAgQIECBAgAABAgSqEtAgVVUuyRIg\nQIAAAQIECBAgUFJAg1RS19wECBAgQIAAAQIECFQloEGqqlySJUCAAAECBAgQIECgpIAGqaSu\nuQkQIECAAAECBAgQqEpAg1RVuSRLgAABAgQIECBAgEBJAQ1SSV1zEyBAgAABAgQIECBQlYAG\nqapySZYAAQIECBAgQIAAgZICGqSSuuYmQIAAAQIECBAgQKAqAQ1SVeWSLAECBAgQIECAAAEC\nJQU0SCV1zU2AAAECBAgQIECAQFUCGqSqyiVZAgQIECBAgAABAgRKCmiQSuqamwABAgQIECBA\ngACBqgQ0SFWVS7IECBAgQIAAAQIECJQU0CCV1DU3AQIECBAgQIAAAQJVCWiQqiqXZAkQIECA\nAAECBAgQKCmgQSqpa24CBAgQIECAAAECBKoS0CBVVS7JEiBAgAABAgQIECBQUkCDVFLX3AQI\nECBAgAABAgQIVCWgQaqqXJIlQIAAAQIECBAgQKCkgAappK65CRAgQIAAAQIECBCoSkCDVFW5\nJEuAAAECBAgQIECAQEkBDVJJXXMTIECAAAECBAgQIFCVgAapqnJJlgABAgQIECBAgACBkgIa\npJK65t6UwPGxw302tZPtBAgQIECAQC8F9o+zfnovz9xJtyqgQWqVv9cHPynO/oyIY3ut4OQJ\nECBAgACBSQI7x8pzIt40aaN1BEoKaJBK6pp7IYHjYsMbF9poPQECBAgQINBrgd3i7D8Yce9e\nKzj51gQ0SK3R9/LAe8RZvyfizIi5Xgo4aQIECBAgQGBjAk+KjRdHPCbilo3taBuBUgIapFKy\n5p0kkC+V53uJT4t4zqQdrCNAgAABAgR6K/DYOPPTI7aJyHebZKNkEJi6gAZp6uS9PuCX4uyP\niXhqxI29lnDyBAgQIECAwLjArbHi1IiDIs4a32iZwLQElk/rQI5DIAROpkCAAAECBAgQWEDg\n3FifYRBoVcArSK3yOzgBAgQIECBAgAABAl0S0CB1qRpyIUCAAAECBAgQIECgVQENUqv8Dk6A\nAAECBAgQIECAQJcENEhdqoZcCBAgQIAAAQIECBBoVUCD1Cq/gxMgQIAAAQIECBAg0CUBDVKX\nqiEXAgQIECBAgAABAgRaFdAgtcrv4AQIECBAgAABAgQIdElAg9SlasiFAAECBAgQIECAAIFW\nBfxHsa3y9/rg+T9kz/RawMkTIECAAAECGxM4YmMbbSNQSsArSKVkzUuAAAECBAgQIECAQHUC\nGqTqSiZhAgQIECBAgAABAgRKCWiQSsmalwABAgQIECBAgACB6gQ0SNWVTMIECBAgQIAAAQIE\nCJQS0CCVkjUvAQIECBAgQIAAAQLVCWiQqiuZhAkQIECAAAECBAgQKCWgQSola14CBAgQIECA\nAAECBKoT0CBVVzIJEyBAgAABAgQIECBQSkCDVErWvAQIECBAgAABAgQIVCegQaquZBImQIAA\nAQIECBAgQKCUgAaplKx5CRAgQIAAAQIECBCoTkCDVF3JJEyAAAECBAgQIECAQCkBDVIpWfMS\nIECAAAECBAgQIFCdgAapupJJmAABAgQIECBAgACBUgIapFKy5iVAgAABAgQIECBAoDoBDVJ1\nJZMwAQIECBAgQIAAAQKlBDRIpWTNS4AAAQIECBAgQIBAdQIapOpKJmECBAgQIECAAAECBEoJ\naJBKyZqXAAECBAgQIECAAIHqBDRI1ZVMwgQIECBAgAABAgQIlBLQIJWSNS8BAgQIECBAgAAB\nAtUJaJCqK5mECRAgQIAAAQIECBAoJaBBKiVrXgIECBAgQIAAAQIEqhPQIFVXMgkTIECAAAEC\nBAgQIFBKQINUSta8BAgQIECAAAECBAhUJ6BBqq5kEiZAgAABAgQIECBAoJSABqmUrHkJECBA\ngAABAgQIEKhOQINUXckkTIAAAQIECBAgQIBAKQENUilZ8xIgQIAAAQIECBAgUJ2ABqm6kkmY\nAAECBAgQIECAAIFSAhqkUrLmJUCAAAECBAgQIECgOgENUnUlkzABAgQIECBAgAABAqUENEil\nZM1LgAABAgQIECBAgEB1Ahqk6komYQIECBAgQIAAAQIESglokErJmpcAAQIECBAgQIAAgeoE\nNEjVlUzCBAgQIECAAAECBAiUEtAglZI1LwECBAgQIECAAAEC1QlokKormYQJECBAgAABAgQI\nECgloEEqJWteAgQIECBAgAABAgSqE9AgVVcyCRMgQIAAAQIECBAgUEpAg1RK1rwECBAgQIAA\nAQIECFQnoEGqrmQSJkCAAAECBAgQIECglIAGqZSseQkQIECAAAECBAgQqE5Ag1RdySRMgAAB\nAgQIECBAgEApAQ1SKVnzEiBAgAABAgQIECBQncDy6jKWMIHyAjPzt968zdzNP9qu/KEcYXEF\n5mcGc+uXqd3iqk5ltvn5mQ2D+cGPB+vc7qYCvngHibrNDObnZtzuFs90WjPl37o41sy0juc4\nBGoRcKOopVLynJ7AzOyawfwGD9KmJ76IR8oXxecWcT5TESBAYIkLzMzeHH/ztl/iZ+n0CGyR\ngFeQtojLzr0QmB/8cNk+R87P7nXE9b043yV0khu+/ObD7jG/49pfGuz5rSV0Wr04lfcPrjj0\nToNtB48a7PONXpzwEjrJMwdXHfyT7XbedsW9T/jqEjqtXpzKhh9cdKe5a77gyfJeVNtJbomA\nBmlLtOzbD4GZZRtmdztw9YoDH/eDfpzw0jnLua++/b57bthu/aMGd1W7ysoaD7LvvetgZTRI\naldZ6QbnDa494MblO2zjPrO2ykW+61ZtM3ftF3eMV5AqTF7KBMoJ+JKGcrZmJkCAAAECBAgQ\nIECgMgENUmUFky4BAgQIECBAgAABAuUENEjlbM1MgAABAgQIECBAgEBlAhqkygomXQIECBAg\nQIAAAQIEyglokMrZmpkAAQIECBAgQIAAgcoENEiVFUy6BAgQIECAAAECBAiUE9AglbM1MwEC\nBAgQIECAAAEClQlokCormHQJECBAgAABAgQIECgnoEEqZ2tmAgQIECBAgAABAgQqE9AgVVYw\n6RIgQIAAAQIECBAgUE5Ag1TO1swECBAgQIAAAQIECFQmoEGqrGDSJUCAAAECBAgQIECgnIAG\nqZytmQkQIECAAAECBAgQqExAg1RZwaRLgAABAgQIECBAgEA5AQ1SOVszEyBAgAABAgQIECBQ\nmYAGqbKCSZcAAQIECBAgQIAAgXICGqRytmYmQIAAAQIECBAgQKAyAQ1SZQWTLgECBAgQIECA\nAAEC5QQ0SOVszUyAAAECBAgQIECAQGUCGqTKCiZdAgQIECBAgAABAgTKCWiQytmamQABAgQI\nECBAgACBygQ0SJUVTLoECBAgQIAAAQIECJQT0CCVszUzAQIECBAgQIAAAQKVCWiQKiuYdAkQ\nIECAAAECBAgQKCegQSpna2YCBAgQIECAAAECBCoT0CBVVjDpEiBAgAABAgQIECBQTkCDVM7W\nzAQIECBAgAABAgQIVCagQaqsYNIlQIAAAQIECBAgQKCcgAapnK2ZCRAgQIAAAQIECBCoTECD\nVFnBpEuAAAECBAgQIECAQDkBDVI5WzMTIECAAAECBAgQIFCZgAapsoJJlwABAgQIECBAgACB\ncgIapHK2ZiZAgAABAgQIECBAoDIBDVJlBZMuAQIECBAgQIAAAQLlBDRI5WzNTIAAAQIECBAg\nQIBAZQIapMoKJl0CBAgQIECAAAECBMoJaJDK2ZqZAAECBAgQIECAAIHKBDRIlRVMugQIECBA\ngAABAgQIlBPQIJWzNTMBAgQIECBAgAABApUJaJAqK5h0CRAgQIAAAQIECBAoJ6BBKmdrZgIE\nCBAgQIAAAQIEKhPQIFVWMOkSIECAAAECBAgQIFBOQINUztbMBAgQIECAAAECBAhUJqBBqqxg\n0iVAgAABAgQIECBAoJyABqmcrZkJECBAgAABAgQIEKhMQINUWcGkS4AAAQIECBAgQIBAOYHl\n5aY2M4FNChwfe1wacfEm97QDAQIECBAg0BeBA+JE7xWxIuKbEd+KMAhMTcArSFOjdqAxgZNi\n+YyIY8fWWyRAgAABAgT6KbBXnPaZEZdHnD28ng3S+RHZNBkEpiKgQZoKs4OMCRwXy28cW2eR\nAAECBAgQ6K9APiZ9f0Q+RvhgxOMijo54x/DyrLjcNsIgUFzAW+yKEzvAiMAecf31EU+PWDey\n3lUCBAgQIECg3wIPi9M/KuKzEU8bofhkXM9XlrJhekLEaREGgaICXkEqymvyMYFzYjmbo7xz\ne87YNosECBAgQIBAfwX2j1O/MiJfMRof7x6uOGR8g2UCJQQ0SCVUzbmQwJdiwzERT424caGd\nrCdAgAABAgR6J/D3ccZ3j3jbhDM/YLguP5tkECgu4C12xYkdYETg5JHrrhIgQIAAAQIENiVw\np9jh9yJ+GnHepna2ncBiCGiQFkPRHAQIECBAgAABAostsENM+C8R2SQ9O+IHEQaB4gLeYlec\n2AEIECBAgAABAgS2UCCbonMjHhzx1xFvjzAITEVAgzQVZgchQIAAAQIECBDYTIEDY7/8Nrsj\nI/404oURBoGpCXiL3dSoHYgAAQIECBAgQGATAofG9o9F3Dkiv/H2rREGgakKaJCmyu1gBAgQ\nIECAAAECCwg8INZ/NGJFxOMjslEyCExdQIM0dXIHJECAAAECBAgQGBPYLpbz/0nML2Z4RES+\nxc4g0IqABqkVdgclQIAAAQIECBAYEfiDuL5/xDURL4uYNPIb7Sb9P0mT9rWOwFYLaJC2ms4P\nEiBAgAABAgQILJLAE4bz7BOXxy0w51ULrLeawKIKaJAWldNkWyBwVuw7swX725UAAQIECBBY\nugKHL91Tc2a1Cfia79oqJl8CBAgQIECAAAECBIoJaJCK0ZqYAAECBAgQIECAAIHaBDRItVVM\nvgQIECBAgAABAgQIFBPQIBWjNTEBAgQIECBAgAABArUJaJBqq5h8CRAgQIAAAQIECBAoJqBB\nKkZrYgIECBAgQIAAAQIEahPQINVWMfkSIECAAAECBAgQIFBMQINUjNbEBAgQIECAAAECBAjU\nJqBBqq1i8iVAgAABAgQIECBAoJiABqkYrYkJECBAgAABAgQIEKhNQINUW8XkS4AAAQIECBAg\nQIBAMQENUjFaExMgQIAAAQIECBAgUJuABqm2ismXAAECBAgQIECAAIFiAhqkYrQmJkCAAAEC\nBAgQIECgNgENUm0Vky8BAgQIECBAgAABAsUENEjFaE1MgAABAgQIECBAgEBtAhqk2iomXwIE\nCBAgQIAAAQIEiglokIrRmpgAAQIECBAgQIAAgdoENEi1VUy+BAgQIECAAAECBAgUE9AgFaM1\nMQECBAgQIECAAAECtQlokGqrmHwJECBAgAABAgQIECgmoEEqRmtiAgQIECBAgAABAgRqE9Ag\n1VYx+RIgQIAAAQIECBAgUExAg1SM1sQECBAgQIAAAQIECNQmoEGqrWLyJUCAAAECBAgQIECg\nmIAGqRitiQkQIECAAAECBAgQqE1Ag1RbxeRLgAABAgQIECBAgEAxAQ1SMVoTEyBAgAABAgQI\nECBQm4AGqbaKyZcAAQIECBAgQIAAgWICGqRitCYmQIAAAQIECBAgQKA2AQ1SbRWTLwECBAgQ\nIECAAAECxQQ0SMVoTUyAAAECBAgQIECAQG0CGqTaKiZfAgQIECBAgAABAgSKCWiQitGamAAB\nAgQIECBAgACB2gQ0SLVVTL4ECBAgQIAAAQIECBQT0CAVozUxAQIECBAgQIAAAQK1CWiQaquY\nfAkQIECAAAECBAgQKCagQSpGa2ICBAgQIECAAAECBGoT0CDVVjH5EiBAgAABAgQIECBQTECD\nVIzWxAQIECBAgAABAgQI1CagQaqtYvIlQIAAAQIECBAgQKCYgAapGK2JCRAgQIAAAQIECBCo\nTUCDVFvF5EuAAAECBAgQIECAQDEBDVIxWhMTIECAAAECBAgQIFCbgAaptorJlwABAgQIECBA\ngACBYgIapGK0JiZAgAABAgQIECBAoDaBmdoSli+B4gIzs6sH8/PbD2bcPIpbL/IBls1vGMzH\nnMsGarfItMWny8pl1dSuOPWiH+C2W12Ub2Y2b35GTQLzc4P4W7dmMD+3Y01py5VAaYHlpQ9g\nfgLVCcwPbpjZ4+CbZna5+6rqcu97wld89MC7DlbecvBg1+/2naK28//U4Nq77zLYZuawwR5X\n1JZ73/P93OC6X4juaOWD5/e8rO8WtZ3/1YPVu1w2/9P10SYZBAiMCGiQRjBcJfCfAjPL1i/f\n6/4/WXHIiVcTqUtg3VXn73+3DTut/a3BQZfWlblsvzT40V33Gmw/ULv6fhe+NVh15/nB/Kza\n1Ve7MwZX7nf54KZ49ciLf/VVT8YlBXwGqaSuuQkQIECAAAECBAgQqEpAg1RVuSRLgAABAgQI\nECBAgEBJAQ1SSV1zEyBAgAABAgQIECBQlYAGqapySZYAAQIECBAgQIAAgZICGqSSuuYmQIAA\nAQIECBAgQKAqAQ1SVeWSLAECBAgQIECAAAECJQU0SCV1zU2AAAECBAgQIECAQFUCGqSqyiVZ\nAgQIECBAgAABAgRKCmiQSuqamwABAgQIECBAgACBqgQ0SFWVS7IECBAgQIAAAQIECJQU0CCV\n1DU3AQIECBAgQIAAAQJVCWiQqiqXZAkQIECAAAECBAgQKCmgQSqpa24CBAgQIECAAAECBKoS\n0CBVVS7JEiBAgAABAgQIECBQUkCDVFLX3AQIECBAgAABAgQIVCWgQaqqXJIlQIAAAQIECBAg\nQKCkgAappK65CRAgQIAAAQIECBCoSkCDVFW5JEuAAAECBAgQIECAQEkBDVJJXXMTIECAAAEC\nBAgQIFCVgAapqnJJlgABAgQIECBAgACBkgIapJK65iZAgAABAgQIECBAoCoBDVJV5ZIsAQIE\nCBAgQIAAAQIlBTRIJXXNTYAAAQIECBAgQIBAVQIapKrKJVkCBAgQIECAAAECBEoKaJBK6pqb\nAAECBAgQIECAAIGqBDRIVZVLsgQIECBAgAABAgQIlBTQIJXUNTcBAgQIECBAgAABAlUJaJCq\nKpdkCRAgQIAAAQIECBAoKaBBKqlrbgIECBAgQIAAAQIEqhLQIFVVLskSIEAp+4mLAAAWkUlE\nQVSAAAECBAgQIFBSQINUUtfcBAgQIECAAAECBAhUJaBBqqpckiVAgAABAgQIECBAoKSABqmk\nrrkJECBAgAABAgQIEKhKQINUVbkkS4AAAQIECBAgQIBASQENUkldcxMgQIAAAQIECBAgUJWA\nBqmqckmWAAECBAgQIECAAIGSAhqkkrrmJkCAAAECBAgQIECgKgENUlXlkiwBAgQIECBAgAAB\nAiUFNEgldc1NgAABAgQIECBAgEBVAhqkqsolWQIECBAgQIAAAQIESgpokErqmpsAAQIECBAg\nQIAAgaoENEhVlUuyBAgQIECAAAECBAiUFNAgldQ1NwECBAgQIECAAAECVQlokKoql2QJECBA\ngAABAgQIECgpoEEqqWtuAgQIECBAgAABAgSqEtAgVVUuyRIgQIAAAQIECBAgUFJgecnJzU1g\nKDATl/tvhsY1sc+6zdjPLgQIECBAgMDSFTg4Tu2QiHxccFHE+giDwNQENEhTo+71gXaMs79i\nMwQeHPt8YTP2swsBAgQIECCw9AR2j1N6V8QTRk7t5rj+ooi3jKxzlUBRAQ1SUV6TDwVuicvX\nLaCxZ6x/esS1EZvTRC0wjdUECBAgQIBA5QLvj/yPiXhrxNsi9o54ScSbIzZEvD3CIFBcQINU\nnNgBQiDfNvf7C0j8c6zPBurXI65fYB+rCRAgQIAAgaUt8IA4vWyOvhjxnJFT/VpcvzzityM0\nSCMwrpYT0CCVszXzpgVOjF1+LeKVEZ/d9O72IECAAAECBJaowJo4r1dHfGrs/L4Tyxn3Hltv\nkUAxAQ1SMVoTb0Jgr9j+NxHfjnjNJva1mQABAgQIEFjaApfE6f3xhFM8PNbtH3H6hG1WESgi\noEEqwmrSzRB4beyTH8b83Yh8C55BgAABAgQIEEiB/Pbb/xnxmIjHR1wc8dIIg8BUBDRIU2F2\nkDGB3WL5qRH5xQxnjG2zSIAAAQIECPRbYO84/XeOEJwV178/suwqgaIC/qPYorwmX0DgGbF+\n24j8yk7/t8ECSFYTIECAAIGeCvwkznu/iAdGvDniZRFficj/NsQgUFzAK0jFiR1ggsBJse7W\niGyQDAIECBAgQIDAqED+30ffHUZ+q90eEU+OyLfc5bffGgSKCngFqSivyScIPCTWHRqRb63L\n/yHbIECAAAECBAhsTKD5eu/8PJJBoLiABqk4sQOMCTxyuPyhsfUWCRAgQIAAgf4K5Jcw5Fvr\nfmUCwdxw3eoJ26wisOgCGqRFJzXhJgSa/8fgG5vYz2YCBAgQIECgPwLfjFPdNeL5E075hcN1\nH5+wzSoCiy7gM0iLTmrCTQgcEts3ROQdoUGAAAECBAgQSIF/ifjXiOMjPhbxroj8z2N/JyI/\ne3RahHefBIJRXkCDVN7YEX4ukK9Y3ivi0gj/99HPXVwjQIAAAQJ9F5gPgBMiTo04OeKYiBzZ\nJP1RRP7/iQaBqQhokKbC7CBDgXwP8fY0CBAgQIAAAQITBH4a614QkV/rfXBENkeXR+Q7TwwC\nUxPQIE2N2oEIECBAgAABAgQ2QyC/5jv/3yODQCsCvqShFXYHJUCAAAECBAgQIECgiwIapC5W\nRU4ECBAgQIAAAQIECLQioEFqhd1BCRAgQIAAAQIECBDoooAGqYtVkRMBAgQIECBAgAABAq0I\naJBaYXdQAgQIECBAgAABAgS6KKBB6mJV5ESAAAECBAgQIECAQCsCGqRW2B2UAAECBAgQIECA\nAIEuCmiQulgVOREgQIAAAQIECBAg0IqABqkVdgclQIAAAQIECBAgQKCLAhqkLlZFTgQIECBA\ngAABAgQItCKgQWqF3UEJECBAgAABAgQIEOiigAapi1WREwECBAgQIECAAAECrQhokFphd1AC\nBAgQIECAAAECBLoooEHqYlXkRIAAAQIECBAgQIBAKwIapFbYHZQAAQIECBAgQIAAgS4KaJC6\nWBU5ESBAgAABAgQIECDQioAGqRV2ByVAgAABAgQIECBAoIsCGqQuVkVOBAgQIECAAAECBAi0\nIqBBaoXdQQkQIECAAAECBAgQ6KKABqmLVZETAQIECBAgQIAAAQKtCGiQWmF3UAIECBAgQIAA\nAQIEuiigQepiVeREgAABAgQIECBAgEArAhqkVtgdlAABAgQIECBAgACBLgpokLpYFTkRIECA\nAAECBAgQINCKgAapFXYHJUCAAAECBAgQIECgiwIapC5WRU4ECBAgQIAAAQIECLQioEFqhd1B\nCRAgQIAAAQIECBDoooAGqYtVkRMBAgQIECBAgAABAq0IaJBaYXdQAgQIECBAgAABAgS6KKBB\n6mJV5ESAAAECBAgQIECAQCsCGqRW2B2UAAECBAgQIECAAIEuCmiQulgVOREgQIAAAQIECBAg\n0IqABqkVdgclQIAAAQIECBAgQKCLAhqkLlZFTgQIECBAgAABAgQItCKgQWqF3UEJECBAgAAB\nAgQIEOiigAapi1WREwECBAgQIECAAAECrQhokFphd1ACBAgQIECAAAECBLoooEHqYlXkRIAA\nAQIECBAgQIBAKwIapFbYHZQAAQIECBAgQIAAgS4KaJC6WBU5ESBAgAABAgQIECDQioAGqRV2\nByVAgAABAgQIECBAoIsCGqQuVkVOBAgQIECAAAECBAi0IqBBaoXdQQkQIECAAAECBAgQ6KKA\nBqmLVZETAQIECBAgQIAAAQKtCGiQWmF3UAIECBAgQIAAAQIEuigw08Wk5ESgVYGZ2UsHsyv2\nHizfdl2reTj4FgssW7tq1+WDmQ3bDmZv2uIf9gOtCtw0WL/L7GBmsP1g+apWE3HwLRZYPVi/\n08xgZnaHwfIbt/iH/UCrArcM5lZGXDs3mL9nq4k4OIGOCWiQOlYQ6XRC4BGRxUGdyEQSWyqw\nX/zA6ogbtvQH7d+6wN7DDK5tPRMJbKnA7vEDO0ZcvaU/aP9OCHw7srigE5lIggABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECCwNQIzW/NDfoYAgSoF7hpZHx7x\ns4jPDy/jwqhAYL/I8b7DPL8el1dXkLMUbxO4W1wcFvGdiKyd0W2B/SO9X4r4x42k6b50IzgL\nbNo+1ud9WN4evh/xjYhVEaNj91jYZXTFhOtrYt11E9ZbRYAAAQIEtljglfET6yPmh3FrXJ4S\nYXRbYGWk97aIuYimdnn9LRHbRhjdFdgtUnt/RFO3vLwq4nkRRjcFdo60Lom4aSPpuS/dCM4C\nm34z1mdTM3pb+Gksv2Bs//83ts/o/s31c8Z+xiIBAgQIENgqgWPip/KPy+kR+QrSgyI+EpHr\nnh9hdFfgdZFa1ikfFGQdHxlxdkSu++sIo7sCH4vUsk4fiLh/RD57/taIbHCPjzC6JZANbXO/\nuFCD5L50y2uWZvk7/52IP4g4NCIbo29G5O3jGRHNOC6u/OUCcVmsz/3/MMIgQIAAAQJ3SCDf\n1pB/mL4XMTsy0zbD9d8dWz+yi6stC+RboPNZ1nywNvq2k52G62+Oy+URRvcEHh8p5YO5bJLG\nRza4WdN8m5bRDYEnRRrXRGTN1kVMapDclwbMVowL4mfS9dFjP/vA4fqLx9ZPWjwiVuY7ID4U\nkfeLBgECBAgQuEMCj42fzj9O/3fCLH863JYP5ozuCewYKeVbIS+akNqnYl3Wdc8J26xqX+DV\nkULW51cnpPLU4bbnTthm1fQFmvvI6+PQT4zI29ukBqnZz33p5tdoWez6hYhsgkafoGtmyFeR\n8j5u0rZmn3wy72sRWZ89mpUuCZQWyF9egwCBpSuQb6fLkX+kxkez7gHjGyx3QmB1ZPHZiHxb\n5P1GMjowrueHyL8a8cOR9a52R+AXhqnkZ47GR74qmMPt7jaHtv/NB+inRhwUcdZGknFfuhGc\nBTblW+vS7T4RG8b2yc9Q7h1xZcT4tlj1X+MVcS3fnvrSiB9HGASmIuDtGVNhdhACrQncZXjk\nSX9Ybhhu27e17Bx4UwInxw7vjfhcxOkR+faffAXiOxEnRRjdFLhymFY2s18fS/EJw+Xdx9Zb\nbEfg3DhsxqaG+