Ch08-01_HierarchicalModel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## インポート"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## データの読み込み"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>KID</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>457</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10</td>\n",
       "      <td>482</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>16</td>\n",
       "      <td>518</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>25</td>\n",
       "      <td>535</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>427</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    X    Y  KID\n",
       "0   7  457    1\n",
       "1  10  482    1\n",
       "2  16  518    1\n",
       "3  25  535    1\n",
       "4   5  427    1"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('chap08/input/data-salary-2.txt')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## サンプルデータの散布図行列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Dispatcher(object):\n",
    "    \n",
    "    def __init__(self, fontsize=20, alpha=0.6, cmap='RdBu', threshold=5):\n",
    "        self.fontsize = fontsize\n",
    "        self.alpha = alpha\n",
    "        self.cmap = plt.get_cmap(cmap)\n",
    " \n",
    "        # 離散値 / 連続値とみなす閾値\n",
    "        self.threshold = threshold\n",
    "        \n",
    "    def comb(self, x_series, y_series, label=None, color=None):\n",
    "        \"\"\" 下三角部分のプロット \"\"\"       \n",
    "\n",
    "        x_nunique = x_series.nunique()\n",
    "        y_nunique = y_series.nunique()\n",
    "\n",
    "        if x_nunique < self.threshold and y_nunique < self.threshold:\n",
    "            # 離散値 x 離散値のプロット\n",
    "            return self._dd_plot(x_series, y_series, label=label, color=color)\n",
    "        \n",
    "        elif x_nunique < self.threshold or y_nunique < self.threshold:\n",
    "            # 離散値 x 連続値のプロット\n",
    "             return self._dc_plot(x_series, y_series, label=label, color=color)\n",
    "            \n",
    "        else:\n",
    "            # 連続値 x 連続値のプロット\n",
    "            return plt.scatter(x_series, y_series, label=label, color=color)\n",
    "\n",
    "    def _dd_plot(self, x_series, y_series, label=None, color=None):\n",
    "        \"\"\" 離散値 x 離散値のプロット \"\"\"\n",
    "\n",
    "        # x, y 各組み合わせの個数を集計\n",
    "        total = y_series.groupby([x_series, y_series]).count()\n",
    "\n",
    "        # x, y軸をプロットする位置を取得\n",
    "        xloc = total.index.labels[0] \n",
    "        yloc = total.index.labels[1] \n",
    "        values = total.values\n",
    "\n",
    "        ax = plt.gca()\n",
    "        for xp, yp, vp in zip(xloc, yloc, values):\n",
    "            ax.annotate(vp, (xp, yp), fontsize=self.fontsize,\n",
    "                        ha='center', va='center')\n",
    "\n",
    "        # 組み合わせの個数を散布図としてプロット\n",
    "        size = values / (values.max() * 1.1) * 100 * 20\n",
    "        ax.scatter(xloc, yloc, s=size, label=label, color=color)\n",
    "        ax.set_ylim(yloc[0] - 0.5, yloc[-1] + 0.5)\n",
    "        \n",
    "    def _dc_plot(self, x_series, y_series, label=None, color=None):\n",
    "        \"\"\" 離散値 x 連続値のプロット \"\"\"\n",
    "\n",
    "        if y_series.nunique() < x_series.nunique():\n",
    "            # y軸が離散値の場合は、x, yを入替\n",
    "            # 水平方向に箱ひげ図をプロット\n",
    "            x_series, y_series = y_series, x_series\n",
    "            vert = False\n",
    "        else:\n",
    "            vert = True\n",
    "\n",
    "        xlab, xun = pd.factorize(x_series)\n",
    "\n",
    "        # 箱ひげ図用のデータの準備\n",
    "        data = []\n",
    "        for i, g in y_series.groupby(xlab):\n",
    "            data.append(g) \n",
    "            \n",
    "        ax = plt.gca()\n",
    "        ax.boxplot(data, positions=np.arange(len(data)), vert=vert)\n",
    "\n",
    "        # 散布図をプロット\n",
    "        xloc = xlab + np.random.normal(scale=0.05, size=len(xlab))\n",
    "        if not vert:\n",
    "            y_series, xloc = xloc, y_series\n",
    "\n",
    "        ax.scatter(xloc, y_series, label=label, color=color,\n",
    "                   alpha=self.alpha)\n",
    "   \n",
    "    def diag(self, series, label=None, color=None):\n",
    "        \"\"\" 対角部分のプロット \"\"\"\n",
    "\n",
    "        ax = series.plot.hist()\n",
    "        ax = series.plot.kde(grid=False, ax=ax.twinx())\n",
    "        ax.yaxis.set_visible(False)\n",
