4_glam_parameters_predict_behavior.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import os\n",
    "from bambi import Model\n",
    "import scipy as sp\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rc(\"axes.spines\", top=False, right=False)\n",
    "\n",
    "from analysis_functions import aggregate_subject_level, sample_corr\n",
    "\n",
    "from plotting_functions import plot_correlation, add_regression_line, cm2inch, show_img\n",
    "from pymc3 import plot_posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(11) # from random.org"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# 4. GLAM parameters predict behavior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load data and split into even and odd trials:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_data = pd.read_csv('data/data_aggregate.csv')\n",
    "even = all_data[(all_data['trial'] % 2) == 0].reset_index(drop=True)\n",
    "odd = all_data[(all_data['trial'] % 2) == 1].reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute behavioural metric summarys for each individual, only from the odd trials:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "odd_summary = pd.DataFrame()\n",
    "\n",
    "for di, dataset in enumerate(odd['dataset'].unique()):\n",
    "    odd_di = odd[odd['dataset'] == dataset].copy()\n",
    "    n_items = odd_di['n_items'].unique()[0]\n",
    "    \n",
    "    odd_summary_di = aggregate_subject_level(odd_di, n_items=n_items)\n",
    "    \n",
    "    odd_summary = pd.concat([odd_summary, odd_summary_di])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>best_chosen</th>\n",
       "      <th colspan=\"8\" halign=\"left\">rt</th>\n",
       "      <th>gaze_influence</th>\n",
       "      <th>dataset</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>max</th>\n",
       "      <th>se</th>\n",
       "      <th>q1</th>\n",
       "      <th>q3</th>\n",
       "      <th>iqr</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>subject</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.822222</td>\n",
       "      <td>1704.177778</td>\n",
       "      <td>881.852300</td>\n",
       "      <td>682.0</td>\n",
       "      <td>4142.0</td>\n",
       "      <td>132.944236</td>\n",
       "      <td>1125.00</td>\n",
       "      <td>1970.00</td>\n",
       "      <td>845.00</td>\n",
       "      <td>-0.020529</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.673469</td>\n",
       "      <td>1728.489796</td>\n",
       "      <td>857.141479</td>\n",
       "      <td>743.0</td>\n",
       "      <td>4602.0</td>\n",
       "      <td>123.717716</td>\n",
       "      <td>1166.00</td>\n",
       "      <td>1937.00</td>\n",
       "      <td>771.00</td>\n",
       "      <td>0.247233</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.840000</td>\n",
       "      <td>4078.660000</td>\n",
       "      <td>2623.044800</td>\n",
       "      <td>943.0</td>\n",
       "      <td>12079.0</td>\n",
       "      <td>374.720686</td>\n",
       "      <td>2104.25</td>\n",
       "      <td>5329.00</td>\n",
       "      <td>3224.75</td>\n",
       "      <td>0.028877</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.704545</td>\n",
       "      <td>1893.545455</td>\n",
       "      <td>633.499496</td>\n",
       "      <td>1045.0</td>\n",
       "      <td>4742.0</td>\n",
       "      <td>96.607767</td>\n",
       "      <td>1436.50</td>\n",
       "      <td>2175.50</td>\n",
       "      <td>739.00</td>\n",
       "      <td>-0.022031</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.840000</td>\n",
       "      <td>1846.640000</td>\n",
       "      <td>1093.485579</td>\n",
       "      <td>692.0</td>\n",
       "      <td>5891.0</td>\n",
       "      <td>156.212226</td>\n",
       "      <td>1221.50</td>\n",
       "      <td>2132.50</td>\n",
       "      <td>911.00</td>\n",
       "      <td>0.103622</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.800000</td>\n",
       "      <td>1217.780000</td>\n",
       "      <td>436.891258</td>\n",
       "      <td>756.0</td>\n",
       "      <td>3768.0</td>\n",
       "      <td>62.413037</td>\n",
       "      <td>998.75</td>\n",
       "      <td>1359.25</td>\n",
       "      <td>360.50</td>\n",
       "      <td>-0.011744</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.720000</td>\n",
       "      <td>3085.400000</td>\n",
       "      <td>1785.189615</td>\n",
       "      <td>986.0</td>\n",
       "      <td>8984.0</td>\n",
       "      <td>255.027088</td>\n",
       "      <td>1727.50</td>\n",
       "      <td>4017.75</td>\n",
       "      <td>2290.25</td>\n",
       "      <td>0.059901</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.920000</td>\n",
       "      <td>1870.980000</td>\n",
       "      <td>582.836083</td>\n",
       "      <td>1181.0</td>\n",
       "      <td>3612.0</td>\n",
       "      <td>83.262298</td>\n",
       "      <td>1508.25</td>\n",
       "      <td>2114.75</td>\n",
       "      <td>606.50</td>\n",
       "      <td>0.290474</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.860000</td>\n",
       "      <td>1401.660000</td>\n",
       "      <td>426.574711</td>\n",
       "      <td>759.0</td>\n",
       "      <td>2818.0</td>\n",
       "      <td>60.939244</td>\n",
       "      <td>1155.25</td>\n",
       "      <td>1532.25</td>\n",
       "      <td>377.00</td>\n",
       "      <td>0.209622</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.780000</td>\n",
       "      <td>2070.280000</td>\n",
       "      <td>984.519762</td>\n",
       "      <td>653.0</td>\n",
       "      <td>4746.0</td>\n",
       "      <td>140.645680</td>\n",
       "      <td>1293.25</td>\n",
       "      <td>2498.75</td>\n",
       "      <td>1205.50</td>\n",
       "      <td>0.372487</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.877551</td>\n",
       "      <td>2679.816327</td>\n",
       "      <td>2435.583789</td>\n",
       "      <td>1111.0</td>\n",
       "      <td>13278.0</td>\n",
       "      <td>351.546239</td>\n",
       "      <td>1521.00</td>\n",
       "      <td>2606.00</td>\n",
       "      <td>1085.00</td>\n",
       "      <td>0.085615</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.836735</td>\n",
       "      <td>3471.816327</td>\n",
       "      <td>3341.510178</td>\n",
       "      <td>881.0</td>\n",
       "      <td>17698.0</td>\n",
       "      <td>482.305450</td>\n",
       "      <td>1480.00</td>\n",
       "      <td>3354.00</td>\n",
       "      <td>1874.00</td>\n",
       "      <td>0.095918</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.805556</td>\n",
       "      <td>1717.250000</td>\n",
       "      <td>947.956028</td>\n",
       "      <td>787.0</td>\n",
       "      <td>5535.0</td>\n",
       "      <td>160.233814</td>\n",
       "      <td>1170.50</td>\n",
       "      <td>1846.00</td>\n",
       "      <td>675.50</td>\n",
       "      <td>0.150453</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.640000</td>\n",
       "      <td>3097.360000</td>\n",
       "      <td>1833.586701</td>\n",
       "      <td>873.0</td>\n",
       "      <td>7926.0</td>\n",
       "      <td>261.940957</td>\n",
       "      <td>1559.75</td>\n",
       "      <td>3952.75</td>\n",
       "      <td>2393.00</td>\n",
       "      <td>-0.084967</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>1558.562500</td>\n",
       "      <td>525.305542</td>\n",
       "      <td>795.0</td>\n",
       "      <td>2937.0</td>\n",
       "      <td>76.623688</td>\n",
       "      <td>1225.75</td>\n",
       "      <td>1835.25</td>\n",
       "      <td>609.50</td>\n",
       "      <td>0.156858</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.880000</td>\n",
       "      <td>3908.260000</td>\n",
       "      <td>2961.066604</td>\n",
       "      <td>1226.0</td>\n",
       "      <td>17782.0</td>\n",
       "      <td>423.009515</td>\n",
       "      <td>2103.00</td>\n",
       "      <td>4749.25</td>\n",
       "      <td>2646.25</td>\n",
       "      <td>0.074715</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.860000</td>\n",
       "      <td>3746.980000</td>\n",
       "      <td>1542.591761</td>\n",
       "      <td>1546.0</td>\n",
       "      <td>8326.0</td>\n",
       "      <td>220.370252</td>\n",
       "      <td>2534.25</td>\n",
       "      <td>4524.75</td>\n",
       "      <td>1990.50</td>\n",
       "      <td>-0.033760</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.857143</td>\n",
       "      <td>3290.408163</td>\n",
       "      <td>2937.206739</td>\n",
       "      <td>936.0</td>\n",
       "      <td>14806.0</td>\n",
       "      <td>423.949275</td>\n",
       "      <td>1396.00</td>\n",
       "      <td>3700.00</td>\n",
       "      <td>2304.00</td>\n",
       "      <td>0.058923</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.897959</td>\n",
       "      <td>2455.510204</td>\n",
       "      <td>1632.151017</td>\n",
       "      <td>874.0</td>\n",
       "      <td>10804.0</td>\n",
       "      <td>235.580707</td>\n",
       "      <td>1460.00</td>\n",
       "      <td>2875.00</td>\n",
       "      <td>1415.00</td>\n",
       "      <td>0.216784</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>1616.250000</td>\n",
       "      <td>1195.824933</td>\n",
       "      <td>743.0</td>\n",
       "      <td>6454.0</td>\n",
       "      <td>249.346735</td>\n",
       "      <td>1030.50</td>\n",
       "      <td>1595.25</td>\n",
       "      <td>564.75</td>\n",
       "      <td>0.322039</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "        best_chosen           rt                                            \\\n",
       "               mean         mean          std     min      max          se   \n",
       "subject                                                                      \n",
       "0          0.822222  1704.177778   881.852300   682.0   4142.0  132.944236   \n",
       "1          0.673469  1728.489796   857.141479   743.0   4602.0  123.717716   \n",
       "2          0.840000  4078.660000  2623.044800   943.0  12079.0  374.720686   \n",
       "3          0.704545  1893.545455   633.499496  1045.0   4742.0   96.607767   \n",
       "4          0.840000  1846.640000  1093.485579   692.0   5891.0  156.212226   \n",
       "5          0.800000  1217.780000   436.891258   756.0   3768.0   62.413037   \n",
       "6          0.720000  3085.400000  1785.189615   986.0   8984.0  255.027088   \n",
       "7          0.920000  1870.980000   582.836083  1181.0   3612.0   83.262298   \n",
       "8          0.860000  1401.660000   426.574711   759.0   2818.0   60.939244   \n",
       "9          0.780000  2070.280000   984.519762   653.0   4746.0  140.645680   \n",
       "10         0.877551  2679.816327  2435.583789  1111.0  13278.0  351.546239   \n",
       "11         0.836735  3471.816327  3341.510178   881.0  17698.0  482.305450   \n",
       "12         0.805556  1717.250000   947.956028   787.0   5535.0  160.233814   \n",
       "13         0.640000  3097.360000  1833.586701   873.0   7926.0  261.940957   \n",
       "14         0.833333  1558.562500   525.305542   795.0   2937.0   76.623688   \n",
       "15         0.880000  3908.260000  2961.066604  1226.0  17782.0  423.009515   \n",
       "16         0.860000  3746.980000  1542.591761  1546.0   8326.0  220.370252   \n",
       "17         0.857143  3290.408163  2937.206739   936.0  14806.0  423.949275   \n",
       "18         0.897959  2455.510204  1632.151017   874.0  10804.0  235.580707   \n",
