Elections Economy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: ggplot2\n",
      "\n",
      "Loading required package: ggstance\n",
      "\n",
      "\n",
      "Attaching package: ‘ggstance’\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:ggplot2’:\n",
      "\n",
      "    geom_errorbarh, GeomErrorbarh\n",
      "\n",
      "\n",
      "Loading required package: scales\n",
      "\n",
      "Loading required package: ggridges\n",
      "\n",
      "\n",
      "New to ggformula?  Try the tutorials: \n",
      "\tlearnr::run_tutorial(\"introduction\", package = \"ggformula\")\n",
      "\tlearnr::run_tutorial(\"refining\", package = \"ggformula\")\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(rstanarm)\n",
    "library(ggformula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "download_if_missing <- function(filename, url) {\n",
    "    if (!file.exists(filename)) {\n",
    "        dir.create(dirname(filename), showWarnings=FALSE, recursive=TRUE)\n",
    "        download.file(url, destfile = filename, method=\"curl\")\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename <- \"./data/ElectionsEconomy/hibbs.dat\"\n",
    "\n",
    "download_if_missing(filename,\n",
    "                    'https://raw.githubusercontent.com/avehtari/ROS-Examples/master/ElectionsEconomy/data/hibbs.dat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "hibbs <- read.table(\"./data/ElectionsEconomy/hibbs.dat\", header=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 16 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>year</th><th scope=col>growth</th><th scope=col>vote</th><th scope=col>inc_party_candidate</th><th scope=col>other_candidate</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1952</td><td> 2.40</td><td>44.60</td><td>Stevenson </td><td>Eisenhower</td></tr>\n",
       "\t<tr><td>1956</td><td> 2.89</td><td>57.76</td><td>Eisenhower</td><td>Stevenson </td></tr>\n",
       "\t<tr><td>1960</td><td> 0.85</td><td>49.91</td><td>Nixon     </td><td>Kennedy   </td></tr>\n",
       "\t<tr><td>1964</td><td> 4.21</td><td>61.34</td><td>Johnson   </td><td>Goldwater </td></tr>\n",
       "\t<tr><td>1968</td><td> 3.02</td><td>49.60</td><td>Humphrey  </td><td>Nixon     </td></tr>\n",
       "\t<tr><td>1972</td><td> 3.62</td><td>61.79</td><td>Nixon     </td><td>McGovern  </td></tr>\n",
       "\t<tr><td>1976</td><td> 1.08</td><td>48.95</td><td>Ford      </td><td>Carter    </td></tr>\n",
       "\t<tr><td>1980</td><td>-0.39</td><td>44.70</td><td>Carter    </td><td>Reagan    </td></tr>\n",
       "\t<tr><td>1984</td><td> 3.86</td><td>59.17</td><td>Reagan    </td><td>Mondale   </td></tr>\n",
       "\t<tr><td>1988</td><td> 2.27</td><td>53.94</td><td>Bush, Sr. </td><td>Dukakis   </td></tr>\n",
       "\t<tr><td>1992</td><td> 0.38</td><td>46.55</td><td>Bush, Sr. </td><td>Clinton   </td></tr>\n",
       "\t<tr><td>1996</td><td> 1.04</td><td>54.74</td><td>Clinton   </td><td>Dole      </td></tr>\n",
       "\t<tr><td>2000</td><td> 2.36</td><td>50.27</td><td>Gore      </td><td>Bush, Jr. </td></tr>\n",
       "\t<tr><td>2004</td><td> 1.72</td><td>51.24</td><td>Bush, Jr. </td><td>Kerry     </td></tr>\n",
       "\t<tr><td>2008</td><td> 0.10</td><td>46.32</td><td>McCain    </td><td>Obama     </td></tr>\n",
       "\t<tr><td>2012</td><td> 0.95</td><td>52.00</td><td>Obama     </td><td>Romney    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 16 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " year & growth & vote & inc\\_party\\_candidate & other\\_candidate\\\\\n",
       " <int> & <dbl> & <dbl> & <fct> & <fct>\\\\\n",
       "\\hline\n",
       "\t 1952 &  2.40 & 44.60 & Stevenson  & Eisenhower\\\\\n",
       "\t 1956 &  2.89 & 57.76 & Eisenhower & Stevenson \\\\\n",
       "\t 1960 &  0.85 & 49.91 & Nixon      & Kennedy   \\\\\n",
       "\t 1964 &  4.21 & 61.34 & Johnson    & Goldwater \\\\\n",
       "\t 1968 &  3.02 & 49.60 & Humphrey   & Nixon     \\\\\n",
       "\t 1972 &  3.62 & 61.79 & Nixon      & McGovern  \\\\\n",
       "\t 1976 &  1.08 & 48.95 & Ford       & Carter    \\\\\n",
       "\t 1980 & -0.39 & 44.70 & Carter     & Reagan    \\\\\n",
       "\t 1984 &  3.86 & 59.17 & Reagan     & Mondale   \\\\\n",
       "\t 1988 &  2.27 & 53.94 & Bush, Sr.  & Dukakis   \\\\\n",
       "\t 1992 &  0.38 & 46.55 & Bush, Sr.  & Clinton   \\\\\n",
       "\t 1996 &  1.04 & 54.74 & Clinton    & Dole      \\\\\n",
       "\t 2000 &  2.36 & 50.27 & Gore       & Bush, Jr. \\\\\n",
       "\t 2004 &  1.72 & 51.24 & Bush, Jr.  & Kerry     \\\\\n",
       "\t 2008 &  0.10 & 46.32 & McCain     & Obama     \\\\\n",
       "\t 2012 &  0.95 & 52.00 & Obama      & Romney    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 16 × 5\n",