9JNCW3Z9pfF7jtHvGkjP3aP2HZKxCUR74owCBAgQIDAogi8J2bJt/rkM3jj\nI9fltn8c32C5MwL5Kv9LIrJOo/GKWPYOgEDo6Dgq8sp6fTFi+5Ecd4jr10bktkmfTxrZ1dWW\nBC6K4056i5370sUrSD7Jk68afTtiu41M+9rYlreV521kH5sIFBHwB7YIq0kJdEZg7TCTSbf1\n5n3fG3t7Q2dOpIeJ5HvvPxORnxX7/Yh8Bjvj9yL+d8T5EfmA2+iewCcjpfdF3D/iyxGvGMZX\n4jIjx89uu/BvJQLuSxenUM+MabLZ/FFEfmvdzRGTxopY+cyIbFb/IcIgQIAAAQKLJvCqmCmf\ngTtqwoxHD7e9YcI2q9oXeMywPn8yIZV8P37W9UkTtlnVDYF8gJfN7U8islbfj/iriAOGy++K\nS6N7Agu9guS+9I7X6o9jirwtXBGRn/na2Pj12Jj7vnFjO9lGoJTAslITm5cAgU4IXDPMYtLn\nHZp1+cDN6J5A8w1oZ05I7Z+G65rPs0zYxaqWBdbH8V8esVvEXhH7Rrwoovl670vjulGPgPvS\nra9VfjX36yNeGfHvEUdG5NvrNjZOGm78243tZBuBUgIapFKy5iXQDYH/GKZx1IR0mnXNt9lN\n2MWqFgXyG6By7Hnbxe3+zbff5WjeJnnbkn+7IrBfJPLsiPsNE7puJLHjh9c/PbLO1e4LuC/d\nuhrl48x3RLwgIp/sOTpi9PYQi/9t5P3a0RGXRVwcYRAgQIAAgUUX+FrMmB8M33lk5vyPR38Q\nkZ+PWD6y3tXuCDwlUsm3mOSrReNPZv3FcFvzLGssGh0SODRyydp9fCynbJyuj/hoRD6rbnRP\nYKG32GWm7ku3vF6/Gz+St4XTIzb3CZ17DH/mjLg0CBAgQIBAEYETY9b8A/WliCdH5APvfBCQ\n///HERFGNwXyAXQ+kM7anRXxtIhjI94WkesujNjcBxyxqzFlgXPjeFmnrNfjIvKbuL4TkR9O\n3zvC6KbAxhok96VbVrM9YvfmM3j5ZEG+gjQpdhyb9omxnLedV4+tt0iAAAECBBZV4Okx2w0R\n+UcnI68/K8LotsAOkd6fR6yLaGp3S1zPDy7nq4BGdwXuFKmdFtHULS+/HvGwCKO7AhtrkDJr\n96WbX7vjYtfR3/+Frufn9EZHfktn7ptPChkEWhHwEn8r7A5KoBWBvL0fGLEyIt/bnQ+6jToE\n8m2Q+baTfKtdfrh/fYRRh8DukeYBET+M+G5EPvAz6hZwX1p3/WRPgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIEFiyAv8fYH78\n8WpdGb0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "md.pattern(nhanes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1表示观察到，0表示缺失\n",
    "\n",
    "最后一列表示缺失变量数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " iter imp variable\n",
      "  1   1  bmi  hyp  chl\n",
      "  1   2  bmi  hyp  chl\n",
      "  1   3  bmi  hyp  chl\n",
      "  1   4  bmi  hyp  chl\n",
      "  1   5  bmi  hyp  chl\n",
      "  2   1  bmi  hyp  chl\n",
      "  2   2  bmi  hyp  chl\n",
      "  2   3  bmi  hyp  chl\n",
      "  2   4  bmi  hyp  chl\n",
      "  2   5  bmi  hyp  chl\n",
      "  3   1  bmi  hyp  chl\n",
      "  3   2  bmi  hyp  chl\n",
      "  3   3  bmi  hyp  chl\n",
      "  3   4  bmi  hyp  chl\n",
      "  3   5  bmi  hyp  chl\n",
      "  4   1  bmi  hyp  chl\n",
      "  4   2  bmi  hyp  chl\n",
      "  4   3  bmi  hyp  chl\n",
      "  4   4  bmi  hyp  chl\n",
      "  4   5  bmi  hyp  chl\n",
      "  5   1  bmi  hyp  chl\n",
      "  5   2  bmi  hyp  chl\n",
      "  5   3  bmi  hyp  chl\n",
      "  5   4  bmi  hyp  chl\n",
      "  5   5  bmi  hyp  chl\n"
     ]
    }
   ],
   "source": [
    "# multiple imputations\n",
    "imp <- mice(nhanes, seed = 23109)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class: mids\n",
      "Number of multiple imputations:  5 \n",
      "Imputation methods:\n",
      "  age   bmi   hyp   chl \n",
      "   \"\" \"pmm\" \"pmm\" \"pmm\" \n",
      "PredictorMatrix:\n",
      "    age bmi hyp chl\n",
      "age   0   1   1   1\n",