       "19         0.833333  1616.250000  1195.824933   743.0   6454.0  249.346735   \n",
       "\n",
       "                                   gaze_influence       dataset  \n",
       "              q1       q3      iqr                               \n",
       "subject                                                          \n",
       "0        1125.00  1970.00   845.00      -0.020529  krajbich2010  \n",
       "1        1166.00  1937.00   771.00       0.247233  krajbich2010  \n",
       "2        2104.25  5329.00  3224.75       0.028877  krajbich2010  \n",
       "3        1436.50  2175.50   739.00      -0.022031  krajbich2010  \n",
       "4        1221.50  2132.50   911.00       0.103622  krajbich2010  \n",
       "5         998.75  1359.25   360.50      -0.011744  krajbich2010  \n",
       "6        1727.50  4017.75  2290.25       0.059901  krajbich2010  \n",
       "7        1508.25  2114.75   606.50       0.290474  krajbich2010  \n",
       "8        1155.25  1532.25   377.00       0.209622  krajbich2010  \n",
       "9        1293.25  2498.75  1205.50       0.372487  krajbich2010  \n",
       "10       1521.00  2606.00  1085.00       0.085615  krajbich2010  \n",
       "11       1480.00  3354.00  1874.00       0.095918  krajbich2010  \n",
       "12       1170.50  1846.00   675.50       0.150453  krajbich2010  \n",
       "13       1559.75  3952.75  2393.00      -0.084967  krajbich2010  \n",
       "14       1225.75  1835.25   609.50       0.156858  krajbich2010  \n",
       "15       2103.00  4749.25  2646.25       0.074715  krajbich2010  \n",
       "16       2534.25  4524.75  1990.50      -0.033760  krajbich2010  \n",
       "17       1396.00  3700.00  2304.00       0.058923  krajbich2010  \n",
       "18       1460.00  2875.00  1415.00       0.216784  krajbich2010  \n",
       "19       1030.50  1595.25   564.75       0.322039  krajbich2010  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odd_summary.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load GLAM parameter estimates, estimated from even trials only:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>subject</th>\n",
       "      <th>tau</th>\n",
       "      <th>v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>0.65</td>\n",
       "      <td>0.008368</td>\n",
       "      <td>0</td>\n",
       "      <td>0.44</td>\n",
       "      <td>0.000098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.05</td>\n",
       "      <td>0.013663</td>\n",
       "      <td>1</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.000096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.80</td>\n",
       "      <td>0.009960</td>\n",
       "      <td>2</td>\n",
       "      <td>1.99</td>\n",
       "      <td>0.000022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.005090</td>\n",
       "      <td>3</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.000090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.16</td>\n",
       "      <td>0.008927</td>\n",
       "      <td>4</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.000091</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gamma         s  subject   tau         v\n",
       "0.0   0.65  0.008368        0  0.44  0.000098\n",
       "1.0   0.05  0.013663        1  0.21  0.000096\n",
       "2.0   0.80  0.009960        2  1.99  0.000022\n",
       "3.0   0.25  0.005090        3  0.07  0.000090\n",
       "4.0   0.16  0.008927        4  0.32  0.000091"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimates = pd.DataFrame()\n",
    "parameter_names = ['v', 'gamma', 's', 'tau']\n",
    "for subject in odd_summary.index:\n",
    "    subject_estimates_df = pd.read_csv(os.path.join('results', 'estimates', 'out_of_sample', 'multiplicative',\n",
    "                                                    'estimates_{}_multiplicative_oos.csv'.format(subject)),\n",
    "                                       index_col=0)\n",
    "    subject_estimates_dict = {parameter: subject_estimates_df.loc[parameter + '__0_0', 'MAP']\n",
    "                              for parameter in parameter_names}\n",
    "    subject_estimates_dict['subject'] = subject\n",
    "    estimates = pd.concat([estimates,\n",
    "                           pd.DataFrame(subject_estimates_dict,\n",
    "                                        index=np.ones(1)*subject)])\n",
    "\n",
    "estimates.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Mixed effects regression models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prepare data for Bayesian Mixed Effects regression models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Format data for mixed model\n",
    "df = pd.concat([estimates, odd_summary], axis=1)\n",
    "df['log_rt'] = np.log(df[('rt', 'mean')])\n",
    "df['log_v'] = np.log(df['v'])\n",
    "df['best_chosen'] = 100 * df[('best_chosen', 'mean')]\n",
    "df['gaze_influence'] = 100 * df[('gaze_influence', '')]\n",
    "df['dataset'] = df[('dataset', '')]\n",
    "\n",
    "df = df[['subject', 'dataset', 'log_rt', 'best_chosen', 'gaze_influence', 'log_v', 'gamma', 's', 'tau']].copy().reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>dataset</th>\n",
       "      <th>log_rt</th>\n",
       "      <th>best_chosen</th>\n",
       "      <th>gaze_influence</th>\n",
       "      <th>log_v</th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>tau</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.440838</td>\n",
       "      <td>82.222222</td>\n",
       "      <td>-2.052946</td>\n",
       "      <td>-9.230543</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.008368</td>\n",
       "      <td>0.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.455003</td>\n",
       "      <td>67.346939</td>\n",
       "      <td>24.723267</td>\n",
       "      <td>-9.251162</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.013663</td>\n",
       "      <td>0.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>8.313524</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>2.887728</td>\n",
       "      <td>-10.724468</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.009960</td>\n",
       "      <td>1.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.546206</td>\n",
       "      <td>70.454545</td>\n",
       "      <td>-2.203105</td>\n",
       "      <td>-9.315701</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.005090</td>\n",
       "      <td>0.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.521123</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>10.362165</td>\n",
       "      <td>-9.304651</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.008927</td>\n",
       "      <td>0.32</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   subject       dataset    log_rt  best_chosen  gaze_influence      log_v  \\\n",
       "0        0  krajbich2010  7.440838    82.222222       -2.052946  -9.230543   \n",
       "1        1  krajbich2010  7.455003    67.346939       24.723267  -9.251162   \n",
       "2        2  krajbich2010  8.313524    84.000000        2.887728 -10.724468   \n",
       "3        3  krajbich2010  7.546206    70.454545       -2.203105  -9.315701   \n",
       "4        4  krajbich2010  7.521123    84.000000       10.362165  -9.304651   \n",
       "\n",
       "   gamma         s   tau  \n",
       "0   0.65  0.008368  0.44  \n",
       "1   0.05  0.013663  0.21  \n",
       "2   0.80  0.009960  1.99  \n",
       "3   0.25  0.005090  0.07  \n",
       "4   0.16  0.008927  0.32  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_samples = 20000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log RT ~ Log v (Figure 6a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading previous results from \"results/mixed_effects_models/4_parameter_behavior_a_v_rt.csv\"...\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd0.95_lower</th>\n",
       "      <th>hpd0.95_upper</th>\n",
       "      <th>effective_n</th>\n",
       "      <th>gelman_rubin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1|dataset[folke2016]</th>\n",
       "      <td>-0.036478</td>\n",
       "      <td>0.247705</td>\n",
       "      <td>-6.865614e-01</td>\n",
       "      <td>0.353188</td>\n",
       "      <td>445</td>\n",
       "      <td>1.010607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2010]</th>\n",
       "      <td>0.091317</td>\n",
       "      <td>0.244611</td>\n",
       "      <td>-2.773712e-01</td>\n",
       "      <td>0.735978</td>\n",
       "      <td>213</td>\n",
       "      <td>1.009996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2011]</th>\n",
       "      <td>-0.104560</td>\n",
       "      <td>0.214484</td>\n",
       "      <td>-6.437239e-01</td>\n",
       "      <td>0.237322</td>\n",
       "      <td>640</td>\n",
       "      <td>1.009184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[tavares2017]</th>\n",
       "      <td>-0.083372</td>\n",
       "      <td>0.228054</td>\n",
       "      <td>-6.615938e-01</td>\n",
       "      <td>0.297323</td>\n",
       "      <td>405</td>\n",
       "      <td>1.013754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset_sd</th>\n",
       "      <td>0.229443</td>\n",
       "      <td>0.256955</td>\n",
       "      <td>1.050007e-05</td>\n",
       "      <td>0.764077</td>\n",
       "      <td>285</td>\n",
       "      <td>1.018211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>0.021761</td>\n",
       "      <td>0.284135</td>\n",
       "      <td>-5.218034e-01</td>\n",
       "      <td>0.570559</td>\n",
       "      <td>1286</td>\n",
       "      <td>1.000392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_rt_sd</th>\n",
       "      <td>0.112200</td>\n",
       "      <td>0.007673</td>\n",
       "      <td>9.760415e-02</td>\n",
       "      <td>0.127399</td>\n",
       "      <td>15918</td>\n",
       "      <td>1.000351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_v</th>\n",
       "      <td>-0.788898</td>\n",
       "      <td>0.034241</td>\n",
       "      <td>-8.475716e-01</td>\n",
       "      <td>-0.709287</td>\n",
       "      <td>372</td>\n",
       "      <td>1.001845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_v|dataset[folke2016]</th>\n",
       "      <td>-0.016826</td>\n",
       "      <td>0.037698</td>\n",
       "      <td>-1.052425e-01</td>\n",
       "      <td>0.036175</td>\n",
       "      <td>125</td>\n",
       "      <td>1.014004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_v|dataset[krajbich2010]</th>\n",
       "      <td>0.005515</td>\n",
       "      <td>0.028332</td>\n",
       "      <td>-5.036431e-02</td>\n",
       "      <td>0.094310</td>\n",
       "      <td>283</td>\n",
       "      <td>1.000254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_v|dataset[krajbich2011]</th>\n",
       "      <td>-0.009291</td>\n",
       "      <td>0.033054</td>\n",
       "      <td>-9.538329e-02</td>\n",
       "      <td>0.039172</td>\n",
       "      <td>125</td>\n",
       "      <td>1.016013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_v|dataset[tavares2017]</th>\n",
       "      <td>-0.011365</td>\n",
       "      <td>0.036022</td>\n",
       "      <td>-9.697433e-02</td>\n",
       "      <td>0.038537</td>\n",
       "      <td>123</td>\n",
       "      <td>1.018848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_v|dataset_sd</th>\n",
       "      <td>0.027401</td>\n",
       "      <td>0.035314</td>\n",
       "      <td>7.168370e-07</td>\n",
       "      <td>0.110140</td>\n",
       "      <td>203</td>\n",
       "      <td>1.021806</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 mean        sd  hpd0.95_lower  hpd0.95_upper  \\\n",
