{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1><center> PPOL564 | DS1: Foundations </center><h1>\n",
    "<h3><center> Lecture 25 <br><br><font color='grey'> \n",
    "Simulation </font></center></h3>\n",
    "\n",
    "### Today's Topics\n",
    "\n",
    "- Simulating data generating processes\n",
    "- Agent Based Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/matplotlib/__init__.py:886: MatplotlibDeprecationWarning: \n",
      "examples.directory is deprecated; in the future, examples will be found relative to the 'datapath' directory.\n",
      "  \"found relative to the 'datapath' directory.\".format(key))\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as st \n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.formula.api as sm\n",
    "import statsmodels.discrete.discrete_model as smd\n",
    "import warnings\n",
    "import requests\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating a data generating process for a linear model"
   ]
  },
  {
   "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>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.226925</td>\n",
       "      <td>0.441227</td>\n",
       "      <td>0.542769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.935195</td>\n",
       "      <td>-0.330870</td>\n",
       "      <td>0.400912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.962403</td>\n",
       "      <td>2.430771</td>\n",
       "      <td>0.719705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.224431</td>\n",
       "      <td>-0.252092</td>\n",
       "      <td>-0.021605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.130109</td>\n",
       "      <td>0.109610</td>\n",
       "      <td>0.024040</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y        x1        x2\n",
       "0  1.226925  0.441227  0.542769\n",
       "1  1.935195 -0.330870  0.400912\n",
       "2  3.962403  2.430771  0.719705\n",
       "3  1.224431 -0.252092 -0.021605\n",
       "4  1.130109  0.109610  0.024040"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(5)\n",
    "N = 1000\n",
    "x1 = np.random.normal(size=N)\n",
    "x2 = np.random.normal(size=N)\n",
    "error = np.random.normal(size=N)\n",
    "y = 1 + .5*x1 + -2*x2 + 3*x1*x2 + error\n",
    "D = pd.DataFrame(dict(y=y,x1 = x1, x2 = x2))\n",
    "D.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.928</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.928</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   4305.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 04 Dec 2019</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>07:52:27</td>     <th>  Log-Likelihood:    </th> <td> -1425.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>   2859.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   996</td>      <th>  BIC:               </th> <td>   2879.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    0.9721</td> <td>    0.032</td> <td>   30.445</td> <td> 0.000</td> <td>    0.909</td> <td>    1.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>        <td>    0.5047</td> <td>    0.032</td> <td>   15.657</td> <td> 0.000</td> <td>    0.441</td> <td>    0.568</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>        <td>   -2.0575</td> <td>    0.032</td> <td>  -64.081</td> <td> 0.000</td> <td>   -2.120</td> <td>   -1.994</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1:x2</th>     <td>    3.0042</td> <td>    0.031</td> <td>   97.633</td> <td> 0.000</td> <td>    2.944</td> <td>    3.065</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 4.346</td> <th>  Durbin-Watson:     </th> <td>   1.960</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.114</td> <th>  Jarque-Bera (JB):  </th> <td>   3.615</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.051</td> <th>  Prob(JB):          </th> <td>   0.164</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.724</td> <th>  Cond. No.          </th> <td>    1.11</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.928\n",
       "Model:                            OLS   Adj. R-squared:                  0.928\n",
       "Method:                 Least Squares   F-statistic:                     4305.\n",
       "Date:                Wed, 04 Dec 2019   Prob (F-statistic):               0.00\n",
       "Time:                        07:52:27   Log-Likelihood:                -1425.5\n",
       "No. Observations:                1000   AIC:                             2859.\n",
       "Df Residuals:                     996   BIC:                             2879.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      0.9721      0.032     30.445      0.000       0.909       1.035\n",
       "x1             0.5047      0.032     15.657      0.000       0.441       0.568\n",
       "x2            -2.0575      0.032    -64.081      0.000      -2.120      -1.994\n",
       "x1:x2          3.0042      0.031     97.633      0.000       2.944       3.065\n",
       "==============================================================================\n",
       "Omnibus:                        4.346   Durbin-Watson:                   1.960\n",
       "Prob(Omnibus):                  0.114   Jarque-Bera (JB):                3.615\n",
       "Skew:                          -0.051   Prob(JB):                        0.164\n",
       "Kurtosis:                       2.724   Cond. No.                         1.11\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.ols('y ~ x1 + x2 + x1*x2', data=D).fit().summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's simulate the data many times, retaining the the coefficients on each iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "coefs = []\n",