    "\n",
    "    def ellipse(self, x_series, y_series, label=None, color=None):\n",
    "        \"\"\" 上三角部分のプロット \"\"\"        \n",
    "\n",
    "        from matplotlib.patches import Ellipse\n",
    "        \n",
    "        # 相関係数を楕円としてプロット\n",
    "        r = x_series.corr(y_series)\n",
    "        c = self.cmap(0.5 * (r + 1))\n",
    "\n",
    "        ax = plt.gca()\n",
    "        ax.axis('off')\n",
    "        ax.add_artist(Ellipse(xy=[.5, .5], width=np.sqrt(1 + r), height=np.sqrt(1 - r),\n",
    "                              angle=45, facecolor=c, edgecolor='none', transform=ax.transAxes))\n",
    "        ax.text(.5, .5, '{:.0f}'.format(r * 100), fontsize=self.fontsize,\n",
    "                ha='center', va='center', transform=ax.transAxes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UqbRY6GWfWMHza41xDVI05Ce72+8C/gjIPumDeyXic72gOoTZvMHwlcB/q84hRixhc7IU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\nOInRMgAyZd6/xFjq/pk1uxQ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eeGwFw+vFnNtTNGza0SRFgxgxTyA0B3gCcKjOksM+AHx1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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf0a4898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = sns.PairGrid(df, diag_sharey=False)\n",
    "\n",
    "d = Dispatcher()\n",
    "# 対角成分\n",
    "g.map_diag(d.diag)\n",
    "# 下三角成分\n",
    "g.map_lower(d.comb);\n",
    "# 上三角成分\n",
    "g.map_upper(d.ellipse);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0xea97828>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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W5C9XH5SYPAmGrLVvA7dP/bsFuNuLdojkknhyeGI9Jta+BVcMVwVqSbOZfXBk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116698d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(data=df, hue='KID')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DIQYCwSyhqAo/P/sbanrruHvB7azJXjHbQ0oYiqLEsoESWRwuYgKrGTCBDTfv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\nQiDBQAghBBIMhBBCIMFACCEE8P+RIvkD3Epa4AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x136e9080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "for KID, df_sub, in df.groupby(by=\"KID\"):\n",
    "    sns.regplot(x=df_sub.X, y=df_sub.Y, label=KID, \n",
    "                ci=0, line_kws={\"linestyle\":\"--\", \"linewidth\":1.0})\n",
    "sns.regplot(x=df.X, y=df.Y, scatter=False, ci=95, line_kws={\"color\":\"gray\"})\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## グループ差を考えない場合\n",
    "\n",
    "$Y[n]$ ~ $ Normal( a + b X[n], \\sigma )$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_61362dfb074914604c7afc054dc80b14 NOW.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_61362dfb074914604c7afc054dc80b14.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "a     375.86    0.58  24.68 325.57 359.51 375.71 392.75 423.73   1808    1.0\n",
       "b      11.06    0.03   1.43   8.24  10.11  11.07  12.02  13.93   1676    1.0\n",
       "sigma  68.45    0.18   8.08  54.73  62.88  67.72  73.26  86.28   2055    1.0\n",
       "lp__  -184.1    0.03   1.28 -187.3 -184.7 -183.7 -183.1 -182.6   1435    1.0\n",
       "\n",
       "Samples were drawn using NUTS at Fri May  4 00:33:35 2018.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_code=\"\"\"\n",
    "data {\n",
    "  int N;\n",
    "  real<lower=0> X[N];\n",
    "  real<lower=0> Y[N];\n",
    "}\n",
    "parameters {\n",
    "  real a;\n",
    "  real b;\n",
    "  real<lower=0> sigma;\n",
    "}\n",
    "model {\n",
    "  for (n in 1:N)\n",
    "    Y[n] ~ normal(a+b*X[n], sigma);\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "from pystan import StanModel\n",
    "data = dict(N=df.shape[0], X=df.X, Y=df.Y)\n",
    "sm = StanModel(model_code=model_code)\n",
    "\n",
    "fit = sm.sampling(data=data, n_jobs=1, seed=123)\n",
    "fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## グループごとに切片と傾きを持つ場合\n",
    "\n",
    "$Y[n]$ ~ $ Normal( a[KID[n]] + b[KID[n]] X[n], \\sigma )$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_665e81ec62636dce2a56ebfc8f1cc926 NOW.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_665e81ec62636dce2a56ebfc8f1cc926.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "a[0]  386.76    0.26  13.58 359.75 377.82 386.84 395.92 412.93   2771    1.0\n",
       "a[1]  328.84    0.35  17.21 294.66 317.46  328.7 340.44 362.41   2414    1.0\n",
       "a[2]  314.17    0.74  36.14 245.65  289.3 313.91 338.23  385.2   2371    1.0\n",