       "\n",
       "| year &lt;int&gt; | growth &lt;dbl&gt; | vote &lt;dbl&gt; | inc_party_candidate &lt;fct&gt; | other_candidate &lt;fct&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1952 |  2.40 | 44.60 | Stevenson  | Eisenhower |\n",
       "| 1956 |  2.89 | 57.76 | Eisenhower | Stevenson  |\n",
       "| 1960 |  0.85 | 49.91 | Nixon      | Kennedy    |\n",
       "| 1964 |  4.21 | 61.34 | Johnson    | Goldwater  |\n",
       "| 1968 |  3.02 | 49.60 | Humphrey   | Nixon      |\n",
       "| 1972 |  3.62 | 61.79 | Nixon      | McGovern   |\n",
       "| 1976 |  1.08 | 48.95 | Ford       | Carter     |\n",
       "| 1980 | -0.39 | 44.70 | Carter     | Reagan     |\n",
       "| 1984 |  3.86 | 59.17 | Reagan     | Mondale    |\n",
       "| 1988 |  2.27 | 53.94 | Bush, Sr.  | Dukakis    |\n",
       "| 1992 |  0.38 | 46.55 | Bush, Sr.  | Clinton    |\n",
       "| 1996 |  1.04 | 54.74 | Clinton    | Dole       |\n",
       "| 2000 |  2.36 | 50.27 | Gore       | Bush, Jr.  |\n",
       "| 2004 |  1.72 | 51.24 | Bush, Jr.  | Kerry      |\n",
       "| 2008 |  0.10 | 46.32 | McCain     | Obama      |\n",
       "| 2012 |  0.95 | 52.00 | Obama      | Romney     |\n",
       "\n"
      ],
      "text/plain": [
       "   year growth vote  inc_party_candidate other_candidate\n",
       "1  1952  2.40  44.60 Stevenson           Eisenhower     \n",
       "2  1956  2.89  57.76 Eisenhower          Stevenson      \n",
       "3  1960  0.85  49.91 Nixon               Kennedy        \n",
       "4  1964  4.21  61.34 Johnson             Goldwater      \n",
       "5  1968  3.02  49.60 Humphrey            Nixon          \n",
       "6  1972  3.62  61.79 Nixon               McGovern       \n",
       "7  1976  1.08  48.95 Ford                Carter         \n",
       "8  1980 -0.39  44.70 Carter              Reagan         \n",
       "9  1984  3.86  59.17 Reagan              Mondale        \n",
       "10 1988  2.27  53.94 Bush, Sr.           Dukakis        \n",
       "11 1992  0.38  46.55 Bush, Sr.           Clinton        \n",
       "12 1996  1.04  54.74 Clinton             Dole           \n",
       "13 2000  2.36  50.27 Gore                Bush, Jr.      \n",
       "14 2004  1.72  51.24 Bush, Jr.           Kerry          \n",
       "15 2008  0.10  46.32 McCain              Obama          \n",
       "16 2012  0.95  52.00 Obama               Romney         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hibbs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
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S0gAcloAUltAQlIRgtIagtIQDJaQFJb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\n7P8DXFlxkQWpnGEAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hibbsplot <- hibbs %>% gf_point(vote ~ growth) + xlab('Economic Growth') + ylab(\"Incumbent Party's Vote Share\")\n",
    "hibbsplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).\n",
      "Chain 1: \n",
      "Chain 1: Gradient evaluation took 0.000129 seconds\n",
      "Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.29 seconds.\n",
      "Chain 1: Adjust your expectations accordingly!\n",
      "Chain 1: \n",
      "Chain 1: \n",
      "Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)\n",
      "Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)\n",
      "Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)\n",
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      "Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)\n",
      "Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)\n",
      "Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)\n",
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      "Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)\n",
      "Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)\n",
      "Chain 1: \n",
      "Chain 1:  Elapsed Time: 0.027713 seconds (Warm-up)\n",
      "Chain 1:                0.025141 seconds (Sampling)\n",
      "Chain 1:                0.052854 seconds (Total)\n",
      "Chain 1: \n",
      "\n",
      "SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).\n",
      "Chain 2: \n",
      "Chain 2: Gradient evaluation took 1.1e-05 seconds\n",
      "Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.\n",
      "Chain 2: Adjust your expectations accordingly!\n",
      "Chain 2: \n",
      "Chain 2: \n",
      "Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)\n",
      "Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)\n",
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      "Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)\n",
      "Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)\n",
      "Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)\n",