    "sims = 1000\n",
    "N = 100\n",
    "b = [1,.5,-2,3]\n",
    "for i in range(sims):\n",
    "    x1 = np.random.normal(size=N)\n",
    "    x2 = np.random.normal(size=N)\n",
    "    error = np.random.normal(size=N)\n",
    "    y = b[0] + b[1]*x1 + b[2]*x2 + b[3]*x1*x2 + error\n",
    "    D = pd.DataFrame(dict(y=y,x1 = x1, x2 = x2))\n",
    "    mod = sm.ols('y ~ x1 + x2 + x1*x2', data=D).fit()\n",
    "    coefs.append(mod.params.tolist())\n",
    "\n",
    "# Convert to a array\n",
    "coefs = np.array(coefs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(4,1, sharex=True, sharey=True,figsize=(10,8))\n",
    "sns.distplot(coefs[:,0],kde=False,ax=axs[0])\n",
    "sns.distplot(coefs[:,1],kde=False,ax=axs[1])\n",
    "sns.distplot(coefs[:,2],kde=False,ax=axs[2])\n",
    "sns.distplot(coefs[:,3],kde=False,ax=axs[3])\n",
    "\n",
    "# Plot the position of the \"true\" coefficient values. \n",
    "axs[0].axvline(b[0],color=\"darkblue\")\n",
    "axs[1].axvline(b[1],color=\"darkblue\")\n",
    "axs[2].axvline(b[2],color=\"darkblue\")\n",
    "axs[3].axvline(b[3],color=\"darkblue\")\n",
    "\n",
    "# Plot the titles for each subplot\n",
    "axs[0].title.set_text('Intercept')\n",
    "axs[1].title.set_text('x1')\n",
    "axs[2].title.set_text('x2')\n",
    "axs[3].title.set_text('x1*x2')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monte Carlo Simulation of a Statistical Error: _omitted variable bias_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now simulate the impact of Omitted variable bias. Let's say there is some unobserved variable $z$ that is correlated with $x_1$ and $x_2$. How would that bias our estimates?\n",
    "\n",
    "In the below code everything is the same except that we're adding variable $z$ that is correlated with the outcomes and the two predictors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "coefs = []\n",
    "sims = 1000\n",
    "N = 100\n",
    "b = [1,.5,-2,3]\n",
    "for i in range(sims):\n",
    "    z = np.random.normal(1,3,size=N) \n",
    "    x1 = np.random.normal(size=N) + z\n",
    "    x2 = np.random.normal(size=N) - z\n",
    "    error = np.random.normal(size=N)\n",
    "    y = b[0] + b[1]*x1 + b[2]*x2 + b[3]*x1*x2 + 5*z  + error\n",
    "    D = pd.DataFrame(dict(y=y,x1 = x1, x2 = x2))\n",
    "    mod = sm.ols('y ~ x1 + x2 + x1*x2', data=D).fit()\n",
    "    coefs.append(mod.params.tolist())\n",
    "\n",
    "# Convert to a array\n",
    "coefs = np.array(coefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the plots below show, $z$ is a confounding variable. By not including it in the model, we are biasing our estimates of $\\beta_1$ and $\\beta_2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(4,1, sharex=True, sharey=True,figsize=(10,8))\n",
    "sns.distplot(coefs[:,0],kde=False,ax=axs[0])\n",
    "sns.distplot(coefs[:,1],kde=False,ax=axs[1])\n",
    "sns.distplot(coefs[:,2],kde=False,ax=axs[2])\n",
    "sns.distplot(coefs[:,3],kde=False,ax=axs[3])\n",
    "\n",
    "# Plot the position of the \"true\" coefficient values. \n",
    "axs[0].axvline(b[0],color=\"darkblue\")\n",
    "axs[1].axvline(b[1],color=\"darkblue\")\n",
    "axs[2].axvline(b[2],color=\"darkblue\")\n",
    "axs[3].axvline(b[3],color=\"darkblue\")\n",
    "\n",
    "# Plot the titles for each subplot\n",
    "axs[0].title.set_text('Intercept')\n",
    "axs[1].title.set_text('x1')\n",
    "axs[2].title.set_text('x2')\n",
    "axs[3].title.set_text('x1*x2')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating Different Types of Outcomes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binary Outcome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x648 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(12345)\n",
    "N = 1000 # Number of observations\n",
    "\n",
    "# Linear combination of predictors\n",
    "x1 = np.random.normal(size=N)            # One continuous predictor \n",
    "x2 = np.random.binomial(1,p=.2,size=N)   # One binary predictor \n",
    "X = np.column_stack([np.ones(N),x1,x2])  # Compose as a matrix\n",
    "\n",
    "B = np.array([.5,.7,-2])                 # True Coefficients\n",
    "mu  = X.dot(B)                           # average prob is a function of x1 and x2\n",
    "\n",
    "# Convert our linear combination into a probability space\n",
    "pr = st.norm.cdf(mu,0,1) \n",
    "\n",
    "# Convert into binary outcome using the Bernoulli distribution\n",
    "y = np.random.binomial(n=1,p = pr)\n",
    "\n",
    "# Visualize\n",
    "sns.pairplot(pd.DataFrame(dict(y=y,x1=x1,x2=x2)),height=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.489036\n",
      "         Iterations 6\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Probit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>y</td>        <th>  No. Observations:  </th>  <td>  1000</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>              <td>Probit</td>      <th>  Df Residuals:      </th>  <td>   997</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Wed, 04 Dec 2019</td> <th>  Pseudo R-squ.:     </th>  <td>0.2895</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>07:52:58</td>     <th>  Log-Likelihood:    </th> <td> -489.04</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -688.34</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>2.782e-87</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.5017</td> <td>    0.051</td> <td>    9.862</td> <td> 0.000</td> <td>    0.402</td> <td>    0.601</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.7307</td> <td>    0.058</td> <td>   12.701</td> <td> 0.000</td> <td>    0.618</td> <td>    0.843</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>   -2.0212</td> <td>    0.150</td> <td>  -13.473</td> <td> 0.000</td> <td>   -2.315</td> <td>   -1.727</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                          Probit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                 1000\n",