       "1|dataset[folke2016]        -0.036478  0.247705  -6.865614e-01       0.353188   \n",
       "1|dataset[krajbich2010]      0.091317  0.244611  -2.773712e-01       0.735978   \n",
       "1|dataset[krajbich2011]     -0.104560  0.214484  -6.437239e-01       0.237322   \n",
       "1|dataset[tavares2017]      -0.083372  0.228054  -6.615938e-01       0.297323   \n",
       "1|dataset_sd                 0.229443  0.256955   1.050007e-05       0.764077   \n",
       "Intercept                    0.021761  0.284135  -5.218034e-01       0.570559   \n",
       "log_rt_sd                    0.112200  0.007673   9.760415e-02       0.127399   \n",
       "log_v                       -0.788898  0.034241  -8.475716e-01      -0.709287   \n",
       "log_v|dataset[folke2016]    -0.016826  0.037698  -1.052425e-01       0.036175   \n",
       "log_v|dataset[krajbich2010]  0.005515  0.028332  -5.036431e-02       0.094310   \n",
       "log_v|dataset[krajbich2011] -0.009291  0.033054  -9.538329e-02       0.039172   \n",
       "log_v|dataset[tavares2017]  -0.011365  0.036022  -9.697433e-02       0.038537   \n",
       "log_v|dataset_sd             0.027401  0.035314   7.168370e-07       0.110140   \n",
       "\n",
       "                             effective_n  gelman_rubin  \n",
       "1|dataset[folke2016]                 445      1.010607  \n",
       "1|dataset[krajbich2010]              213      1.009996  \n",
       "1|dataset[krajbich2011]              640      1.009184  \n",
       "1|dataset[tavares2017]               405      1.013754  \n",
       "1|dataset_sd                         285      1.018211  \n",
       "Intercept                           1286      1.000392  \n",
       "log_rt_sd                          15918      1.000351  \n",
       "log_v                                372      1.001845  \n",
       "log_v|dataset[folke2016]             125      1.014004  \n",
       "log_v|dataset[krajbich2010]          283      1.000254  \n",
       "log_v|dataset[krajbich2011]          125      1.016013  \n",
       "log_v|dataset[tavares2017]           123      1.018848  \n",
       "log_v|dataset_sd                     203      1.021806  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_file = os.path.join('results', 'mixed_effects_models', '4_parameter_behavior_a_v_rt.csv')\n",
    "if not os.path.isfile(result_file):\n",
    "    model_a = Model(df)\n",
    "    result_a = model_a.fit('log_rt ~ log_v',\n",
    "                           random=['log_v|dataset'],\n",
    "                           categorical=['dataset'],\n",
    "                           samples=n_samples,\n",
    "                           chains=2)\n",
    "\n",
    "    summary_a = result_a.summary(ranefs=True)\n",
    "    summary_a.to_csv(result_file)\n",
    "else:\n",
    "    print('Loading previous results from \"{}\"...'.format(result_file))\n",
    "    summary_a = pd.read_csv(result_file, index_col=0)\n",
    "summary_a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P(choose best) ~ sigma (text only)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading previous results from \"results/mixed_effects_models/4_parameter_behavior_x_sigma_best_chosen.csv\"...\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd0.95_lower</th>\n",
       "      <th>hpd0.95_upper</th>\n",
       "      <th>effective_n</th>\n",
       "      <th>gelman_rubin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1|dataset[folke2016]</th>\n",
       "      <td>-8.545108</td>\n",
       "      <td>7.331179</td>\n",
       "      <td>-23.777436</td>\n",
       "      <td>4.264606</td>\n",
       "      <td>4349</td>\n",
       "      <td>1.000180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2010]</th>\n",
       "      <td>4.768121</td>\n",
       "      <td>6.567035</td>\n",
       "      <td>-7.625270</td>\n",
       "      <td>19.290832</td>\n",
       "      <td>6823</td>\n",
       "      <td>1.001005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2011]</th>\n",
       "      <td>-1.870483</td>\n",
       "      <td>6.461943</td>\n",
       "      <td>-16.071978</td>\n",
       "      <td>10.901057</td>\n",
       "      <td>7152</td>\n",
       "      <td>1.000474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[tavares2017]</th>\n",
       "      <td>4.899419</td>\n",
       "      <td>7.719676</td>\n",
       "      <td>-9.732400</td>\n",
       "      <td>21.445327</td>\n",
       "      <td>4254</td>\n",
       "      <td>1.001644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset_sd</th>\n",
       "      <td>10.358782</td>\n",
       "      <td>6.109188</td>\n",
       "      <td>0.000745</td>\n",
       "      <td>21.961919</td>\n",
       "      <td>6460</td>\n",
       "      <td>1.000807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>78.450993</td>\n",
       "      <td>6.756091</td>\n",
       "      <td>65.036001</td>\n",
       "      <td>92.221394</td>\n",
       "      <td>2392</td>\n",
       "      <td>1.003105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>best_chosen_sd</th>\n",
       "      <td>9.185626</td>\n",
       "      <td>0.617824</td>\n",
       "      <td>8.032478</td>\n",
       "      <td>10.445387</td>\n",
       "      <td>19230</td>\n",
       "      <td>0.999995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s</th>\n",
       "      <td>-227.307077</td>\n",
       "      <td>805.640506</td>\n",
       "      <td>-2323.485403</td>\n",
       "      <td>1253.102795</td>\n",
       "      <td>92</td>\n",
       "      <td>1.005153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s|dataset[folke2016]</th>\n",
       "      <td>-436.188506</td>\n",
       "      <td>1003.744617</td>\n",
       "      <td>-2760.955012</td>\n",
       "      <td>1353.253771</td>\n",
       "      <td>247</td>\n",
       "      <td>1.000023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s|dataset[krajbich2010]</th>\n",
       "      <td>-15.320234</td>\n",
       "      <td>780.518984</td>\n",
       "      <td>-1863.082392</td>\n",
       "      <td>1646.875592</td>\n",
       "      <td>103</td>\n",
       "      <td>1.002357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s|dataset[krajbich2011]</th>\n",
       "      <td>-97.627955</td>\n",
       "      <td>747.252170</td>\n",
       "      <td>-1766.732359</td>\n",
       "      <td>1535.619427</td>\n",
       "      <td>125</td>\n",
       "      <td>1.001386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s|dataset[tavares2017]</th>\n",
       "      <td>472.220373</td>\n",
       "      <td>819.766446</td>\n",
       "      <td>-1063.322247</td>\n",
       "      <td>2462.947176</td>\n",
       "      <td>141</td>\n",
       "      <td>1.003842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s|dataset_sd</th>\n",
       "      <td>1000.847500</td>\n",
       "      <td>899.384735</td>\n",
       "      <td>0.020340</td>\n",
       "      <td>2740.647425</td>\n",
       "      <td>340</td>\n",
       "      <td>1.003600</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                mean           sd  hpd0.95_lower  \\\n",
       "1|dataset[folke2016]       -8.545108     7.331179     -23.777436   \n",
       "1|dataset[krajbich2010]     4.768121     6.567035      -7.625270   \n",
       "1|dataset[krajbich2011]    -1.870483     6.461943     -16.071978   \n",
       "1|dataset[tavares2017]      4.899419     7.719676      -9.732400   \n",
       "1|dataset_sd               10.358782     6.109188       0.000745   \n",
       "Intercept                  78.450993     6.756091      65.036001   \n",
       "best_chosen_sd              9.185626     0.617824       8.032478   \n",
       "s                        -227.307077   805.640506   -2323.485403   \n",
       "s|dataset[folke2016]     -436.188506  1003.744617   -2760.955012   \n",
       "s|dataset[krajbich2010]   -15.320234   780.518984   -1863.082392   \n",
       "s|dataset[krajbich2011]   -97.627955   747.252170   -1766.732359   \n",
       "s|dataset[tavares2017]    472.220373   819.766446   -1063.322247   \n",
       "s|dataset_sd             1000.847500   899.384735       0.020340   \n",
       "\n",
       "                         hpd0.95_upper  effective_n  gelman_rubin  \n",
       "1|dataset[folke2016]          4.264606         4349      1.000180  \n",
       "1|dataset[krajbich2010]      19.290832         6823      1.001005  \n",
       "1|dataset[krajbich2011]      10.901057         7152      1.000474  \n",
       "1|dataset[tavares2017]       21.445327         4254      1.001644  \n",
       "1|dataset_sd                 21.961919         6460      1.000807  \n",
       "Intercept                    92.221394         2392      1.003105  \n",
       "best_chosen_sd               10.445387        19230      0.999995  \n",
       "s                          1253.102795           92      1.005153  \n",
       "s|dataset[folke2016]       1353.253771          247      1.000023  \n",
       "s|dataset[krajbich2010]    1646.875592          103      1.002357  \n",
       "s|dataset[krajbich2011]    1535.619427          125      1.001386  \n",
       "s|dataset[tavares2017]     2462.947176          141      1.003842  \n",
       "s|dataset_sd               2740.647425          340      1.003600  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_file = os.path.join('results', 'mixed_effects_models', '4_parameter_behavior_x_sigma_best_chosen.csv')\n",
    "if not os.path.isfile(result_file):\n",
    "    model_x = Model(df)\n",
    "    result_x = model_x.fit('best_chosen ~ s',\n",
    "                           random=['s|dataset'],\n",
    "                           categorical=['dataset'],\n",
    "                           samples=n_samples,\n",
    "                           chains=2)\n",
    "    summary_x = result_x.summary(ranefs=True)\n",
    "    summary_x.to_csv(result_file)\n",
    "else:\n",
    "    print('Loading previous results from \"{}\"...'.format(result_file))\n",
    "    summary_x = pd.read_csv(result_file, index_col=0)\n",
    "summary_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaze_influence ~ gamma (Figure 6c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading previous results from \"results/mixed_effects_models/4_parameter_behavior_c_gamma_gaze_influence.csv\"...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd0.95_lower</th>\n",
       "      <th>hpd0.95_upper</th>\n",
       "      <th>effective_n</th>\n",
       "      <th>gelman_rubin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1|dataset[folke2016]</th>\n",
       "      <td>3.102115</td>\n",
       "      <td>3.426230</td>\n",
       "      <td>-3.163433</td>\n",
       "      <td>10.392981</td>\n",
       "      <td>2492</td>\n",
       "      <td>1.000072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2010]</th>\n",
       "      <td>0.340725</td>\n",
       "      <td>3.175260</td>\n",
       "      <td>-6.407941</td>\n",
       "      <td>6.927720</td>\n",
       "      <td>2340</td>\n",
       "      <td>1.000118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2011]</th>\n",
       "      <td>0.660119</td>\n",
       "      <td>3.217392</td>\n",
       "      <td>-6.010809</td>\n",
       "      <td>7.287773</td>\n",
       "      <td>2222</td>\n",
       "      <td>1.000127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[tavares2017]</th>\n",
       "      <td>-3.738438</td>\n",
       "      <td>3.450434</td>\n",
       "      <td>-11.546460</td>\n",
       "      <td>2.048900</td>\n",
       "      <td>2690</td>\n",