       "a[3]  748.52    3.11 157.13 443.37  645.8 746.37 852.07 1065.2   2558    1.0\n",
       "b[0]    7.53    0.02   0.84   5.91   6.98   7.51   8.09   9.26   2735    1.0\n",
       "b[1]   19.84    0.03   1.26  17.42  18.99  19.86  20.69   22.3   2458    1.0\n",
       "b[2]   12.44    0.04   1.78   8.89  11.24  12.45  13.66  15.87   2412    1.0\n",
       "b[3]   -0.94    0.13   6.33 -13.55  -5.15   -0.9   3.21  11.37   2558    1.0\n",
       "sigma  27.19    0.07   3.48  21.41  24.75  26.84  29.16  35.22   2291    1.0\n",
       "lp__  -148.0    0.07   2.42 -153.7 -149.4 -147.6 -146.2 -144.5   1310    1.0\n",
       "\n",
       "Samples were drawn using NUTS at Fri May  4 00:34:05 2018.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_code=\"\"\"\n",
    "data {\n",
    "  int N;\n",
    "  int K;\n",
    "  real<lower=0> X[N];\n",
    "  real<lower=0> Y[N];\n",
    "  int<lower=1,upper=K> KID[N];\n",
    "}\n",
    "parameters {\n",
    "  real a[K];\n",
    "  real b[K];\n",
    "  real<lower=0> sigma;\n",
    "}\n",
    "model {\n",
    "  for (n in 1:N)\n",
    "    Y[n] ~ normal(a[KID[n]]+b[KID[n]]*X[n], sigma);\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "from pystan import StanModel\n",
    "data = dict(N=df.shape[0], K=df.KID.nunique(), X=df.X, KID=df.KID, Y=df.Y)\n",
    "sm = StanModel(model_code=model_code)\n",
    "\n",
    "fit = sm.sampling(data=data, n_jobs=1, seed=123)\n",
    "fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\eX\\Anaconda3\\lib\\site-packages\\seaborn\\categorical.py:454: FutureWarning: remove_na is deprecated and is a private function. Do not use.\n",
      "  box_data = remove_na(group_data)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166ad160>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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79fQuK7sFoP59DA11xndSxMylqt38WTrF6tX1sZTfZXvUahNAd3yfs/0YFQr6zLxsqo6I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\nJaniDHpJqjiDXpIqzqCXpIoz6CWp4v4/7bw0NgROdg8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13e761d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(data=fit.extract()['a'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 階層モデル\n",
    "\n",
    "$a[k]$ ~ $ Normal(a_{avg}, \\sigma_a)$\n",
    "\n",
    "$b[k]$ ~ $ Normal(b_{avg}, \\sigma_b)$\n",
    "\n",
    "$Y[n]$ ~ $ Normal( a[KID[n]] + b[KID[n]] X[n], \\sigma )$\n",
    "\n",
    "$k = 1, ..., K$\n",
    "\n",
    "$n = 1, ..., N$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## シミュレーション"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "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>KID</th>\n",
       "      <th>X</th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>Y_sim</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>326.661362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>564.123866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>34</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>669.708323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>497.239848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>486.882787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>548.806346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>668.019735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>677.484672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>353.026717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>662.689700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>630.097598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>25</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>531.216370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>529.239398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>466.208171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>308.241129</td>\n",
       "      <td>10.621433</td>\n",
       "      <td>700.013477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>392.343832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>324.948676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>301.810728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>284.595622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>20</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>437.206074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>264.877690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>20</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>420.608100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>289.050179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>28</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>483.090504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>33</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>522.021470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>21</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>438.560970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>30</td>\n",
