6. Qualitative Response Model .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b2ebc3f6-505f-4c2c-9463-5d34b01c6a86",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import scipy.stats\n",
    "import statsmodels.api as sm\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ffce874-3d61-4dad-a179-aa1f2fb7db18",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\">What Is Qualitative Response Model?</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76c0fa22-cd7e-4727-9fb2-df9ece1cf899",
   "metadata": {},
   "source": [
    "So far we have only discussed the model that takes $Y$ as a quantitative variable by default, however there are situations we want $Y$ to be qualitative variable, for example, $Y = 1$ represents a family owns house, $Y=0$ means not owning a flat, independent variables can be quantitative variables such as their income, ages, education and etc.\n",
    "\n",
    "Specifically, if the response variables only takes two values, such as $1$ or $0$, we call them **binary variable**, the regression model with binary variable as dependent variable is called **binary response regression model**, similarly there is also **trichotomous response regression model** or more generally **polychotomous response regression model**, but names do not matter, they are all **qualitative response model** as in the question of this section.\n",
    "\n",
    "For easy demonstration, we will mostly deal with _binary response model_, there are four approaches to develop this type of model: **linear probability model**, **logit model**, **probit model** and **tobit model**. \n",
    "\n",
    "We will go through all of them in this chapter."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6df86b8-ba84-4bea-b091-d680f122b7f7",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\">The Linear Probability Model (LPM)</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db69ebdf-e008-48bd-98fd-4811f73285a4",
   "metadata": {},
   "source": [
    "Consider a simple regression model\n",
    "$$\n",
    "Y_{i}=\\beta_{1}+\\beta_{2} X_{i}+u_{i}\n",
    "$$\n",
    "where $X$ represents family income, $Y=1$ represents if the family owns a flat and $0$ the opposite. There are only two outcomes, either own a flat or not, so $Y_i$ follows **Bernoulli Distribution**.\n",
    "\n",
    "It would be fast to recognize the $u_i$ can't be normally distributed, since\n",
    "$$\n",
    "u_{i}=Y_{i}-\\beta_{1}-\\beta_{2} X_{i}\n",
    "$$\n",
    "If we denote the probability $Y_i=1$ as $P_i$ and $Y_i=0$ as $1-P_i$, then\n",
    "$$\n",
    "\\begin{array}{lcc} \n",
    "& u_{i} & \\text { Probability } \\\\\n",
    "\\text { When } Y_{i}=1 & 1-\\beta_{1}-\\beta_{2} X_{i} & P_{i} \\\\\n",
    "\\text { When } Y_{i}=0 & -\\beta_{1}-\\beta_{2} X_{i} & \\left(1-P_{i}\\right)\n",
    "\\end{array}\n",
    "$$\n",
    "it shows that $u_i$ also follows Bernoulli distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10aecef9-9e8b-4d9c-a3ff-3e055cd5293a",
   "metadata": {},
   "source": [
    "Recall the fact from statistics course, that the variance of Bernoulli distribution is $P_i(1-P_i)$, what's more\n",
    "$$\n",
    "E\\left(Y_{i} \\mid X_{i}\\right)=\\beta_{1}+\\beta_{2} X_{i}=0\\left(1-P_{i}\\right)+1\\left(P_{i}\\right)=P_{i}\n",
    "$$\n",
    "The $P_i$ is a function of $X_i$, hence $u_i$ is heteroskedastic. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f55d5c0-9b6a-4472-b4af-37024a001aa7",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\">Home Owners' Example</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69322a7b-7474-49f7-a3d1-c537a52d969c",
