01 spelling/spelling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical model for spelling performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We analyze the data from the study `D. Thissen, Steinberg, and Wainer 1993` which can be found in the R [spelling](https://rdrr.io/cran/edstan/man/spelling.html) package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import pymc3 as pm\n",
    "import matplotlib.pyplot as plt\n",
    "import theano.tensor as tt\n",
    "import arviz as az\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "%config InlineBackend.figure_format='retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading the data"
   ]
  },
  {
   "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>student</th>\n",
       "      <th>male</th>\n",
       "      <th>word</th>\n",
       "      <th>correct</th>\n",
       "      <th>word_i</th>\n",
       "      <th>g</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>871</th>\n",
       "      <td>217</td>\n",
       "      <td>1</td>\n",
       "      <td>girder</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>834</th>\n",
       "      <td>208</td>\n",
       "      <td>1</td>\n",
       "      <td>succumb</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1502</th>\n",
       "      <td>375</td>\n",
       "      <td>0</td>\n",
       "      <td>succumb</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1660</th>\n",
       "      <td>415</td>\n",
       "      <td>0</td>\n",
       "      <td>infidelity</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>748</th>\n",
       "      <td>187</td>\n",
       "      <td>0</td>\n",
       "      <td>infidelity</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      student  male        word  correct  word_i    g\n",
       "871       217     1      girder        0       0  0.5\n",
       "834       208     1     succumb        0       3  0.5\n",
       "1502      375     0     succumb        0       3 -0.5\n",
       "1660      415     0  infidelity        1       1 -0.5\n",
       "748       187     0  infidelity        1       1 -0.5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('spelling.csv')\n",
    "data.index = data.index.rename('student')\n",
    "data = data.set_index('male', append=True)\n",
    "data.columns = data.columns.rename('word') \n",
    "data = data.stack().rename('correct').reset_index()\n",
    "data = data.assign(word_i = data.word.astype('category').cat.codes)\n",
    "data = data.assign(g = data.male - 0.5)\n",
    "data.sample(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row here has information about the person id (enumerated), whether the person is male, what is the word they need to spell (enumerated as in the chart below) and if they successfully spelled it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 259,
       "width": 399
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.groupby('word').correct.mean().plot.barh()\n",
    "plt.grid(axis='y')\n",
    "plt.gca().set(\n",
    "    title='raw rates',\n",
    "    ylabel=''\n",
    ")\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model\n",
    "\n",
    "We model the rate of spelling success as a logistic regression, where the probability of correct spelling is modeled for each individual person $i$ and word $j$:\n",
    "\n",
    "\n",
    "of the individual capability of the person, as well as the word effect on the success - some words are easier to spell. Furthermore, we expect the word effect to have an interaction with the person's sex, so we use covariate effects. Both are done with a non-centered parametarization.\n",
    "\n",
    "$$ \\text{correct}_{i, j} \\sim \\text{Bernouilli}(p_{i, j}) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We split the dependence $b$ of gender $ g = 0.5 $ for male, otherwise $-0.5  $:\n",
    "\n",
    "$$ \\text{logit}(p_{i, j}) = a_{i, j} + b_{j} g $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the intercept, we model the individual capability $\\beta$ for spelling as well as the specific word effect $\\gamma$ (some words are more difficult to spell than others):\n",
    "\n",
    "$$ a_{i, j} = \\alpha + \\beta_i + \\gamma_j $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Furthermore, words might have marginal effects depending on gender:\n",
    "\n",
    "$$ b_j = \\kappa + \\lambda_j $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We model both the person and word effects hierarchically with non-centered parametrization:\n",
    "\n",
    "$$ \\beta_i \\sim \\mathcal{N}(0, \\rho) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\gamma_j \\sim \\mathcal N (0, \\sigma_{\\gamma} ) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\lambda_j \\sim \\mathcal N (0, \\sigma_{\\lambda} ) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the hyperpriors we use:\n",