       "      <td>243.551956</td>\n",
       "      <td>9.099871</td>\n",
       "      <td>523.711883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2</td>\n",
       "      <td>27</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>949.666487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>1072.770463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2</td>\n",
       "      <td>33</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>1077.620090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>2</td>\n",
       "      <td>12</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>679.694936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>534.369304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>545.534714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>520.775689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2</td>\n",
       "      <td>11</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>682.500999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>1087.191645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "      <td>491.696076</td>\n",
       "      <td>16.158425</td>\n",
       "      <td>670.669423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>3</td>\n",
       "      <td>22</td>\n",
       "      <td>352.099585</td>\n",
       "      <td>11.033088</td>\n",
       "      <td>590.285287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>3</td>\n",
       "      <td>13</td>\n",
       "      <td>352.099585</td>\n",
       "      <td>11.033088</td>\n",
       "      <td>484.973210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>3</td>\n",
       "      <td>18</td>\n",
       "      <td>352.099585</td>\n",
       "      <td>11.033088</td>\n",
       "      <td>575.988177</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    KID   X           a          b        Y_sim\n",
       "0     0   2  308.241129  10.621433   326.661362\n",
       "1     0  28  308.241129  10.621433   564.123866\n",
       "2     0  34  308.241129  10.621433   669.708323\n",
       "3     0  17  308.241129  10.621433   497.239848\n",
       "4     0  19  308.241129  10.621433   486.882787\n",
       "5     0  22  308.241129  10.621433   548.806346\n",
       "6     0  33  308.241129  10.621433   668.019735\n",
       "7     0  32  308.241129  10.621433   677.484672\n",
       "8     0   9  308.241129  10.621433   353.026717\n",
       "9     0  32  308.241129  10.621433   662.689700\n",
       "10    0  32  308.241129  10.621433   630.097598\n",
       "11    0  25  308.241129  10.621433   531.216370\n",
       "12    0  19  308.241129  10.621433   529.239398\n",
       "13    0  14  308.241129  10.621433   466.208171\n",
       "14    0  32  308.241129  10.621433   700.013477\n",
       "15    1  16  243.551956   9.099871   392.343832\n",
       "16    1   4  243.551956   9.099871   324.948676\n",
       "17    1   3  243.551956   9.099871   301.810728\n",
       "18    1   2  243.551956   9.099871   284.595622\n",
       "19    1  20  243.551956   9.099871   437.206074\n",
       "20    1   2  243.551956   9.099871   264.877690\n",
       "21    1  20  243.551956   9.099871   420.608100\n",
       "22    1   7  243.551956   9.099871   289.050179\n",
       "23    1  28  243.551956   9.099871   483.090504\n",
       "24    1  33  243.551956   9.099871   522.021470\n",
       "25    1  21  243.551956   9.099871   438.560970\n",
       "26    1  30  243.551956   9.099871   523.711883\n",
       "27    2  27  491.696076  16.158425   949.666487\n",
       "28    2  34  491.696076  16.158425  1072.770463\n",
       "29    2  33  491.696076  16.158425  1077.620090\n",
       "30    2  12  491.696076  16.158425   679.694936\n",
       "31    2   3  491.696076  16.158425   534.369304\n",
       "32    2   5  491.696076  16.158425   545.534714\n",
       "33    2   0  491.696076  16.158425   520.775689\n",
       "34    2  11  491.696076  16.158425   682.500999\n",
       "35    2  34  491.696076  16.158425  1087.191645\n",