      "bmi   1   0   1   1\n",
      "hyp   1   1   0   1\n",
      "chl   1   1   1   0\n"
     ]
    }
   ],
   "source": [
    "print(imp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# modeling\n",
    "fit <- with(imp, lm(chl ~ age + bmi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "call :\n",
      "with.mids(data = imp, expr = lm(chl ~ age + bmi))\n",
      "\n",
      "call1 :\n",
      "mice(data = nhanes, seed = 23109)\n",
      "\n",
      "nmis :\n",
      "age bmi hyp chl \n",
      "  0   9   8  10 \n",
      "\n",
      "analyses :\n",
      "[[1]]\n",
      "\n",
      "Call:\n",
      "lm(formula = chl ~ age + bmi)\n",
      "\n",
      "Coefficients:\n",
      "(Intercept)          age          bmi  \n",
      "    -41.404       36.478        6.627  \n",
      "\n",
      "\n",
      "[[2]]\n",
      "\n",
      "Call:\n",
      "lm(formula = chl ~ age + bmi)\n",
      "\n",
      "Coefficients:\n",
      "(Intercept)          age          bmi  \n",
      "     28.554       23.084        4.576  \n",
      "\n",
      "\n",
      "[[3]]\n",
      "\n",
      "Call:\n",
      "lm(formula = chl ~ age + bmi)\n",
      "\n",
      "Coefficients:\n",
      "(Intercept)          age          bmi  \n",
      "     25.312       23.882        4.834  \n",
      "\n",
      "\n",
      "[[4]]\n",
      "\n",
      "Call:\n",
      "lm(formula = chl ~ age + bmi)\n",
      "\n",
      "Coefficients:\n",
      "(Intercept)          age          bmi  \n",
      "    -32.897       45.292        5.486  \n",
      "\n",
      "\n",
      "[[5]]\n",
      "\n",
      "Call:\n",
      "lm(formula = chl ~ age + bmi)\n",
      "\n",
      "Coefficients:\n",
      "(Intercept)          age          bmi  \n",
      "     50.227       19.891        4.172  \n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# one model per imputation\n",
    "print(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class: mipo    m = 5 \n",
      "             estimate        ubar          b           t dfcom        df\n",
      "(Intercept)  5.958468 3575.717813 1649.43830 5555.043768    22  9.216954\n",
      "age         29.725360   82.553435  115.72029  221.417779    22  4.331856\n",
      "bmi          5.138790    3.686724    0.91985    4.790544    22 12.907767\n",
      "                  riv    lambda       fmi\n",
      "(Intercept) 0.5535465 0.3563115 0.4616878\n",
      "age         1.6821147 0.6271599 0.7288640\n",
      "bmi         0.2994040 0.2304164 0.3271721\n"
     ]
    }
   ],
   "source": [
    "# pool to form one solution\n",
    "\n",
    "print(pool(fit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* lambda is the proportion of the total variance that is attributable to the missing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>estimate</th><th scope=col>std.error</th><th scope=col>statistic</th><th scope=col>df</th><th scope=col>p.value</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td> 5.958468 </td><td>74.532166 </td><td>0.07994492</td><td> 9.216954 </td><td>0.93750725</td></tr>\n",