       "      <td>1.000218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset_sd</th>\n",
       "      <td>4.780091</td>\n",
       "      <td>3.091689</td>\n",
       "      <td>0.000086</td>\n",
       "      <td>10.908243</td>\n",
       "      <td>2866</td>\n",
       "      <td>0.999975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>26.682299</td>\n",
       "      <td>3.008994</td>\n",
       "      <td>20.329528</td>\n",
       "      <td>32.773307</td>\n",
       "      <td>1929</td>\n",
       "      <td>1.000166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma</th>\n",
       "      <td>-26.594773</td>\n",
       "      <td>4.900976</td>\n",
       "      <td>-37.102983</td>\n",
       "      <td>-17.239387</td>\n",
       "      <td>6578</td>\n",
       "      <td>1.000328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[folke2016]</th>\n",
       "      <td>-1.708566</td>\n",
       "      <td>5.791617</td>\n",
       "      <td>-14.877712</td>\n",
       "      <td>9.304559</td>\n",
       "      <td>12020</td>\n",
       "      <td>1.000090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2010]</th>\n",
       "      <td>1.946703</td>\n",
       "      <td>4.961793</td>\n",
       "      <td>-7.387357</td>\n",
       "      <td>13.230886</td>\n",
       "      <td>7260</td>\n",
       "      <td>1.000294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2011]</th>\n",
       "      <td>-1.866250</td>\n",
       "      <td>5.242162</td>\n",
       "      <td>-13.392973</td>\n",
       "      <td>8.164298</td>\n",
       "      <td>7607</td>\n",
       "      <td>1.000292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[tavares2017]</th>\n",
       "      <td>-1.956638</td>\n",
       "      <td>6.088230</td>\n",
       "      <td>-15.696355</td>\n",
       "      <td>9.609921</td>\n",
       "      <td>12226</td>\n",
       "      <td>1.000196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset_sd</th>\n",
       "      <td>6.181896</td>\n",
       "      <td>5.755173</td>\n",
       "      <td>0.000568</td>\n",
       "      <td>17.433997</td>\n",
       "      <td>5079</td>\n",
       "      <td>0.999976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gaze_influence_sd</th>\n",
       "      <td>10.922476</td>\n",
       "      <td>0.746120</td>\n",
       "      <td>9.536118</td>\n",
       "      <td>12.438558</td>\n",
       "      <td>30451</td>\n",
       "      <td>1.000002</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  mean        sd  hpd0.95_lower  \\\n",
       "1|dataset[folke2016]          3.102115  3.426230      -3.163433   \n",
       "1|dataset[krajbich2010]       0.340725  3.175260      -6.407941   \n",
       "1|dataset[krajbich2011]       0.660119  3.217392      -6.010809   \n",
       "1|dataset[tavares2017]       -3.738438  3.450434     -11.546460   \n",
       "1|dataset_sd                  4.780091  3.091689       0.000086   \n",
       "Intercept                    26.682299  3.008994      20.329528   \n",
       "gamma                       -26.594773  4.900976     -37.102983   \n",
       "gamma|dataset[folke2016]     -1.708566  5.791617     -14.877712   \n",
       "gamma|dataset[krajbich2010]   1.946703  4.961793      -7.387357   \n",
       "gamma|dataset[krajbich2011]  -1.866250  5.242162     -13.392973   \n",
       "gamma|dataset[tavares2017]   -1.956638  6.088230     -15.696355   \n",
       "gamma|dataset_sd              6.181896  5.755173       0.000568   \n",
       "gaze_influence_sd            10.922476  0.746120       9.536118   \n",
       "\n",
       "                             hpd0.95_upper  effective_n  gelman_rubin  \n",
       "1|dataset[folke2016]             10.392981         2492      1.000072  \n",
       "1|dataset[krajbich2010]           6.927720         2340      1.000118  \n",
       "1|dataset[krajbich2011]           7.287773         2222      1.000127  \n",
       "1|dataset[tavares2017]            2.048900         2690      1.000218  \n",
       "1|dataset_sd                     10.908243         2866      0.999975  \n",
       "Intercept                        32.773307         1929      1.000166  \n",
       "gamma                           -17.239387         6578      1.000328  \n",
       "gamma|dataset[folke2016]          9.304559        12020      1.000090  \n",
       "gamma|dataset[krajbich2010]      13.230886         7260      1.000294  \n",
       "gamma|dataset[krajbich2011]       8.164298         7607      1.000292  \n",
       "gamma|dataset[tavares2017]        9.609921        12226      1.000196  \n",
       "gamma|dataset_sd                 17.433997         5079      0.999976  \n",
       "gaze_influence_sd                12.438558        30451      1.000002  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_file = os.path.join('results', 'mixed_effects_models', '4_parameter_behavior_c_gamma_gaze_influence.csv')\n",
    "if not os.path.isfile(result_file):\n",
    "    model_c = Model(df)\n",
    "    result_c = model_c.fit('gaze_influence ~ gamma',\n",
    "                           random=['gamma|dataset'],\n",
    "                           categorical=['dataset'],\n",
    "                           samples=n_samples,\n",
    "                           chains=2)\n",
    "    summary_c = result_c.summary(ranefs=True)\n",
    "    summary_c.to_csv(result_file)\n",
    "else:\n",
    "    print('Loading previous results from \"{}\"...'.format(result_file))\n",
    "    summary_c = pd.read_csv(result_file, index_col=0)\n",
    "summary_c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P(choose best) ~ gamma (Figure 6b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading previous results from \"results/mixed_effects_models/4_parameter_behavior_b_gamma_best_chosen.csv\"...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd0.95_lower</th>\n",
       "      <th>hpd0.95_upper</th>\n",
       "      <th>effective_n</th>\n",
       "      <th>gelman_rubin</th>\n",
       "      <th>P(&gt;0)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1|dataset[folke2016]</th>\n",
       "      <td>-8.338383</td>\n",
       "      <td>4.161054</td>\n",
       "      <td>-17.111028</td>\n",
       "      <td>-0.422510</td>\n",
       "      <td>9964</td>\n",
       "      <td>1.000172</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2010]</th>\n",
       "      <td>3.599083</td>\n",
       "      <td>4.118807</td>\n",
       "      <td>-4.474070</td>\n",
       "      <td>12.083067</td>\n",
       "      <td>9659</td>\n",
       "      <td>1.000095</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2011]</th>\n",
       "      <td>-4.227917</td>\n",
       "      <td>4.131861</td>\n",
       "      <td>-12.610917</td>\n",
       "      <td>4.009374</td>\n",
       "      <td>9749</td>\n",
       "      <td>1.000184</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[tavares2017]</th>\n",
       "      <td>8.701591</td>\n",
       "      <td>4.147166</td>\n",
       "      <td>0.591699</td>\n",
       "      <td>17.194108</td>\n",
       "      <td>10088</td>\n",
       "      <td>1.000332</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset_sd</th>\n",
       "      <td>8.059083</td>\n",
       "      <td>2.656935</td>\n",
       "      <td>3.696207</td>\n",
       "      <td>13.416032</td>\n",
       "      <td>18394</td>\n",
       "      <td>1.000094</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>76.683290</td>\n",
       "      <td>3.992970</td>\n",
       "      <td>68.773546</td>\n",
       "      <td>84.916721</td>\n",
       "      <td>9056</td>\n",
       "      <td>1.000262</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>best_chosen_sd</th>\n",
       "      <td>7.549834</td>\n",
       "      <td>0.514356</td>\n",
       "      <td>6.564367</td>\n",
       "      <td>8.565155</td>\n",
       "      <td>34180</td>\n",
       "      <td>0.999994</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma</th>\n",
       "      <td>12.651590</td>\n",
       "      <td>7.757765</td>\n",
       "      <td>-3.192698</td>\n",
       "      <td>28.841020</td>\n",
       "      <td>7307</td>\n",
       "      <td>0.999980</td>\n",
       "      <td>0.94485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[folke2016]</th>\n",
       "      <td>17.173733</td>\n",
       "      <td>9.188220</td>\n",
       "      <td>0.121935</td>\n",
       "      <td>36.408555</td>\n",
       "      <td>9959</td>\n",
       "      <td>0.999979</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2010]</th>\n",
       "      <td>-9.339527</td>\n",
       "      <td>7.915352</td>\n",
       "      <td>-25.709131</td>\n",
       "      <td>7.006315</td>\n",
       "      <td>7633</td>\n",
       "      <td>0.999991</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2011]</th>\n",
       "      <td>2.051617</td>\n",
       "      <td>8.128556</td>\n",
       "      <td>-14.001619</td>\n",
       "      <td>19.361891</td>\n",
       "      <td>8173</td>\n",
       "      <td>0.999981</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[tavares2017]</th>\n",
       "      <td>-3.217596</td>\n",
       "      <td>8.837724</td>\n",
       "      <td>-21.075818</td>\n",
       "      <td>14.678272</td>\n",
       "      <td>10318</td>\n",
       "      <td>0.999976</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset_sd</th>\n",
       "      <td>15.453899</td>\n",
       "      <td>7.202848</td>\n",
       "      <td>4.235814</td>\n",
       "      <td>30.136999</td>\n",
       "      <td>11800</td>\n",
       "      <td>0.999976</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  mean        sd  hpd0.95_lower  \\\n",
       "1|dataset[folke2016]         -8.338383  4.161054     -17.111028   \n",
       "1|dataset[krajbich2010]       3.599083  4.118807      -4.474070   \n",
       "1|dataset[krajbich2011]      -4.227917  4.131861     -12.610917   \n",
       "1|dataset[tavares2017]        8.701591  4.147166       0.591699   \n",
       "1|dataset_sd                  8.059083  2.656935       3.696207   \n",
       "Intercept                    76.683290  3.992970      68.773546   \n",
       "best_chosen_sd                7.549834  0.514356       6.564367   \n",
       "gamma                        12.651590  7.757765      -3.192698   \n",
       "gamma|dataset[folke2016]     17.173733  9.188220       0.121935   \n",
       "gamma|dataset[krajbich2010]  -9.339527  7.915352     -25.709131   \n",
       "gamma|dataset[krajbich2011]   2.051617  8.128556     -14.001619   \n",
       "gamma|dataset[tavares2017]   -3.217596  8.837724     -21.075818   \n",
       "gamma|dataset_sd             15.453899  7.202848       4.235814   \n",
       "\n",
       "                             hpd0.95_upper  effective_n  gelman_rubin    P(>0)  \n",
       "1|dataset[folke2016]             -0.422510         9964      1.000172      NaN  \n",
       "1|dataset[krajbich2010]          12.083067         9659      1.000095      NaN  \n",
       "1|dataset[krajbich2011]           4.009374         9749      1.000184      NaN  \n",
       "1|dataset[tavares2017]           17.194108        10088      1.000332      NaN  \n",
       "1|dataset_sd                     13.416032        18394      1.000094      NaN  \n",
       "Intercept                        84.916721         9056      1.000262      NaN  \n",
       "best_chosen_sd                    8.565155        34180      0.999994      NaN  \n",
       "gamma                            28.841020         7307      0.999980  0.94485  \n",
       "gamma|dataset[folke2016]         36.408555         9959      0.999979      NaN  \n",