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      "Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)\n",
      "Chain 2: \n",
      "Chain 2:  Elapsed Time: 0.029501 seconds (Warm-up)\n",
      "Chain 2:                0.022326 seconds (Sampling)\n",
      "Chain 2:                0.051827 seconds (Total)\n",
      "Chain 2: \n",
      "\n",
      "SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).\n",
      "Chain 3: \n",
      "Chain 3: Gradient evaluation took 1.2e-05 seconds\n",
      "Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds.\n",
      "Chain 3: Adjust your expectations accordingly!\n",
      "Chain 3: \n",
      "Chain 3: \n",
      "Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)\n",
      "Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)\n",
      "Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)\n",
      "Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)\n",
      "Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)\n",
      "Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)\n",
      "Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)\n",
      "Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)\n",
      "Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)\n",
      "Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)\n",
      "Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)\n",
      "Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)\n",
      "Chain 3: \n",
      "Chain 3:  Elapsed Time: 0.028046 seconds (Warm-up)\n",
      "Chain 3:                0.034051 seconds (Sampling)\n",
      "Chain 3:                0.062097 seconds (Total)\n",
      "Chain 3: \n",
      "\n",
      "SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).\n",
      "Chain 4: \n",
      "Chain 4: Gradient evaluation took 1.2e-05 seconds\n",
      "Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds.\n",
      "Chain 4: Adjust your expectations accordingly!\n",
      "Chain 4: \n",
      "Chain 4: \n",
      "Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)\n",
      "Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)\n",
      "Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)\n",
      "Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)\n",
      "Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)\n",
      "Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)\n",
      "Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)\n",
      "Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)\n",
      "Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)\n",
      "Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)\n",
      "Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)\n",
      "Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)\n",
      "Chain 4: \n",
      "Chain 4:  Elapsed Time: 0.027305 seconds (Warm-up)\n",
      "Chain 4:                0.024787 seconds (Sampling)\n",
      "Chain 4:                0.052092 seconds (Total)\n",
      "Chain 4: \n"
     ]
    }
   ],
   "source": [
    "M1 <- stan_glm(vote ~ growth, data=hibbs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stan_glm\n",
      " family:       gaussian [identity]\n",
      " formula:      vote ~ growth\n",
      " observations: 16\n",
      " predictors:   2\n",
      "------\n",
      "            Median MAD_SD\n",
      "(Intercept) 46.3    1.7  \n",
      "growth       3.1    0.7  \n",
      "\n",
      "Auxiliary parameter(s):\n",
      "      Median MAD_SD\n",
      "sigma 3.8    0.7   \n",
      "\n",
      "------\n",
      "* For help interpreting the printed output see ?print.stanreg\n",
      "* For info on the priors used see ?prior_summary.stanreg\n"
     ]
    }
   ],
   "source": [
    "print(M1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>46.2795888767876</dd><dt>growth</dt><dd>3.06036542139075</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 46.2795888767876\n",
       "\\item[growth] 3.06036542139075\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   46.2795888767876growth\n",
       ":   3.06036542139075\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)      growth \n",
       "  46.279589    3.060365 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef(M1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iBxW46BtOcWajTX9xIgmW4BErflFEjL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\nAcmgdXEh5aZFVXlFrgVI3FYFQkpu/5v+5HSHawDJoHVRIWX1oSb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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hibbsplot + geom_abline(intercept=coef(M1)[1], slope=coef(M1)[2]) + ggtitle('Data and Linear Fit')"
   ]
  }
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