       "\t<tr><th scope=row>age</th><td>29.725360 </td><td>14.880114 </td><td>1.99765683</td><td> 4.331856 </td><td>0.06727696</td></tr>\n",
       "\t<tr><th scope=row>bmi</th><td> 5.138790 </td><td> 2.188731 </td><td>2.34783949</td><td>12.907767 </td><td>0.03549532</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & estimate & std.error & statistic & df & p.value\\\\\n",
       "\\hline\n",
       "\t(Intercept) &  5.958468  & 74.532166  & 0.07994492 &  9.216954  & 0.93750725\\\\\n",
       "\tage & 29.725360  & 14.880114  & 1.99765683 &  4.331856  & 0.06727696\\\\\n",
       "\tbmi &  5.138790  &  2.188731  & 2.34783949 & 12.907767  & 0.03549532\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | estimate | std.error | statistic | df | p.value | \n",
       "|---|---|---|\n",
       "| (Intercept) |  5.958468  | 74.532166  | 0.07994492 |  9.216954  | 0.93750725 | \n",
       "| age | 29.725360  | 14.880114  | 1.99765683 |  4.331856  | 0.06727696 | \n",
       "| bmi |  5.138790  |  2.188731  | 2.34783949 | 12.907767  | 0.03549532 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "            estimate  std.error statistic  df        p.value   \n",
       "(Intercept)  5.958468 74.532166 0.07994492  9.216954 0.93750725\n",
       "age         29.725360 14.880114 1.99765683  4.331856 0.06727696\n",
       "bmi          5.138790  2.188731 2.34783949 12.907767 0.03549532"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(pool(fit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " iter imp variable\n",
      "  1   1  bmi  hyp  chl\n",
      "  1   2  bmi  hyp  chl\n",
      "  1   3  bmi  hyp  chl\n",
      "  1   4  bmi  hyp  chl\n",
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      "  1   50  bmi  hyp  chl\n",
      "  2   1  bmi  hyp  chl\n",
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      "  3   1  bmi  hyp  chl\n",
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      "  4   1  bmi  hyp  chl\n",
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      "  5   48  bmi  hyp  chl\n",
      "  5   49  bmi  hyp  chl\n",
      "  5   50  bmi  hyp  chl\n"
     ]
    }
   ],
   "source": [
    "# increase the number of imputations\n",
    "\n",
    "imp50 <- mice(nhanes, m = 50, seed = 23109)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "fit50 <- with(imp50, lm(chl ~ age + bmi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>estimate</th><th scope=col>std.error</th><th scope=col>statistic</th><th scope=col>df</th><th scope=col>p.value</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td>-7.276001 </td><td>66.466513 </td><td>-0.1094687</td><td>14.30395  </td><td>0.91425164</td></tr>\n",