       "gamma|dataset[krajbich2010]       7.006315         7633      0.999991      NaN  \n",
       "gamma|dataset[krajbich2011]      19.361891         8173      0.999981      NaN  \n",
       "gamma|dataset[tavares2017]       14.678272        10318      0.999976      NaN  \n",
       "gamma|dataset_sd                 30.136999        11800      0.999976      NaN  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_file = os.path.join('results', 'mixed_effects_models', '4_parameter_behavior_b_gamma_best_chosen.csv')\n",
    "if not os.path.isfile(result_file):\n",
    "    model_b = Model(df)\n",
    "    result_b = model_b.fit('best_chosen ~ gamma',\n",
    "                           random=['gamma|dataset'],\n",
    "                           categorical=['dataset'],\n",
    "                           samples=n_samples,\n",
    "                           chains=2)\n",
    "    summary_b = result_b.summary(ranefs=True)\n",
    "    summary_b.loc['gamma', 'P(>0)'] = np.mean(model_b.backend.trace.get_values('gamma') > 0)\n",
    "    summary_b.to_csv(result_file)\n",
    "else:\n",
    "    print('Loading previous results from \"{}\"...'.format(result_file))\n",
    "    summary_b = pd.read_csv(result_file, index_col=0)\n",
    "summary_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results loaded from: results/mixed_effects_models/4_parameter_behavior_b_gamma_best_chosen_posteriorplot.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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7du3y9rdw4UJt2bIl5WsAemvR47/zHq8TJkxQR0eHJCk/P98bf//992Nuu2bNGm9OZJhE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106dee358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_path = os.path.join('results', 'mixed_effects_models', '4_parameter_behavior_b_gamma_best_chosen_posteriorplot.png')\n",
    "if not os.path.isfile(plot_path):\n",
    "    plot_posterior(model_b.backend.trace, varnames=['gamma'], ref_val=0, color='lightblue', point_estimate='mode');\n",
    "    plt.savefig(plot_path, dpi=330)\n",
    "else:\n",
    "    print('Results loaded from: {}'.format(plot_path))\n",
    "    show_img(plot_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.patches as mpatches\n",
    "\n",
    "def figure_6(estimates, summary, figsize=cm2inch(18., 6), alpha=0.5, fontsize=7):\n",
    "    \n",
    "    fig, axs = plt.subplots(1, 3, figsize=figsize)\n",
    "    \n",
    "    colors = np.array(['C{}'.format(i)\n",
    "                       for i in range(summary['dataset'].unique().size)])\n",
    "    color_idx = pd.Categorical(summary['dataset'],\n",
    "                               categories=['krajbich2010', 'krajbich2011', 'folke2016', 'tavares2017'],\n",
    "                               ordered=True).codes.astype(int)\n",
    "    \n",
    "    plot_correlation(np.log(estimates['v']),\n",
    "                     np.log(summary['rt']['mean']),\n",
    "                     marker='+',\n",
    "                     alpha=alpha,\n",
    "                     markercolor=colors[color_idx],\n",
    "                     regression=False,\n",
    "                     color='gray',\n",
    "                     xlabel=r'Log $\\hat{v}$',\n",
    "                     ylabel='Log mean RT (ms)',\n",
    "                     xticks=[-11, -10, -9],\n",
    "                     yticks=np.arange(6, 9.5, 0.5),\n",
    "                     ylim=(6, 9.125),\n",
    "                     ax=axs[0])\n",
    "    \n",
    "\n",
    "    plot_correlation(estimates['gamma'],\n",
    "                     summary['gaze_influence'],\n",
    "                     marker='+',\n",
    "                     alpha=alpha,\n",
    "                     markercolor=colors[color_idx],\n",
    "                     regression=False,\n",
    "                     xlabel=r'$\\hat{\\gamma}$',\n",
    "                     ylabel='Gaze influence on\\nP(choice | value)',\n",
    "                     xticks=[-1, 0, 1],\n",
    "                     ax=axs[1],\n",
    "                     annotation_pos=(0.1, 0.9),\n",
    "                     color='gray')\n",
    "    \n",
    "    \n",
    "    plot_correlation(estimates['gamma'],\n",
    "                     summary['best_chosen']['mean'],\n",
    "                     marker='+',\n",
    "                     alpha=alpha,\n",
    "                     markercolor=colors[color_idx],\n",
    "                     regression=False,\n",
    "                     color='gray',\n",
    "                     xlabel=r'$\\hat{\\gamma}$',\n",
    "                     ylabel='P(choose best)',\n",
    "                     xticks=[-1, 0, 1],\n",
    "                     ylim=(0.3, 1.0),\n",
    "                     yticks=(np.arange(0.3, 1.1, 0.1)),\n",
    "                     ax=axs[2])\n",
    "    \n",
    "    patches = [mpatches.Patch(color=color, label=label)\n",
    "               for color, label in zip(colors, ['Krajbich 2010', 'Krajbich 2011', 'Folke 2016', 'Tavares 2017'])]\n",
    "    axs[0].legend(patches,\n",
    "                  ['Krajbich 2010', 'Krajbich 2011', 'Folke 2016', 'Tavares 2017'],\n",
    "                  loc='lower left',\n",
    "                  handlelength=1, handleheight=1,\n",
    "                  fontsize=6, \n",
    "                  frameon=False)\n",
    "\n",
    "    # Labels\n",
    "    for label, ax in zip(list('abc'), axs.ravel()):\n",
    "        ax.text(-0.25, 1.1, label, transform=ax.transAxes,\n",
    "                fontsize=fontsize, fontweight='bold', va='top')\n",
    "        ax.spines['top'].set_visible(False)\n",
    "        ax.spines['right'].set_visible(False)\n",
    "        \n",
    "        # Font sizes\n",
    "        ax.tick_params(axis='both', labelsize=fontsize)\n",
    "        \n",
    "    fig.tight_layout(pad=1)\n",
    "    \n",
    "    return fig, axs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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VyfkAGNLghR0v8vNlP+dP6/6EN+odXOFNTEw+yhwye6MQ4rJU23zgl4Mp4IkSbWhk5hsL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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12fe2f978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = figure_6(estimates, odd_summary)\n",
    "\n",
    "add_regression_line(axs[0], summary_a.loc['Intercept', 'mean'], summary_a.loc['log_v', 'mean'], linewidth=1)\n",
    "add_regression_line(axs[1], summary_c.loc['Intercept', 'mean'] / 100, summary_c.loc['gamma', 'mean'] / 100, linewidth=1)\n",
    "add_regression_line(axs[2], summary_b.loc['Intercept', 'mean'] / 100, summary_b.loc['gamma', 'mean'] / 100, linewidth=1)\n",
    "\n",
    "plt.savefig('results/figures/figure_6_glam_parameters_predict_behavior.png', dpi=330, bbox_inches='tight')\n",
    "plt.savefig('results/figures/figure_6_glam_parameters_predict_behavior.pdf', dpi=330, bbox_inches='tight')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Robustness checks\n",
    "\n",
    "## Correlation of $\\gamma$ and P(choose best) within each dataset (post-hoc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "krajbich2010\n",
      "Normality assumption violated: True\n",
      "spearman r = 0.15149076923716442, p = 0.35725530056987154\n",
      "\n",
      "krajbich2011\n",
      "pearson r = 0.619938901335866, p = 0.00025836360658335663\n",
      "\n",
      "folke2016\n",
      "pearson r = 0.7492087972674608, p = 2.5215551320240124e-05\n",
      "\n",
      "tavares2017\n",
      "pearson r = 0.4124097728541537, p = 0.040492836788055056\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "\n",
    "for dataset in df['dataset'].unique():\n",
    "    df_i = df.loc[df['dataset'] == dataset].copy()\n",
    "    \n",
    "    print('\\n'+dataset)\n",
    "    sample_corr(df_i['best_chosen'], df_i['gamma'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relationship between $\\gamma$ and P(choose best) without first fixations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load data without first fixations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_data_nofirst = pd.read_csv('data/data_nofirst.csv')\n",
    "even_nofirst = all_data_nofirst[(all_data_nofirst['trial'] % 2) == 0].reset_index(drop=True)\n",
    "odd_nofirst = all_data_nofirst[(all_data_nofirst['trial'] % 2) == 1].reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute behavioural summaries for each individual, from odd trials without first fixations only:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "odd_nofirst_summary = pd.DataFrame()\n",
    "\n",
    "for di, dataset in enumerate(odd_nofirst['dataset'].unique()):\n",
    "    odd_nofirst_di = odd_nofirst[odd_nofirst['dataset'] == dataset].copy()\n",
    "    n_items = odd_nofirst_di['n_items'].unique()[0]\n",
    "    \n",
    "    odd_nofirst_summary_di = aggregate_subject_level(odd_nofirst_di, n_items=n_items)\n",
    "    \n",
    "    odd_nofirst_summary = pd.concat([odd_nofirst_summary, odd_nofirst_summary_di])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>best_chosen</th>\n",
       "      <th colspan=\"8\" halign=\"left\">rt</th>\n",
       "      <th>gaze_influence</th>\n",
       "      <th>dataset</th>\n",
       "    </tr>\n",
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       "      <th></th>\n",
       "      <th>mean</th>\n",
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       "      <th>std</th>\n",
       "      <th>min</th>\n",
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       "      <th>se</th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>subject</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th>0</th>\n",
       "      <td>0.818182</td>\n",
       "      <td>1710.500000</td>\n",
       "      <td>890.808047</td>\n",
       "      <td>682.0</td>\n",
       "      <td>4142.0</td>\n",
       "      <td>135.846954</td>\n",
       "      <td>1121.75</td>\n",
       "      <td>1990.25</td>\n",
       "      <td>868.50</td>\n",
       "      <td>0.021164</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.673469</td>\n",
       "      <td>1728.489796</td>\n",
       "      <td>857.141479</td>\n",
       "      <td>743.0</td>\n",
       "      <td>4602.0</td>\n",
       "      <td>123.717716</td>\n",
       "      <td>1166.00</td>\n",
       "      <td>1937.00</td>\n",
       "      <td>771.00</td>\n",
       "      <td>-0.123755</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.840000</td>\n",
       "      <td>4078.660000</td>\n",
       "      <td>2623.044800</td>\n",
       "      <td>943.0</td>\n",
       "      <td>12079.0</td>\n",
       "      <td>374.720686</td>\n",
       "      <td>2104.25</td>\n",
       "      <td>5329.00</td>\n",
       "      <td>3224.75</td>\n",
       "      <td>0.165827</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.789474</td>\n",
       "      <td>2076.368421</td>\n",
       "      <td>746.767012</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>4742.0</td>\n",
       "      <td>176.014673</td>\n",
       "      <td>1535.50</td>\n",
       "      <td>2299.00</td>\n",
       "      <td>763.50</td>\n",
       "      <td>-0.218261</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.836735</td>\n",
       "      <td>1867.693878</td>\n",
       "      <td>1094.508877</td>\n",
       "      <td>692.0</td>\n",
       "      <td>5891.0</td>\n",
       "      <td>157.978749</td>\n",
       "      <td>1247.00</td>\n",
       "      <td>2134.00</td>\n",
       "      <td>887.00</td>\n",
       "      <td>-0.113096</td>\n",
       "      <td>krajbich2010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        best_chosen           rt                                            \\\n",