   "metadata": {},
   "source": [
    "Here is an excerpt data from a real estate survey in Manchester, UK. The family income is measured in thousand pounds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "445a0ab0-9f82-4655-a3b2-ed9ac4bc6372",
   "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>Annual_Family_Income</th>\n",
       "      <th>Own_House</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>56</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>78</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>34</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>23</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Annual_Family_Income  Own_House\n",
       "0                    56          1\n",
       "1                    78          1\n",
       "2                    67          0\n",
       "3                    34          1\n",
       "4                    23          0"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel('Basic_Econometrics_practice_data.xlsx', sheet_name = 'HouseOwn_Quali_Resp'); df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cab4839-412a-4411-9277-5958d6913135",
   "metadata": {},
   "source": [
    "Perform a quick OLS estimation (ignoring the heteroskedasticity for now) and plot the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "01a2c606-1513-421e-b342-0ca9bc1d5014",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Own_House   R-squared:                       0.583\n",
      "Model:                            OLS   Adj. R-squared:                  0.571\n",
      "Method:                 Least Squares   F-statistic:                     50.32\n",
      "Date:                Thu, 02 Sep 2021   Prob (F-statistic):           2.47e-08\n",
      "Time:                        14:34:24   Log-Likelihood:                -10.752\n",
      "No. Observations:                  38   AIC:                             25.50\n",
      "Df Residuals:                      36   BIC:                             28.78\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "========================================================================================\n",
      "                           coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------\n",
      "const                   -0.1981      0.119     -1.671      0.103      -0.439       0.042\n",
      "Annual_Family_Income     0.0162      0.002      7.094      0.000       0.012       0.021\n",
      "==============================================================================\n",
      "Omnibus:                        0.225   Durbin-Watson:                   2.640\n",
      "Prob(Omnibus):                  0.894   Jarque-Bera (JB):                0.112\n",
      "Skew:                          -0.123   Prob(JB):                        0.945\n",
      "Kurtosis:                       2.900   Cond. No.                         115.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "X = df['Annual_Family_Income']\n",
    "Y = df['Own_House']\n",
    "\n",
    "X = sm.add_constant(X) # adding a constant\n",
    "\n",
    "model = sm.OLS(Y, X).fit() \n",
    "\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "b87da3ff-b9ac-49a2-a65d-680f9244b211",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 7))\n",