       "\t<tr><th scope=row>age</th><td>32.075691 </td><td>11.515704 </td><td> 2.7853869</td><td>11.58145  </td><td>0.01364981</td></tr>\n",
       "\t<tr><th scope=row>bmi</th><td> 5.470019 </td><td> 2.081697 </td><td> 2.6276726</td><td>15.32201  </td><td>0.01877129</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & estimate & std.error & statistic & df & p.value\\\\\n",
       "\\hline\n",
       "\t(Intercept) & -7.276001  & 66.466513  & -0.1094687 & 14.30395   & 0.91425164\\\\\n",
       "\tage & 32.075691  & 11.515704  &  2.7853869 & 11.58145   & 0.01364981\\\\\n",
       "\tbmi &  5.470019  &  2.081697  &  2.6276726 & 15.32201   & 0.01877129\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | estimate | std.error | statistic | df | p.value | \n",
       "|---|---|---|\n",
       "| (Intercept) | -7.276001  | 66.466513  | -0.1094687 | 14.30395   | 0.91425164 | \n",
       "| age | 32.075691  | 11.515704  |  2.7853869 | 11.58145   | 0.01364981 | \n",
       "| bmi |  5.470019  |  2.081697  |  2.6276726 | 15.32201   | 0.01877129 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "            estimate  std.error statistic  df       p.value   \n",
       "(Intercept) -7.276001 66.466513 -0.1094687 14.30395 0.91425164\n",
       "age         32.075691 11.515704  2.7853869 11.58145 0.01364981\n",
       "bmi          5.470019  2.081697  2.6276726 15.32201 0.01877129"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(pool(fit50)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " iter imp variable\n",
      "  1   1  bmi  hyp  chl\n",
      "  1   2  bmi  hyp  chl\n",
      "  1   3  bmi  hyp  chl\n",
      "  1   4  bmi  hyp  chl\n",
      "  1   5  bmi  hyp  chl\n",
      "  2   1  bmi  hyp  chl\n",
      "  2   2  bmi  hyp  chl\n",
      "  2   3  bmi  hyp  chl\n",
      "  2   4  bmi  hyp  chl\n",
      "  2   5  bmi  hyp  chl\n",
      "  3   1  bmi  hyp  chl\n",
      "  3   2  bmi  hyp  chl\n",
      "  3   3  bmi  hyp  chl\n",
      "  3   4  bmi  hyp  chl\n",
      "  3   5  bmi  hyp  chl\n",
      "  4   1  bmi  hyp  chl\n",
      "  4   2  bmi  hyp  chl\n",
      "  4   3  bmi  hyp  chl\n",
      "  4   4  bmi  hyp  chl\n",
      "  4   5  bmi  hyp  chl\n",
      "  5   1  bmi  hyp  chl\n",
      "  5   2  bmi  hyp  chl\n",
      "  5   3  bmi  hyp  chl\n",
      "  5   4  bmi  hyp  chl\n",
      "  5   5  bmi  hyp  chl\n"
     ]
    }
   ],
   "source": [
    "# choose approriate models to imputate different types of variables\n",
    "\n",
    "imp_meth <- mice(nhanes, method = c(\"\", \"norm\", \"pmm\", \"mean\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 延伸阅读\n",
    "* Van Buuren, S., Groothuis-Oudshoorn, K. (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67. http://www.jstatsoft.org/v45/i03/\n",
    "\n"
   ]
  }
 ],
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