       "               mean         mean          std     min      max          se   \n",
       "subject                                                                      \n",
       "0          0.818182  1710.500000   890.808047   682.0   4142.0  135.846954   \n",
       "1          0.673469  1728.489796   857.141479   743.0   4602.0  123.717716   \n",
       "2          0.840000  4078.660000  2623.044800   943.0  12079.0  374.720686   \n",
       "3          0.789474  2076.368421   746.767012  1340.0   4742.0  176.014673   \n",
       "4          0.836735  1867.693878  1094.508877   692.0   5891.0  157.978749   \n",
       "\n",
       "                                   gaze_influence       dataset  \n",
       "              q1       q3      iqr                               \n",
       "subject                                                          \n",
       "0        1121.75  1990.25   868.50       0.021164  krajbich2010  \n",
       "1        1166.00  1937.00   771.00      -0.123755  krajbich2010  \n",
       "2        2104.25  5329.00  3224.75       0.165827  krajbich2010  \n",
       "3        1535.50  2299.00   763.50      -0.218261  krajbich2010  \n",
       "4        1247.00  2134.00   887.00      -0.113096  krajbich2010  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odd_nofirst_summary.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load GLAM parameter estimates, estimated from even trials that had the first fixation removed from the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>subject</th>\n",
       "      <th>tau</th>\n",
       "      <th>v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>0.82</td>\n",
       "      <td>0.009022</td>\n",
       "      <td>0</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.000094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.95</td>\n",
       "      <td>0.009931</td>\n",
       "      <td>1</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.000101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.81</td>\n",
       "      <td>0.009600</td>\n",
       "      <td>2</td>\n",
       "      <td>1.79</td>\n",
       "      <td>0.000022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.70</td>\n",
       "      <td>0.004988</td>\n",
       "      <td>3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.000083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.72</td>\n",
       "      <td>0.010225</td>\n",
       "      <td>4</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.000087</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gamma         s  subject   tau         v\n",
       "0.0   0.82  0.009022        0  0.40  0.000094\n",
       "1.0   0.95  0.009931        1  0.13  0.000101\n",
       "2.0   0.81  0.009600        2  1.79  0.000022\n",
       "3.0   0.70  0.004988        3  0.01  0.000083\n",
       "4.0   0.72  0.010225        4  0.29  0.000087"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimates_nofirst = pd.DataFrame()\n",
    "parameter_names = ['v', 'gamma', 's', 'tau']\n",
    "for subject in odd_nofirst_summary.index:\n",
    "    subject_estimates_nofirst_df = pd.read_csv(os.path.join('results', 'estimates', 'out_of_sample', 'GLAM_nofirst',\n",
    "                                                    'estimates_{}_GLAM_nofirst_oos.csv'.format(subject)),\n",
    "                                       index_col=0)\n",
    "    subject_estimates_nofirst_dict = {parameter: subject_estimates_nofirst_df.loc[parameter + '__0_0', 'MAP']\n",
    "                              for parameter in parameter_names}\n",
    "    subject_estimates_nofirst_dict['subject'] = subject\n",
    "    estimates_nofirst = pd.concat([estimates_nofirst,\n",
    "                           pd.DataFrame(subject_estimates_nofirst_dict,\n",
    "                                        index=np.ones(1)*subject)])\n",
    "\n",
    "estimates_nofirst.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Mixed effects regressions with random slope and intercept for data sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prepare data for Bayesian mixed effects modeling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Format data for mixed model\n",
    "df = pd.concat([estimates_nofirst, odd_nofirst_summary], axis=1)\n",
    "df['log_rt'] = np.log(df[('rt', 'mean')])\n",
    "df['log_v'] = np.log(df['v'])\n",
    "df['best_chosen'] = 100 * df[('best_chosen', 'mean')]\n",
    "df['gaze_influence'] = 100 * df[('gaze_influence', '')]\n",
    "df['dataset'] = df[('dataset', '')]\n",
    "\n",
    "df = df[['subject', 'dataset', 'log_rt', 'best_chosen', 'gaze_influence', 'log_v', 'gamma', 's', 'tau']].copy().reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>dataset</th>\n",
       "      <th>log_rt</th>\n",
       "      <th>best_chosen</th>\n",
       "      <th>gaze_influence</th>\n",
       "      <th>log_v</th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>tau</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.444541</td>\n",
       "      <td>81.818182</td>\n",
       "      <td>2.116404</td>\n",
       "      <td>-9.272216</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.009022</td>\n",
       "      <td>0.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.455003</td>\n",
       "      <td>67.346939</td>\n",
       "      <td>-12.375518</td>\n",
       "      <td>-9.200390</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.009931</td>\n",
       "      <td>0.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>8.313524</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>16.582693</td>\n",
       "      <td>-10.724468</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.009600</td>\n",
       "      <td>1.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.638376</td>\n",
       "      <td>78.947368</td>\n",
       "      <td>-21.826137</td>\n",
       "      <td>-9.396670</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.004988</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>krajbich2010</td>\n",
       "      <td>7.532460</td>\n",
       "      <td>83.673469</td>\n",
       "      <td>-11.309615</td>\n",
       "      <td>-9.349602</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.010225</td>\n",
       "      <td>0.29</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   subject       dataset    log_rt  best_chosen  gaze_influence      log_v  \\\n",
       "0        0  krajbich2010  7.444541    81.818182        2.116404  -9.272216   \n",
       "1        1  krajbich2010  7.455003    67.346939      -12.375518  -9.200390   \n",
       "2        2  krajbich2010  8.313524    84.000000       16.582693 -10.724468   \n",
       "3        3  krajbich2010  7.638376    78.947368      -21.826137  -9.396670   \n",
       "4        4  krajbich2010  7.532460    83.673469      -11.309615  -9.349602   \n",
       "\n",
       "   gamma         s   tau  \n",
       "0   0.82  0.009022  0.40  \n",
       "1   0.95  0.009931  0.13  \n",
       "2   0.81  0.009600  1.79  \n",
       "3   0.70  0.004988  0.01  \n",
       "4   0.72  0.010225  0.29  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_samples = 20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading previous results from \"results/mixed_effects_models/4_robustness-check_gamma_pchoosebest_nofirst.csv\"...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd0.95_lower</th>\n",
       "      <th>hpd0.95_upper</th>\n",
       "      <th>effective_n</th>\n",
       "      <th>gelman_rubin</th>\n",
       "      <th>P(&gt;0)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2010]</th>\n",
       "      <td>0.165662</td>\n",
       "      <td>4.048481</td>\n",
       "      <td>-9.166179</td>\n",
       "      <td>7.768126</td>\n",
       "      <td>3792</td>\n",
       "      <td>1.000011</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2011]</th>\n",
       "      <td>-4.860355</td>\n",
       "      <td>4.247710</td>\n",
       "      <td>-14.291647</td>\n",
       "      <td>2.983733</td>\n",
       "      <td>3393</td>\n",
       "      <td>0.999986</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[tavares2017]</th>\n",
       "      <td>3.471447</td>\n",
       "      <td>4.371224</td>\n",
       "      <td>-4.975883</td>\n",
       "      <td>13.007316</td>\n",
       "      <td>5602</td>\n",
       "      <td>1.000035</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset_sd</th>\n",
       "      <td>6.293406</td>\n",
       "      <td>3.616410</td>\n",
       "      <td>0.508740</td>\n",
       "      <td>13.522915</td>\n",
       "      <td>5273</td>\n",
       "      <td>0.999975</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>74.869793</td>\n",
       "      <td>4.129430</td>\n",
       "      <td>66.912973</td>\n",
       "      <td>83.665470</td>\n",
       "      <td>3204</td>\n",
       "      <td>0.999994</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>best_chosen_sd</th>\n",
       "      <td>7.767048</td>\n",
       "      <td>0.572194</td>\n",
       "      <td>6.704250</td>\n",
       "      <td>8.931710</td>\n",
       "      <td>20074</td>\n",
       "      <td>0.999982</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma</th>\n",
       "      <td>8.780299</td>\n",
       "      <td>4.085390</td>\n",
       "      <td>0.141217</td>\n",
       "      <td>17.084060</td>\n",
       "      <td>2447</td>\n",
       "      <td>0.999997</td>\n",
       "      <td>0.972725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2010]</th>\n",
       "      <td>-0.389844</td>\n",
       "      <td>3.855768</td>\n",
       "      <td>-9.237151</td>\n",
       "      <td>7.973158</td>\n",
       "      <td>2743</td>\n",
       "      <td>0.999984</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2011]</th>\n",
       "      <td>0.651618</td>\n",
       "      <td>4.117170</td>\n",
       "      <td>-7.516587</td>\n",
       "      <td>10.327755</td>\n",
       "      <td>2315</td>\n",
       "      <td>0.999996</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[tavares2017]</th>\n",
       "      <td>1.075043</td>\n",
       "      <td>4.578789</td>\n",
       "      <td>-7.897731</td>\n",
       "      <td>12.063872</td>\n",
       "      <td>3804</td>\n",
       "      <td>0.999980</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset_sd</th>\n",
       "      <td>5.056036</td>\n",
       "      <td>5.039937</td>\n",
       "      <td>0.000025</td>\n",
       "      <td>15.283775</td>\n",
       "      <td>3558</td>\n",
       "      <td>1.000135</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  mean        sd  hpd0.95_lower  \\\n",
       "1|dataset[krajbich2010]       0.165662  4.048481      -9.166179   \n",
       "1|dataset[krajbich2011]      -4.860355  4.247710     -14.291647   \n",
       "1|dataset[tavares2017]        3.471447  4.371224      -4.975883   \n",
       "1|dataset_sd                  6.293406  3.616410       0.508740   \n",
       "Intercept                    74.869793  4.129430      66.912973   \n",
       "best_chosen_sd                7.767048  0.572194       6.704250   \n",
       "gamma                         8.780299  4.085390       0.141217   \n",
       "gamma|dataset[krajbich2010]  -0.389844  3.855768      -9.237151   \n",
       "gamma|dataset[krajbich2011]   0.651618  4.117170      -7.516587   \n",
       "gamma|dataset[tavares2017]    1.075043  4.578789      -7.897731   \n",
       "gamma|dataset_sd              5.056036  5.039937       0.000025   \n",
       "\n",
       "                             hpd0.95_upper  effective_n  gelman_rubin  \\\n",
