Item level effects

2afc_items.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling item-effects in two-alternative forced choice data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "sns.set_context('notebook', font_scale=1.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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></th>\n",
       "      <th>looked_at_target</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>target</th>\n",
       "      <th>distractor</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">0</th>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">1</th>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2</th>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   looked_at_target\n",
       "target distractor                  \n",
       "0      1                          1\n",
       "       2                          0\n",
       "1      0                          1\n",
       "       2                          0\n",
       "2      0                          1\n",
       "       1                          1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame({\n",
    "    'target':     [0, 1, 2, 0, 1, 2],  # the item_id of the target\n",
    "    'distractor': [1, 2, 0, 2, 0, 1],  # the item_id of the distractor\n",
    "    'looked_at_target': [1, 0, 1, 0, 1, 1]\n",
    "})\n",
    "# Note that item 2 always wins.\n",
    "data.set_index(['target', 'distractor']).sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Each item should occur as a target and a distractor.\n",
    "# Although this requirement could be removed if you used\n",
    "# tighter priors to encourage the model to use the universal\n",
    "# target_pref parameter rather than each specific item_pref\n",
    "assert set(data.target) == set(data.distractor)\n",
    "n_items = len(set(data.target))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/miniconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "/usr/local/lib/miniconda3/lib/python3.6/site-packages/pymc3/model.py:384: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  if not np.issubdtype(var.dtype, float):\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [target_pref, item_prefs]\n",
      "100%|██████████| 1000/1000 [00:02<00:00, 429.57it/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    # Latent variables.\n",
    "    item_prefs = pm.Normal('item_prefs', mu=0, sd=10, shape=n_items)\n",
    "    target_pref = pm.Normal('target_pref', mu=0, sd=10)\n",
    "    \n",
    "    # Softmax looking probability\n",
    "    pref_distractor = item_prefs[data.distractor.as_matrix()]\n",
    "    pref_target = item_prefs[data.target.as_matrix()] + target_pref\n",
    "    p_look_target = np.exp(pref_target) / (np.exp(pref_target) + np.exp(pref_distractor))\n",
    "    \n",
    "    # Likelihood.\n",
    "    pm.Bernoulli('looked_at_target', p=p_look_target, observed=data.looked_at_target)\n",
    "    \n",
    "    # Sample two chains of 500 samples using NUTS.\n",
    "    trace = pm.sample(500, njobs=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.gridspec.GridSpec at 0x11ea7bf60>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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uSBuEiACwxIhE6dGjh9QRiEgOS4xIhKCgIKkjEJEc7hOjSisqMRWBp28hKjFV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\nERGprP8HIJY+iaz7/tcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bb04668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Look at these nice sensical results!\n",
    "pm.plots.forestplot(trace, varnames=['item_prefs', 'target_pref'])"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  },
  "nav_menu": {},
  "toc": {
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 6,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}