    "ax.scatter(df['Annual_Family_Income'], df['Own_House'])\n",
    "ax.plot(df['Annual_Family_Income'], model.fittedvalues, color = 'tomato')\n",
    "ax.grid()\n",
    "ax.set_xlabel('Income')\n",
    "ax.set_ylabel('Owning a flat = 1, Not Owning = 0')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "581c58bb-6043-4cc6-8158-cffbc5e94d2a",
   "metadata": {},
   "source": [
    "Let's interpret the results, the constant term is $-0.1981$, but probability can never be negative, hence we ignore constant term, or simply treat it as $0$. The slope term $0.0162$ indicates that in average with every $1000$ pounds increment in family income, the probability of owning a house will increase $1.6\\%$.\n",
    "\n",
    "However, you could doubt its reliability that assuming income and probability is linear relation, actually it's more rational to assume there is some threshold to afford a house, if the house cost $500000$ pounds, earning $20000$ shouldn't be any obvious improvement than earning $10000$. Similarly, family with income of $200000$ wouldn't be much different than family with income of $190000$. We will talk about how to model this assumption in next section. So far we will stick with LPM.\n",
    "\n",
    "What if a family has $39000$ pounds of annual income? Our model predicts the probability they own a house is $-0.1981 + 39\\times0.0162=.43$. But how about family income of $11000$ pounds? The models says $-0.1981 + 11\\times0.0162=-0.0199$, it predicts a negative probability and apparent it has no sense. Similarly, if a family has $99000$ pounds income, the model predicts a probability $-0.1981 + 99\\times0.0162=1.4057$ which is more than $1$.\n",
    "\n",
    "If the vertical axis represents probabilities, i.e. $0 \\leq E\\left(Y_{i} \\mid X_{i}\\right) \\leq 1 $, it would be a natural defects of LPM to predict out of this range."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d320a657-2c4c-4a48-afcc-c3183b149d06",
   "metadata": {},
   "source": [
    "However, we still haven't address the heteroskedasticity issue of LPM, which means the estimated results above are actually all _invalid_! For fast remedy, you can invoke the White's robust standard error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "3838467c-88c9-4aa5-9373-d2fe5df51dff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const                   0.086859\n",
       "Annual_Family_Income    0.001809\n",
       "dtype: float64"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.HC0_se"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fe93e84-b8b4-4386-a647-0e05c3dbe5e3",
   "metadata": {},
   "source": [
    "To handle the issue more seriously, we use WLS to obtain more efficient estimates. Because variance of disturbance term is \n",
    "$$\n",
    "\\operatorname{var}\\left(u_{i}\\right)=P_{i}\\left(1-P_{i}\\right)=\\sqrt{E\\left(Y_{i} \\mid X_{i}\\right)\\left[1-E\\left(Y_{i} \\mid X_{i}\\right)\\right]}\n",
    "$$\n",
    "So we estimate the disturbance term by using fitted values, note that these are different than residuals!\n",
    "$$\n",
    "w_i=\\hat{Y}_{i}\\left(1-\\hat{Y}_{i}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1b66e3a-d9b8-4621-aab9-e8ce727a7c23",
   "metadata": {},
   "source": [
    "Add fitted value into the data frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "3439f127-c5be-4803-bf14-ef703b3f016b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Annual_Family_Income</th>\n",
       "      <th>Own_House</th>\n",