       "36    2  10  491.696076  16.158425   670.669423\n",
       "37    3  22  352.099585  11.033088   590.285287\n",
       "38    3  13  352.099585  11.033088   484.973210\n",
       "39    3  18  352.099585  11.033088   575.988177"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "N =  40\n",
    "K = 4\n",
    "N_k = [15,12,10,3]\n",
    "a0=350\n",
    "b0=12\n",
    "s_a=60\n",
    "s_b=4\n",
    "s_Y=25\n",
    "X = np.random.randint(0, 35, size=N)\n",
    "KID = np.repeat([0,1,2,3], N_k)\n",
    "\n",
    "a = np.random.normal(size=K, loc=a0, scale=s_a)\n",
    "b = np.random.normal(size=K, loc=b0, scale=s_b)\n",
    "\n",
    "df_sim = pd.DataFrame({'X':X, 'KID':KID, 'a':a[KID], 'b':b[KID]})\n",
    "#df_sim['a'] = a[df_sim.KID]\n",
    "df_sim['Y_sim'] = np.random.normal(loc=df_sim.a + df_sim.b * df_sim.X, scale=s_Y)\n",
    "df_sim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MSDeyFbrlha7rHHnuLN1dXcRUH5gCqVXCBObCHvtSuJw2eofHCGflIBw2E43V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\nEhBCCCFM/T+lkAnqpYXLTgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14da5128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "for KID, df_sub, in df_sim.groupby(by=\"KID\"):\n",
    "    sns.regplot(x=df_sub.X, y=df_sub.Y_sim, label=KID, \n",
    "                ci=0, line_kws={\"linestyle\":\"--\", \"linewidth\":1.0})\n",
    "sns.regplot(x=df_sim.X, y=df_sim.Y_sim, scatter=False, ci=95, line_kws={\"color\":\"gray\"})\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_2b6cc21669ebc0749dd208adf369b9d7 NOW.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_2b6cc21669ebc0749dd208adf369b9d7.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "       mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "a0   389.76    4.02 138.14 186.67 337.29 370.34 420.57 680.73   1182    1.0\n",
       "b0    11.91    0.41   9.01  -6.03   9.33  12.43  15.13  26.99    489   1.01\n",
       "a[0]  384.2    0.36  15.08  354.2 374.54 384.33 394.04 414.21   1744    1.0\n",
       "a[1] 334.13    0.36  17.34 300.09  322.4 333.89 345.98 368.27   2268    1.0\n",
       "a[2]  322.5    0.78   32.7 256.27 301.47 322.66 344.46 383.98   1742    1.0\n",
       "a[3] 491.09     4.6 139.16  302.0 383.15 461.22 573.55 825.44    915    1.0\n",
       "b[0]   7.69    0.02   0.92   5.86   7.08   7.67   8.29   9.52   1850    1.0\n",
       "b[1]  19.44    0.03   1.28  16.89  18.58  19.47   20.3  21.94   2306    1.0\n",
       "b[2]  12.04    0.04   1.63   8.92  10.94  12.01  13.12  15.37   1725    1.0\n",
       "b[3]    9.4    0.19   5.61  -3.87   6.02  10.55  13.64  17.14    914    1.0\n",
       "s_a  169.62     7.0 207.58  16.95  54.98 108.07 209.89 654.18    879    1.0\n",
       "s_b   12.46    0.66  17.12   3.27   5.58   8.23  13.11  49.37    669    1.0\n",
       "s_y   28.44    0.09   3.86  22.14  25.71  28.05  30.66  37.02   1861    1.0\n",
       "lp__ -173.3    0.13    3.5 -181.0 -175.4 -172.8 -170.8 -167.5    695    1.0\n",
       "\n",
       "Samples were drawn using NUTS at Fri May  4 00:17:37 2018.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_code=\"\"\"\n",
    "data {\n",
    "  int N;\n",
    "  int K;\n",
    "  real<lower=0> X[N];\n",
    "  real<lower=0> Y[N];\n",
    "  int<lower=1,upper=K> KID[N];\n",
    "}\n",
    "parameters {\n",
    "  real a0;\n",
    "  real b0;\n",
    "  real a[K];\n",
    "  real b[K];\n",
    "  real<lower=0> s_a;\n",
    "  real<lower=0> s_b;\n",
    "  real<lower=0> s_y;\n",
    "}\n",
    "model {\n",
    "  for (k in 1:K) {\n",
    "    a[k] ~ normal(a0, s_a);\n",
    "    b[k] ~ normal(b0, s_b);  \n",
    "  }\n",
    "\n",
    "  for (n in 1:N)\n",
    "    Y[n] ~ normal(a[KID[n]]+b[KID[n]]*X[n], s_y);\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "from pystan import StanModel\n",
    "data = dict(N=df.shape[0], K=df.KID.nunique(), X=df.X, KID=df.KID, Y=df.Y)\n",
    "sm = StanModel(model_code=model_code)\n",
    "\n",
    "fit = sm.sampling(data=data, n_jobs=1, seed=123)\n",
    "fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\eX\\Anaconda3\\lib\\site-packages\\seaborn\\categorical.py:454: FutureWarning: remove_na is deprecated and is a private function. Do not use.\n",
      "  box_data = remove_na(group_data)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x162b2e48>"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x162f4b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(data=fit.extract()['a'])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}