    "\n",
    "$$ \\alpha \\sim \\mathcal N (0, 1.5^2)$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\kappa \\sim \\mathcal N (0, 1^2) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\rho \\sim \\text{Exponential}(1) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\sigma_{\\gamma} \\sim \\text{Exponential}(1) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\sigma_{\\lambda} \\sim \\text{Exponential}(1) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_206994/1043957047.py:32: FutureWarning: In v4.0, pm.sample will return an `arviz.InferenceData` object instead of a `MultiTrace` by default. You can pass return_inferencedata=True or return_inferencedata=False to be safe and silence this warning.\n",
      "  trace1 = pm.sample(8000, tune=8000, chains=2)\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [lambda, sigma_lambda, gamma, sigma_gamma, beta, rho, kappa, alpha]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='32000' class='' max='32000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [32000/32000 03:56<00:00 Sampling 2 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 8_000 tune and 8_000 draw iterations (16_000 + 16_000 draws total) took 237 seconds.\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "n_person = data.student.nunique()\n",
    "n_word = data.word.nunique()\n",
    "\n",
    "with pm.Model() as m1:\n",
    "    alpha = pm.Normal('alpha', 0, 1.5)\n",
    "    kappa = pm.Normal('kappa', 0, 1)\n",
    "\n",
    "    rho = pm.Exponential('rho', 1)\n",
    "    beta = pm.Normal('beta', mu=0, sd=rho, shape=n_person)\n",
    "\n",
    "    sigma_gamma = pm.Exponential('sigma_gamma', 1)\n",
    "    gamma = pm.Normal('gamma', 0, sigma_gamma, shape=n_word)\n",
    "    \n",
    "    sigma_lambda = pm.Exponential('sigma_lambda', 1)\n",
    "    lambda_ = pm.Normal('lambda', 0, sigma_lambda, shape=n_word)\n",
    "\n",
    "    a = alpha + beta[data.student.values] + gamma[data.word_i.values]\n",
    "    b = kappa + lambda_[data.word_i.values]\n",
    "\n",
    "    p = pm.math.invlogit(a + b * data.g.values)\n",
    "\n",
    "    pm.Bernoulli('obs', p=p, observed=data.correct.values)\n",
    "\n",
    "    # word rates for an average individual, by gender\n",
    "    pm.Deterministic(\n",
    "        'word_p',\n",
    "        pm.math.invlogit(\n",
    "            alpha + gamma + (kappa + lambda_) * np.array([[-0.5, 0.5]]).T\n",
    "        )\n",
    "    )\n",
    "\n",
    "    trace1 = pm.sample(8000, tune=8000, chains=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/petrushev/etc/jupenv/lib/python3.9/site-packages/arviz/data/io_pymc3.py:96: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n",
      "  warnings.warn(\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 296,
       "width": 584
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(trace1, var_names=['alpha', 'kappa', 'rho', 'sigma_gamma', 'sigma_lambda'],\n",
    "               figsize=(8, 4))\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/petrushev/etc/jupenv/lib/python3.9/site-packages/arviz/data/io_pymc3.py:96: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 584
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(trace1, var_names=['gamma', 'lambda'],\n",
    "               figsize=(8, 6))\n",
    "plt.axvline(0, color='gray')\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/petrushev/etc/jupenv/lib/python3.9/site-packages/arviz/stats/stats.py:456: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 259,
       "width": 518
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_f = az.hdi(trace1['word_p'][:, 0, :], hdi_prob=0.95)\n",
    "tmp_m = az.hdi(trace1['word_p'][:, 1, :], hdi_prob=0.95)\n",
    "\n",
    "fig = plt.figure(figsize=(8, 4))\n",
    "\n",
    "for y in range(4):\n",
    "    labels = ['female', 'male'] if y == 0 else ['', '']\n",
    "    plt.plot(tmp_f[y, :], (y + 0.1, y + 0.1), color='C3', linewidth=3, label=labels[0])\n",
    "    plt.plot(tmp_m[y, :], (y - 0.1, y - 0.1), color='C0', linewidth=3, label=labels[1])\n",
    "\n",
    "plt.gca().set(\n",
    "    yticks=range(4),\n",
    "    yticklabels=data[['word', 'word_i']].drop_duplicates().set_index('word_i').word.sort_index(),\n",
    "    xlim=(0, 1),\n",
    "    ylim=(-0.3, 3.3),\n",
    "    title='adjusted spelling rate'\n",
    ")\n",
    "\n",
    "plt.grid(axis='y')\n",
    "plt.legend(title='average student', frameon=True)\n",
    "fig.savefig('average_actor.svg')\n",
    "None"
   ]
  }
 ],
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