       "      <th>fitted_value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>1.067667</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>67</td>\n",
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       "      <td>0.889155</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>34</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Annual_Family_Income  Own_House  fitted_value\n",
       "0                    56          1      0.710644\n",
       "1                    78          1      1.067667\n",
       "2                    67          0      0.889155\n",
       "3                    34          1      0.353621\n",
       "4                    23          0      0.175110"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['fitted_value'] = model.fittedvalues\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8870934-7137-448d-8dca-ace56baa791a",
   "metadata": {},
   "source": [
    "Exclude all values out of probabilistic range, then calculate the weight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "aee0b6a1-9e96-4a0d-b428-d9efad62c840",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[df['fitted_value']>0]\n",
    "df = df[df['fitted_value']<1]\n",
    "df['weight'] = np.sqrt(df['fitted_value']*(1-df['fitted_value']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "fe0c0bd3-43b1-42a1-aec7-4a662344954b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Annual_Family_Income</th>\n",
       "      <th>Own_House</th>\n",
       "      <th>fitted_value</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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      ],
      "text/plain": [
       "   Annual_Family_Income  Own_House  fitted_value    weight\n",
       "0                    56          1      0.710644  0.453463\n",
       "2                    67          0      0.889155  0.313940\n",
       "3                    34          1      0.353621  0.478093\n",
       "4                    23          0      0.175110  0.380061\n",
       "5                    19          0      0.110197  0.313135"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3c62153-8caa-4096-96bf-d3c217c423d9",
   "metadata": {},
   "source": [
    "Divide weight onto every terms in the model\n",
    "$$\n",
    "\\frac{Y_{i}}{\\sqrt{w_{i}}}=\\frac{\\beta_{1}}{\\sqrt{w_{i}}}+\\beta_{2} \\frac{X_{i}}{\\sqrt{w_{i}}}+\\frac{u_{i}}{\\sqrt{w_{i}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "42993b97-86bf-414b-ba27-23b3e0c2511c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Annual_Family_Income_WLS'] = df['Annual_Family_Income']/df['weight']\n",
    "df['Own_House_WLS'] = df['Own_House']/df['weight']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "692b307d-132f-477b-a98b-42df52903626",
   "metadata": {},
   "source": [
    "Here's the more reliable result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "2e401f00-aff8-496d-b279-b668be53f8f4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:          Own_House_WLS   R-squared:                       0.765\n",
      "Model:                            OLS   Adj. R-squared:                  0.757\n",
      "Method:                 Least Squares   F-statistic:                     94.47\n",
      "Date:                Thu, 02 Sep 2021   Prob (F-statistic):           1.25e-10\n",
      "Time:                        14:17:57   Log-Likelihood:                -40.040\n",
      "No. Observations:                  31   AIC:                             84.08\n",