       "1|dataset[krajbich2010]           7.768126         3792      1.000011   \n",
       "1|dataset[krajbich2011]           2.983733         3393      0.999986   \n",
       "1|dataset[tavares2017]           13.007316         5602      1.000035   \n",
       "1|dataset_sd                     13.522915         5273      0.999975   \n",
       "Intercept                        83.665470         3204      0.999994   \n",
       "best_chosen_sd                    8.931710        20074      0.999982   \n",
       "gamma                            17.084060         2447      0.999997   \n",
       "gamma|dataset[krajbich2010]       7.973158         2743      0.999984   \n",
       "gamma|dataset[krajbich2011]      10.327755         2315      0.999996   \n",
       "gamma|dataset[tavares2017]       12.063872         3804      0.999980   \n",
       "gamma|dataset_sd                 15.283775         3558      1.000135   \n",
       "\n",
       "                                P(>0)  \n",
       "1|dataset[krajbich2010]           NaN  \n",
       "1|dataset[krajbich2011]           NaN  \n",
       "1|dataset[tavares2017]            NaN  \n",
       "1|dataset_sd                      NaN  \n",
       "Intercept                         NaN  \n",
       "best_chosen_sd                    NaN  \n",
       "gamma                        0.972725  \n",
       "gamma|dataset[krajbich2010]       NaN  \n",
       "gamma|dataset[krajbich2011]       NaN  \n",
       "gamma|dataset[tavares2017]        NaN  \n",
       "gamma|dataset_sd                  NaN  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pymc3 import plot_posterior\n",
    "\n",
    "result_file = os.path.join('results', 'mixed_effects_models', '4_robustness-check_gamma_pchoosebest_nofirst.csv')\n",
    "\n",
    "if not os.path.isfile(result_file):\n",
    "    model = Model(df)\n",
    "    result = model.fit('best_chosen ~ gamma',\n",
    "                       random=['gamma|dataset'],\n",
    "                       categorical=['dataset'],\n",
    "                       samples=n_samples,\n",
    "                       chains=2)\n",
    "    summary = result.summary(ranefs=True)\n",
    "    summary.loc['gamma', 'P(>0)'] = np.mean(model.backend.trace.get_values('gamma') > 0)\n",
    "    summary.to_csv(result_file)\n",
    "else:\n",
    "    print('Loading previous results from \"{}\"...'.format(result_file))\n",
    "    summary = pd.read_csv(result_file, index_col=0)\n",
    "summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results loaded from: results/mixed_effects_models/4_robustness-check_gamma_pchoosebest_nofirst_posteriorplot.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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q1ar0FQMYc11XjuPIcRwNGzYs0u44jg4dOpTByhCNkU4/Mnbs2KT6lZeX92oajdOgkW63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\nAMDM/wN9b8C6JCiAlAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12fbe6978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_path = os.path.join('results', 'mixed_effects_models', '4_robustness-check_gamma_pchoosebest_nofirst_posteriorplot.png')\n",
    "if not os.path.isfile(plot_path):\n",
    "    plot_posterior(model.backend.trace, varnames=['gamma'], ref_val=0, color='lightblue', point_estimate='mode');\n",
    "    plt.savefig(plot_path, dpi=330)\n",
    "else:\n",
    "    print('Results loaded from: {}'.format(plot_path))\n",
    "    show_img(plot_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The effect is still present, even after removing all first fixations from the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The relationship with $\\gamma$ estimates from additive variant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>subject</th>\n",
       "      <th>tau</th>\n",
       "      <th>v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>1.78</td>\n",
       "      <td>0.008020</td>\n",
       "      <td>0</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.000096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>7.87</td>\n",
       "      <td>0.010117</td>\n",
       "      <td>1</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.000100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.49</td>\n",
       "      <td>0.008944</td>\n",
       "      <td>2</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.000023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>1.11</td>\n",
       "      <td>0.004812</td>\n",
       "      <td>3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.000089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>6.00</td>\n",
       "      <td>0.009909</td>\n",
       "      <td>4</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.000092</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gamma         s  subject   tau         v\n",
       "0.0   1.78  0.008020        0  0.36  0.000096\n",
       "1.0   7.87  0.010117        1  0.10  0.000100\n",
       "2.0   0.49  0.008944        2  1.00  0.000023\n",
       "3.0   1.11  0.004812        3  0.01  0.000089\n",
       "4.0   6.00  0.009909        4  0.20  0.000092"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimates_additive = pd.DataFrame()\n",
    "parameter_names = ['v', 'gamma', 's', 'tau']\n",
    "for subject in odd_summary.index:\n",
    "    subject_estimates_additive_df = pd.read_csv(os.path.join('results', 'estimates', 'out_of_sample', 'additive',\n",
    "                                                    'estimates_{}_additive_oos.csv'.format(subject)),\n",
    "                                       index_col=0)\n",
    "    subject_estimates_additive_dict = {parameter: subject_estimates_additive_df.loc[parameter + '__0_0', 'MAP']\n",
    "                                       for parameter in parameter_names}\n",
    "    subject_estimates_additive_dict['subject'] = subject\n",
    "    estimates_additive = pd.concat([estimates_additive,\n",
    "                                    pd.DataFrame(subject_estimates_additive_dict,\n",
    "                                                 index=np.ones(1)* subject)])\n",
    "\n",
    "estimates_additive.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Format data for mixed model\n",
    "df = pd.concat([estimates_additive, odd_summary], axis=1)\n",
    "df['log_rt'] = np.log(df[('rt', 'mean')])\n",
    "df['log_v'] = np.log(df['v'])\n",
    "df['best_chosen'] = 100 * df[('best_chosen', 'mean')]\n",
    "df['gaze_influence'] = 100 * df[('gaze_influence', '')]\n",
    "df['dataset'] = df[('dataset', '')]\n",
    "\n",
    "df = df[['subject', 'dataset', 'log_rt', 'best_chosen', 'gaze_influence', 'log_v', 'gamma', 's', 'tau']].copy().reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading previous results from \"results/mixed_effects_models/4_robustness-check_gamma-additive_pchoosebest.csv\"...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd0.95_lower</th>\n",
       "      <th>hpd0.95_upper</th>\n",
       "      <th>effective_n</th>\n",
       "      <th>gelman_rubin</th>\n",
       "      <th>P(&gt;0)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1|dataset[folke2016]</th>\n",
       "      <td>-6.124273</td>\n",
       "      <td>4.229299</td>\n",
       "      <td>-14.692578</td>\n",
       "      <td>1.952894</td>\n",
       "      <td>7707</td>\n",
       "      <td>1.000071</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2010]</th>\n",
       "      <td>1.207260</td>\n",
       "      <td>3.924695</td>\n",
       "      <td>-6.717945</td>\n",
       "      <td>9.284345</td>\n",
       "      <td>6826</td>\n",
       "      <td>1.000188</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[krajbich2011]</th>\n",
       "      <td>-1.733099</td>\n",
       "      <td>4.074861</td>\n",
       "      <td>-10.179785</td>\n",
       "      <td>6.365572</td>\n",
       "      <td>7552</td>\n",
       "      <td>1.000005</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset[tavares2017]</th>\n",
       "      <td>7.609854</td>\n",
       "      <td>4.434981</td>\n",
       "      <td>-0.734537</td>\n",
       "      <td>16.626238</td>\n",
       "      <td>8804</td>\n",
       "      <td>1.000221</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1|dataset_sd</th>\n",
       "      <td>7.204440</td>\n",
       "      <td>3.203371</td>\n",
       "      <td>1.954305</td>\n",
       "      <td>14.144801</td>\n",
       "      <td>12574</td>\n",
       "      <td>1.000011</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>81.956893</td>\n",
       "      <td>3.809756</td>\n",
       "      <td>74.028124</td>\n",
       "      <td>89.702657</td>\n",
       "      <td>6263</td>\n",
       "      <td>1.000199</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>best_chosen_sd</th>\n",
       "      <td>8.067291</td>\n",
       "      <td>0.546230</td>\n",
       "      <td>7.017159</td>\n",
       "      <td>9.149817</td>\n",
       "      <td>33114</td>\n",
       "      <td>0.999975</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma</th>\n",
       "      <td>-0.536286</td>\n",
       "      <td>0.222777</td>\n",
       "      <td>-0.978055</td>\n",
       "      <td>-0.056238</td>\n",
       "      <td>8212</td>\n",
       "      <td>1.000015</td>\n",
       "      <td>0.02175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[folke2016]</th>\n",
       "      <td>-0.142734</td>\n",
       "      <td>0.245243</td>\n",
       "      <td>-0.699783</td>\n",
       "      <td>0.292865</td>\n",
       "      <td>7849</td>\n",
       "      <td>1.000053</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2010]</th>\n",
       "      <td>0.087989</td>\n",
       "      <td>0.235987</td>\n",
       "      <td>-0.354013</td>\n",
       "      <td>0.645164</td>\n",
       "      <td>10709</td>\n",
       "      <td>1.000002</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[krajbich2011]</th>\n",
       "      <td>-0.147693</td>\n",
       "      <td>0.263740</td>\n",
       "      <td>-0.758272</td>\n",
       "      <td>0.292129</td>\n",
       "      <td>8671</td>\n",
       "      <td>1.000145</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset[tavares2017]</th>\n",
       "      <td>0.127075</td>\n",
       "      <td>0.273924</td>\n",
       "      <td>-0.353639</td>\n",
       "      <td>0.785364</td>\n",
       "      <td>15236</td>\n",
       "      <td>0.999978</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma|dataset_sd</th>\n",
       "      <td>0.318561</td>\n",
       "      <td>0.270524</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0.842738</td>\n",
       "      <td>7294</td>\n",
       "      <td>1.000813</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  mean        sd  hpd0.95_lower  \\\n",
       "1|dataset[folke2016]         -6.124273  4.229299     -14.692578   \n",
       "1|dataset[krajbich2010]       1.207260  3.924695      -6.717945   \n",
       "1|dataset[krajbich2011]      -1.733099  4.074861     -10.179785   \n",
       "1|dataset[tavares2017]        7.609854  4.434981      -0.734537   \n",
       "1|dataset_sd                  7.204440  3.203371       1.954305   \n",
       "Intercept                    81.956893  3.809756      74.028124   \n",
       "best_chosen_sd                8.067291  0.546230       7.017159   \n",
       "gamma                        -0.536286  0.222777      -0.978055   \n",
       "gamma|dataset[folke2016]     -0.142734  0.245243      -0.699783   \n",
       "gamma|dataset[krajbich2010]   0.087989  0.235987      -0.354013   \n",
       "gamma|dataset[krajbich2011]  -0.147693  0.263740      -0.758272   \n",
       "gamma|dataset[tavares2017]    0.127075  0.273924      -0.353639   \n",