       "Model:                         Probit   Df Residuals:                      997\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Wed, 04 Dec 2019   Pseudo R-squ.:                  0.2895\n",
       "Time:                        07:52:58   Log-Likelihood:                -489.04\n",
       "converged:                       True   LL-Null:                       -688.34\n",
       "                                        LLR p-value:                 2.782e-87\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.5017      0.051      9.862      0.000       0.402       0.601\n",
       "x1             0.7307      0.058     12.701      0.000       0.618       0.843\n",
       "x2            -2.0212      0.150    -13.473      0.000      -2.315      -1.727\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smd.Probit(y,X).fit().summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Count Outcome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x648 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(12345)\n",
    "N = 1000 # Number of observations\n",
    "\n",
    "# Linear combination of predictors\n",
    "x1 = np.random.normal(size=N)            # One continuous predictor \n",
    "x2 = np.random.binomial(1,p=.2,size=N)   # One binary predictor \n",
    "X = np.column_stack([np.ones(N),x1,x2])  # Compose as a matrix\n",
    "                     \n",
    "B = np.array([.5,.7,-2])                 # True Coefficients\n",
    "mu  = X.dot(B)                           # average rate is a function of x1 and x2\n",
    "\n",
    "# Convert our linear combination into a \"rate\" space (i.e. positively defined)\n",
    "lamb = np.exp(mu) \n",
    "\n",
    "# Convert into binary outcome using the Bernoulli distribution\n",
    "y = np.random.poisson(lam=lamb)\n",
    "\n",
    "# Visualize\n",
    "sns.pairplot(pd.DataFrame(dict(y=y,x1=x1,x2=x2)),height=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 1.414652\n",
      "         Iterations 7\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Poisson Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>y</td>        <th>  No. Observations:  </th>   <td>  1000</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>              <td>Poisson</td>     <th>  Df Residuals:      </th>   <td>   997</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>   <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Wed, 04 Dec 2019</td> <th>  Pseudo R-squ.:     </th>   <td>0.2950</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>07:53:00</td>     <th>  Log-Likelihood:    </th>  <td> -1414.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th>  <td> -2006.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>9.449e-258</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.5047</td> <td>    0.029</td> <td>   17.409</td> <td> 0.000</td> <td>    0.448</td> <td>    0.562</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.6753</td> <td>    0.023</td> <td>   29.288</td> <td> 0.000</td> <td>    0.630</td> <td>    0.721</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>   -1.8784</td> <td>    0.126</td> <td>  -14.852</td> <td> 0.000</td> <td>   -2.126</td> <td>   -1.631</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                          Poisson Regression Results                          \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                 1000\n",
       "Model:                        Poisson   Df Residuals:                      997\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Wed, 04 Dec 2019   Pseudo R-squ.:                  0.2950\n",
       "Time:                        07:53:00   Log-Likelihood:                -1414.7\n",
       "converged:                       True   LL-Null:                       -2006.5\n",
       "                                        LLR p-value:                9.449e-258\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.5047      0.029     17.409      0.000       0.448       0.562\n",
       "x1             0.6753      0.023     29.288      0.000       0.630       0.721\n",
       "x2            -1.8784      0.126    -14.852      0.000      -2.126      -1.631\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smd.Poisson(y,X).fit().summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Agent Based Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> \"An agent-based model (ABM) is a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole. It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming. Monte Carlo methods are used to introduce randomness.\" ([Wiki](https://en.wikipedia.org/wiki/Agent-based_model))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Schelling's Model of Segregation](http://nifty.stanford.edu/2014/mccown-schelling-model-segregation/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A walkthrough regarding how to construct Schelling's model in Python:\n",
    "\n",
    "- [From Scratch](https://www.binpress.com/simulating-segregation-with-python/)\n",
    "- [Using Mesa](https://towardsdatascience.com/introduction-to-mesa-agent-based-modeling-in-python-bcb0596e1c9a)"
   ]
  }
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