      "Df Residuals:                      29   BIC:                             86.95\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "============================================================================================\n",
      "                               coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------------\n",
      "const                       -0.3322      0.245     -1.358      0.185      -0.833       0.168\n",
      "Annual_Family_Income_WLS     0.0146      0.002      9.720      0.000       0.012       0.018\n",
      "==============================================================================\n",
      "Omnibus:                        5.495   Durbin-Watson:                   2.649\n",
      "Prob(Omnibus):                  0.064   Jarque-Bera (JB):                3.808\n",
      "Skew:                          -0.720   Prob(JB):                        0.149\n",
      "Kurtosis:                       3.934   Cond. No.                         244.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "X = df['Annual_Family_Income_WLS']\n",
    "Y = df['Own_House_WLS']\n",
    "\n",
    "X = sm.add_constant(X) # adding a constant\n",
    "\n",
    "model = sm.OLS(Y, X).fit() \n",
    "\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec653d5c-4c76-4cb0-8ac6-59000227bdfc",
   "metadata": {},
   "source": [
    "The slope estimates of WLS is similar but higher significance due to smaller standard error and $R^2$ also much higher than previous model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2575796b-11f4-4596-bb76-fbda483b45cc",
   "metadata": {},
   "source": [
    "Though we have fixed heteroskedasticity to some extent, the model is not attractive in either breaking probabilistic range or its unrealistic linear shape. In Next section we will discuss about alternatives to LPM that fulfill both probabilistic range and nonlinear shape."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5d019cb-9af3-452a-a812-0077bd630f6b",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Logit Model</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8a726a4-d3a4-4297-a780-b2c0fdb5dc65",
   "metadata": {},
   "source": [
    "The **logit model** hypothesizes a sigmoid shape function \n",
    "$$\n",
    "P_i = \\frac{1}{1+e^{-(\\beta_1+\\beta_2X_i)}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "044be4dd-feb1-484e-84c1-aa52d2d27ddf",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta1, beta2 = 2, 3\n",
    "X = np.linspace(-3, 2)\n",
    "P = 1/(1 + np.exp(-beta1-beta2*X))\n",
    "fig, ax = plt.subplots(figsize = (12, 7))\n",
    "ax.plot(X, P)\n",
    "ax.set_title(r'$P = 1/(1+e^{-Z})$')\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "465224ba-c927-4a27-a32a-cc52b25a455d",
   "metadata": {},
   "source": [
    "We usually denote $Z_i = \\beta_1+\\beta_2X_i$, ranges from $(-\\infty, +\\infty) $. This model solves the issues of probabilistic range and linear model. \n",
    "\n",
    "In order to estimate the logit model, we are seeking ways to linearize it. It might look confusing at first sight, here is the steps\n",
    "$$\n",
    "P_{i}=\\frac{1}{1+e^{-Z_{i}}}=\\frac{e^{Z_i}}{e^{Z_i}}\\frac{1}{1+\\frac{1}{e^{Z_i}}}=\\frac{e^{Z_i}}{1+e^{Z}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "970d9bfd-f897-43e5-aa2b-e9bc2737a11e",
   "metadata": {},
   "source": [
    "And $1-P_i$\n",
    "$$\n",