       "gamma|dataset_sd              0.318561  0.270524       0.000045   \n",
       "\n",
       "                             hpd0.95_upper  effective_n  gelman_rubin    P(>0)  \n",
       "1|dataset[folke2016]              1.952894         7707      1.000071      NaN  \n",
       "1|dataset[krajbich2010]           9.284345         6826      1.000188      NaN  \n",
       "1|dataset[krajbich2011]           6.365572         7552      1.000005      NaN  \n",
       "1|dataset[tavares2017]           16.626238         8804      1.000221      NaN  \n",
       "1|dataset_sd                     14.144801        12574      1.000011      NaN  \n",
       "Intercept                        89.702657         6263      1.000199      NaN  \n",
       "best_chosen_sd                    9.149817        33114      0.999975      NaN  \n",
       "gamma                            -0.056238         8212      1.000015  0.02175  \n",
       "gamma|dataset[folke2016]          0.292865         7849      1.000053      NaN  \n",
       "gamma|dataset[krajbich2010]       0.645164        10709      1.000002      NaN  \n",
       "gamma|dataset[krajbich2011]       0.292129         8671      1.000145      NaN  \n",
       "gamma|dataset[tavares2017]        0.785364        15236      0.999978      NaN  \n",
       "gamma|dataset_sd                  0.842738         7294      1.000813      NaN  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pymc3 import plot_posterior\n",
    "\n",
    "result_file = os.path.join('results', 'mixed_effects_models', '4_robustness-check_gamma-additive_pchoosebest.csv')\n",
    "\n",
    "if not os.path.isfile(result_file):\n",
    "    model = Model(df)\n",
    "    result = model.fit('best_chosen ~ gamma',\n",
    "                       random=['gamma|dataset'],\n",
    "                       categorical=['dataset'],\n",
    "                       samples=n_samples,\n",
    "                       chains=2)\n",
    "    summary = result.summary(ranefs=True)\n",
    "    summary.loc['gamma', 'P(>0)'] = np.mean(model.backend.trace.get_values('gamma') > 0)\n",
    "    summary.to_csv(result_file)\n",
    "else:\n",
    "    print('Loading previous results from \"{}\"...'.format(result_file))\n",
    "    summary = pd.read_csv(result_file, index_col=0)\n",
    "summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results loaded from: results/mixed_effects_models/4_robustness-check_gamma-additive_pchoosebest_posteriorplot.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZvHlzzxuJjGB5RWrveBozZoz27Nmjb7/9Vg899JBmzpwp13X19ddfM+rJAYROngieCjt4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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x140b4fb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_path = os.path.join('results', 'mixed_effects_models', '4_robustness-check_gamma-additive_pchoosebest_posteriorplot.png')\n",
    "if not os.path.isfile(plot_path):\n",
    "    plot_posterior(model.backend.trace, varnames=['gamma'], ref_val=0, color='lightblue', point_estimate='mode');\n",
    "    plt.savefig(plot_path, dpi=330)\n",
    "else:\n",
    "    print('Results loaded from: {}'.format(plot_path))\n",
    "    show_img(plot_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\gamma$ estimates for multiplicative and additive variant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>subject</th>\n",
       "      <th>tau</th>\n",
       "      <th>v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>0.79</td>\n",
       "      <td>0.010750</td>\n",
       "      <td>0</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.000084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>-0.13</td>\n",
       "      <td>0.009213</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.000095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.82</td>\n",
       "      <td>0.009846</td>\n",
       "      <td>2</td>\n",
       "      <td>1.17</td>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.58</td>\n",
       "      <td>0.006562</td>\n",
       "      <td>3</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.000089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.51</td>\n",
       "      <td>0.009910</td>\n",
       "      <td>4</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.000090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gamma         s  subject   tau         v\n",
       "0.0   0.79  0.010750        0  0.49  0.000084\n",
       "1.0  -0.13  0.009213        1  0.22  0.000095\n",
       "2.0   0.82  0.009846        2  1.17  0.000024\n",
       "3.0   0.58  0.006562        3  0.09  0.000089\n",
       "4.0   0.51  0.009910        4  0.30  0.000090"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimates_multiplicative = pd.DataFrame()\n",
    "parameter_names = ['v', 'gamma', 's', 'tau']\n",
    "for subject in odd_summary.index:\n",
    "    subject_estimates_multiplicative_df = pd.read_csv(os.path.join('results', 'estimates', 'in_sample', 'GLAM',\n",
    "                                                    'estimates_{}_GLAM_ins.csv'.format(subject)),\n",
    "                                       index_col=0)\n",
    "    subject_estimates_multiplicative_dict = {parameter: subject_estimates_multiplicative_df.loc[parameter + '__0_0', 'MAP']\n",
    "                              for parameter in parameter_names}\n",
    "    subject_estimates_multiplicative_dict['subject'] = subject\n",
    "    estimates_multiplicative = pd.concat([estimates_multiplicative,\n",
    "                           pd.DataFrame(subject_estimates_multiplicative_dict,\n",
    "                                        index=np.ones(1)*subject)])\n",
    "\n",
    "estimates_multiplicative.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>subject</th>\n",
       "      <th>tau</th>\n",
       "      <th>v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>0.79</td>\n",
       "      <td>0.010750</td>\n",
       "      <td>0</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.000084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>-0.13</td>\n",
       "      <td>0.009213</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.000095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.82</td>\n",
       "      <td>0.009846</td>\n",
       "      <td>2</td>\n",
       "      <td>1.17</td>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.58</td>\n",
       "      <td>0.006562</td>\n",
       "      <td>3</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.000089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.51</td>\n",
       "      <td>0.009910</td>\n",
       "      <td>4</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.000090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gamma         s  subject   tau         v\n",
       "0.0   0.79  0.010750        0  0.49  0.000084\n",
       "1.0  -0.13  0.009213        1  0.22  0.000095\n",
       "2.0   0.82  0.009846        2  1.17  0.000024\n",
       "3.0   0.58  0.006562        3  0.09  0.000089\n",
       "4.0   0.51  0.009910        4  0.30  0.000090"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimates_multiplicative = pd.DataFrame()\n",
    "parameter_names = ['v', 'gamma', 's', 'tau']\n",
    "for subject in odd_summary.index:\n",
    "    subject_estimates_multiplicative_df = pd.read_csv(os.path.join('results', 'estimates', 'in_sample', 'GLAM',\n",
    "                                                    'estimates_{}_GLAM_ins.csv'.format(subject)),\n",
    "                                       index_col=0)\n",
    "    subject_estimates_multiplicative_dict = {parameter: subject_estimates_multiplicative_df.loc[parameter + '__0_0', 'MAP']\n",
    "                              for parameter in parameter_names}\n",
    "    subject_estimates_multiplicative_dict['subject'] = subject\n",
    "    estimates_multiplicative = pd.concat([estimates_multiplicative,\n",
    "                           pd.DataFrame(subject_estimates_multiplicative_dict,\n",
    "                                        index=np.ones(1)*subject)])\n",
    "\n",
    "estimates_multiplicative.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gamma</th>\n",
       "      <th>s</th>\n",
       "      <th>subject</th>\n",
       "      <th>tau</th>\n",
       "      <th>v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>1.21</td>\n",
       "      <td>0.010469</td>\n",
       "      <td>0</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.000085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>8.71</td>\n",
       "      <td>0.009414</td>\n",
       "      <td>1</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.000094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.91</td>\n",
       "      <td>0.010088</td>\n",
       "      <td>2</td>\n",
       "      <td>1.70</td>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>1.38</td>\n",
       "      <td>0.006449</td>\n",
       "      <td>3</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.000090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>3.66</td>\n",
       "      <td>0.009996</td>\n",
       "      <td>4</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.000089</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gamma         s  subject   tau         v\n",
       "0.0   1.21  0.010469        0  0.40  0.000085\n",
       "1.0   8.71  0.009414        1  0.11  0.000094\n",
       "2.0   0.91  0.010088        2  1.70  0.000024\n",
       "3.0   1.38  0.006449        3  0.08  0.000090\n",
       "4.0   3.66  0.009996        4  0.24  0.000089"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimates_additive = pd.DataFrame()\n",
    "parameter_names = ['v', 'gamma', 's', 'tau']\n",
    "for subject in odd_summary.index:\n",
    "    subject_estimates_additive_df = pd.read_csv(os.path.join('results', 'estimates', 'in_sample', 'additive',\n",
    "                                                    'estimates_{}_additive_ins.csv'.format(subject)),\n",
    "                                       index_col=0)\n",
    "    subject_estimates_additive_dict = {parameter: subject_estimates_additive_df.loc[parameter + '__0_0', 'MAP']\n",
    "                              for parameter in parameter_names}\n",
    "    subject_estimates_additive_dict['subject'] = subject\n",
    "    estimates_additive = pd.concat([estimates_additive,\n",
    "                           pd.DataFrame(subject_estimates_additive_dict,\n",
    "                                        index=np.ones(1)*subject)])\n",
    "\n",
    "estimates_additive.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normality assumption violated: True\n",
      "spearman r = -0.8581596122523555, p = 2.2136512452440841e-35\n"
     ]
    },
    {
     "data": {
      "image/png": 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6GueYyrKM3W5H30D3LYxGIyqVqsYh2JIkIcsyBoOhQZ5DENydCPbTqVTK6pPwcCXko6JO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\nLL3xRjvhOnu2XbEDGtg7ooFdKdVnLnPTU4DaWpu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      "text/plain": [
       "<matplotlib.figure.Figure at 0x140b9a6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_correlation(estimates_multiplicative['gamma'],\n",
    "                 estimates_additive['gamma'], annotate=False)\n",
    "sample_corr(estimates_multiplicative['gamma'], estimates_additive['gamma'])"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "174px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": false,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": false,
   "widenNotebook": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}