    "1-P_{i}=\\frac{1}{1+e^{Z_{i}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "095498cc-58eb-4939-a549-9e92ccecb257",
   "metadata": {},
   "source": [
    "Combine them, we have the odds ratios\n",
    "$$\n",
    "\\frac{P_{i}}{1-P_{i}}=\\frac{1+e^{Z_{i}}}{1+e^{-Z_{i}}}=e^{Z_{i}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd3a616f-2064-40a0-a61b-6dc271833c1b",
   "metadata": {},
   "source": [
    "Here's the interesting part, take natural log, we get a linearized model and we commonly call the log odds ratios the **logit**.\n",
    "$$\n",
    "\\underbrace{\\ln{\\bigg(\\frac{P_{i}}{1-P_{i}}\\bigg)}}_{\\text{logit}}= Z_i =\\beta_1+\\beta_2X_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4623c027-c2ea-494a-850a-0c1606cab5bf",
   "metadata": {},
   "source": [
    "To estimate the model, some technical procedures have to be carried out, because logit wouldn't make any sense, if we simply plug in the data $Y_i$, because we don't observe $P_i$, the results are nonsensical.\n",
    "$$\n",
    "\\ln \\left(\\frac{1}{0}\\right) \\quad \\text{if a family own a house}\\\\\n",
    "\\ln \\left(\\frac{0}{1}\\right) \\quad \\text{if a family does not own a house}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad79dcb7-6d0f-4118-9fcc-039f08f5e976",
   "metadata": {},
   "source": [
    "One way to circumvent this technical issue, the data can be grouped to compute\n",
    "$$\n",
    "\\hat{P}_{i}=\\frac{n_{i}}{N_{i}}\n",
    "$$\n",
    "where $N_i$ is number of families in a certain income level, e.g. $[20000, 29999]$, and $n_i$ is the number of family owning a house in the that level."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "120d1233-e26d-4c5e-a736-59267a7dc16c",
   "metadata": {},
   "source": [
    "However, this is not a preferred method, since we have nonlinear tools. Recall that owning a house is following a Bernoulli distribution whose probability mass function is\n",
    "$$\n",
    "f_i(Y_i)= P_i^{Y_i}(1-P_i)^{1-Y_i}\n",
    "$$\n",
    "The joint distribution is the product of Bernoulli PMF due to their independence\n",
    "$$\n",
    "f\\left(Y_{1}, Y_{2}, \\ldots, Y_{n}\\right)=\\prod_{i=1}^{n} f_{i}\\left(Y_{i}\\right)=\\prod_{i=1}^{n} P_{i}^{Y_{i}}\\left(1-P_{i}\\right)^{1-Y_{i}}\n",
    "$$\n",
    "In order to get its log likelihood function, we take natural log\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\ln f\\left(Y_{1}, Y_{2}, \\ldots, Y_{n}\\right) &=\\sum_{i=1}^{n}\\left[Y_{i} \\ln P_{i}+\\left(1-Y_{i}\\right) \\ln \\left(1-P_{i}\\right)\\right] \\\\\n",
    "&=\\sum_{i=1}^{n}\\left[Y_{i} \\ln P_{i}-Y_{i} \\ln \\left(1-P_{i}\\right)+\\ln \\left(1-P_{i}\\right)\\right] \\\\\n",
    "&=\\sum_{i=1}^{n}\\left[Y_{i} \\ln \\left(\\frac{P_{i}}{1-P_{i}}\\right)\\right]+\\sum_{i=1}^{n} \\ln \\left(1-P_{i}\\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "Replace \n",
    "$$\n",
    "\\ln{\\bigg(\\frac{P_{i}}{1-P_{i}}\\bigg)}=\\beta_1+\\beta_2X_i\\\\\n",
    "1-P_{i}=\\frac{1}{1+e^{\\beta_1+\\beta_2X_i}}\n",
    "$$\n",
    "Finally we have log likelihood function of $\\beta$'s\n",
    "$$\n",
    "\\ln f\\left(Y_{1}, Y_{2}, \\ldots, Y_{n}\\right)=\\sum_{i=1}^{n} Y_{i}\\left(\\beta_{1}+\\beta_{2} X_{i}\\right)-\\sum_{i=1}^{n} \\ln \\left[1+e^{\\left(\\beta_{1}+\\beta_{2} X_{i}\\right)}\\right]\n",
    "$$\n",
    "Take partial derivative w.r.t to $\\beta_2$\n",
    "$$\n",
    "\\frac{\\partial LF}{\\partial \\beta_2} = n\\beta_2 -\\sum_{i=1}^n\\frac{e^{\\beta_1+\\beta_2X_i}X_i}{1+e^{\\beta_1+\\beta_2X_i}}=0\n",
    "$$\n",
    "And stop here, apparently there won't be analytical solutions, i.e. numerical solutions are needed. And this is exactly what Python is doing for us below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "278e2171-c593-4234-8231-36bc99d4a600",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Single Variable Logit Model </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01a5d91e-b94a-4a3e-9f58-3eeb15d5ff57",
   "metadata": {},
   "source": [
    "Here we come back to the house owning example.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "aa14ab17-f25c-498a-b064-f3eb905daaa5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.257124\n",
      "         Iterations 8\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_excel('Basic_Econometrics_practice_data.xlsx', sheet_name = 'HouseOwn_Quali_Resp'); df.head()\n",
    "\n",
    "Y = df[['Own_House']]\n",
    "X = df[['Annual_Family_Income']]\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "log_reg = sm.Logit(Y, X).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "834a1a62-aa88-4ccd-9d09-5361ca5430a8",
   "metadata": {},
   "source": [
    "Optimization of likelihood function is an iterative process and global optimization has been reached as the notice shows. \n",
    "\n",
    "Print the estimation results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "713ee3c5-0d95-4339-8607-631964b57c5c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:              Own_House   No. Observations:                   38\n",
      "Model:                          Logit   Df Residuals:                       36\n",
      "Method:                           MLE   Df Model:                            1\n",
      "Date:                Wed, 08 Sep 2021   Pseudo R-squ.:                  0.6261\n",
      "Time:                        20:42:19   Log-Likelihood:                -9.7707\n",
      "converged:                       True   LL-Null:                       -26.129\n",
      "Covariance Type:            nonrobust   LLR p-value:                 1.067e-08\n",
      "========================================================================================\n",
      "                           coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------\n",
      "const                   -6.7617      2.189     -3.088      0.002     -11.053      -2.471\n",
      "Annual_Family_Income     0.1678      0.053      3.176      0.001       0.064       0.271\n",
      "========================================================================================\n"
     ]
    }
   ],
   "source": [
    "print(log_reg.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5212ea16-a24d-43d5-95a4-679bfbc291bc",
   "metadata": {},
   "source": [
    "Here is the estimated model\n",
    "$$\n",
    "\\hat{P_i} = \\frac{1}{1+e^{6.7617-0.1678 X_i}}\n",
    "$$\n",
    "And the fitted curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "43d83892-c8d8-4ebc-a1c2-65b702042b25",
   "metadata": {},
   "outputs": [
    {
     "data": {
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3WEBLUq1LCX7xHVg4J+v36ZsVz96iW5K2iAW0JNW6O/4I0+4r9j/4KdhtbH55JKnKWUBLUi37y5Nw9U+L/QmnwVEn5JdHkmqABbQk1aqlb2z8ocE99oH3X5xvJkmqARbQklSLWlvhystg2RtZf8i2cMk/ZfOfJUlbxQJakmrR7dfA023uNPixL8B2I/LLI0k1xAJakmrN7Jnwx18U+yefA/sfnFscSao1FtCSVEtWr4SffANaWrL+HvvAmRfmm0mSaowFtCTVkt/8ABYvzNoDBsLHvwhNTflmkqQaYwEtSbVi2v3wyN3F/oWfgRE75hZHkmqVBbQk1YKlr8Ovv1fsH3kCHPqO/PJIUg2zgJakapcS/Oq7sGJZ1t9uBJz3t/lmkqQaZgEtSdXuwdvhiUeL/Ys+CwMH5ZdHkmpcWQvoiDg5ImZGxKyI+GIH+7eNiBsj4omIeDoiLipnHkmqOa8tgqsuL/aPezfsOy6/PJJUB8pWQEdEI/AD4BRgP+C8iNiv3WGfAJ5JKb0VmAB8KyK8TZYklWLD1I21q7P+yNHw3o/km0mS6kA5r0AfBsxKKc1OKa0DJgFntDsmAUMiIoDBwOvA+jJmkqTa8fBdxbsNRsBH/h769c83kyTVgUgplefEEWcDJ6eUPlbofxA4PKV0aZtjhgA3APsAQ4D3p5Ru7uBcFwMXA4wcOfKQSZMmlSXz5qxYsYLBgwfn8t7qHY5xfaiFce6zZiWH3fAT+qxbA8C8vQ9h1qEn5pyqstTCOGvzHOfal+cYT5w4cXpKaXz77eVcXT862Na+Wj8JeBw4DtgTuCMi7k8pLdvoRSldAVwBMH78+DRhwoQeD1uKKVOmkNd7q3c4xvWhJsb5x1+HQvHM9juw8ye/zM79B+SbqcLUxDhrsxzn2leJY1zOKRzzgF3a9HcGFrQ75iLg2pSZBbxIdjVaktSZxx+BqfcW+x/8FFg8S1KvKWcBPRUYGxG7Fz4YeC7ZdI225gDHA0TESGBvYHYZM0lSdVuzCn7z/WL/yBPggE3+d1GSVEZlm8KRUlofEZcCk4FG4MqU0tMRcUlh/+XAV4FfRMSTZFM+vpBSerVcmSSp6t3wG3ij8GtyyLbw/ovzzSNJdaicc6BJKd0C3NJu2+Vt2guAd5YzgyTVjHkvwp1/LPbPuRgGb5NfHkmqU96JUJKqQUrZ1I3W1qz/lgPhiOPyzSRJdcoCWpKqwUN3wvNPZ+3GRrjg0mztZ0lSr7OAlqRKt2I5XP3TYv/E98Ko3fLLI0l1zgJakird9b+E5Uuz9nYj4PQP5JtHkuqcBbQkVbL5f4UpbT6Lfe4l3q5bknJmAS1JlSolmPRjSIUPDu53MIw7Kt9MkiQLaEmqWE88Cs/OyNrRkK357AcHJSl3FtCSVInWN8MfflLsH3sqjB6TWxxJUpEFtCRVortvgEXzs/aAQXDGB/PNI0l6kwW0JFWa5Uvgxt8W+6efn922W5JUESygJanSXP9rWL0ya48cDcednm8eSdJGLKAlqZLM/yvc22bZunMuhqY+ucWRJG3KAlqSKskffrbxsnUHHZZvHknSJpq62hkR+wBnAKOBBCwAbkgpPdsL2SSpvsz8Mzw1NWtHwDkfd9k6SapAnV6BjogvAJOAAP4ETC20r4qIL/ZOPEmqEynBNVcW+0ceDzvvnl8eSVKnuroC/VFg/5RSc9uNEfFt4GngG+UMJkl1ZcZDMPu5rN3Ux2XrJKmCdTUHuhUY1cH2nQr7JEk9oaUFrv1FsT/xNNh+ZG5xJEld6+oK9GeAuyLieWBuYduuwF7ApWXOJUn146E74OXCr9kBA+HUc/PNI0nqUqcFdErptoh4C3AY2YcIA5gHTE0ptfRSPkmqbevWwg2/LvZPOtubpkhShetyFY6UUivwSC9lkaT6c/cN8MarWXubYXDiWfnmkSRtlutAS1JeVq2AW35X7J/+AejXP788kqSSWEBLUl4mX50V0QAjdoJjTsk3jySpJBbQkpSHFcvgzuuL/TMvhKYuZ9VJkipESQV0RPy+7bMkaSvdfg2sXZ21R+0Kh74j3zySpJKVegV6r8Lz2HIFkaS6sXwJ3NXm6vPpF0BDY25xJEnd4xQOSeptk6+BtWuy9ugxcMjbc40jSeoeC2hJ6k3LlmRL123w7gugwV/FklRN/K0tSb1p8h+ym6cA7Lw7jDsq3zySpG4rtYCOsqaQpHqw9A2456Zi36vPklSVSv3NfVm7Z0lSd93W5urzLnt69VmSqlRJBXRK6bdtnyVJ3bT0dbj35mL/jAsg/M89SapG/t+hJPWG268pXn3ebSy89Yh880iStpgFtCSV24plMKXN1efTP+DVZ0mqYhbQklRud12/8brPBx2eaxxJ0tZp2twBEfHZDjYvBaanlB7v8USSVEvWrNr4roOnvt+VNySpypXyW3w8cAkwuvC4GJgA/CQiPl++aJJUA+65GVatyNo7jIJD35FvHknSVtvsFWhge+DglNIKgIj4V+Bq4B3AdOC/yxdPkqrYurVwx7XF/innQENjfnkkST2ilCvQuwLr2vSbgd1SSquBtWVJJUm14IHJsOyNrD1sOBx5fL55JEk9opQr0L8FHomIDZP4TgeuiohBwDNlSyZJ1Wz9erjt6mL/pLOhqU9+eSRJPWazBXRK6asRcStwNNktvS9JKU0r7D6/nOEkqWo9eje8/krWHrItHHNyvnkkST2mlCvQADOABRuOj4hdU0pzypZKkqpZawvc8rti/8T3QL/++eWRJPWoUpax+yTwr8AioIXsKnQCDipvNEmqUjMehkXzs/aAQTDh9HzzSJJ6VClXoD8N7J1Seq3cYSSp6qUEk9vMfZ54OgwclF8eSVKPK2UVjrlkN06RJG3O80/D7OeydlMfOP7d+eaRJPW4Uq5AzwamRMTNtFm2LqX07bKlkqRqNfkPxfaRx8O22+WXRZJUFqUU0HMKj76FhySpIwvmwBOPFvvvfG9+WSRJZVPKMnb/1htBJKnq3X5Nsf22I2CnXfLLIkkqm04L6Ij4n5TSZyLiRrJVNzaSUnJinyRtsOQ1eOTuYv+ks/PLIkkqq66uQP9f4fmbvRFEkqra3TfC+uasvcc+sNf++eaRJJVNpwV0Sml64fne3osjSVVozWqYclOxf9LZEJFfHklSWZVyI5Wjga8AuxWODyCllPYobzRJqhIPTIZVK7L2DqNg3JH55pEklVUpq3D8DPg7YDrZnQglSRu0tMAd1xb7J54FDY355ZEklV0pBfTSlNKtZU8iSdVo2n3w2itZe/C2cPSJ+eaRJJVdKQX0PRFxGXAtG99I5bGypZKkatD+tt3HnQ59++WXR5LUK0opoA8vPI9vsy0Bx/V8HEmqIs89AXNeyNp9+8HE0/PNI0nqFaXcSGVibwSRpKpzxx+L7aNOhCHb5pdFktRrSlmF4wXgEeB+4L6U0jNlTyVJlW7RfPhzm9t2n3BmblEkSb2roYRj9gN+DGwPfDMiZkfEHzfzGkmqbXddX2wfdBjsuHN+WSRJvaqUAroFaC48twKLgFfKGUqSKtqqFfDg7cW+V58lqa6U8iHCZcCTwLeBn6SUXitvJEmqcPdPhrVrsvboMbDvuFzjSJJ6VylXoM8D7gP+HzApIv4tIo4v5eQRcXJEzIyIWRHxxU6OmRARj0fE0xHhbcMlVbaWlo2nb5xwprftlqQ6U8oqHNcD10fEPsApwGeAzwMDunpdRDQCPwBOBOYBUyPihrYfQoyIocAPgZNTSnMiYoct/DokqXfMeAheb3PjlMNdqEiS6s1mr0BHxDWFlTi+CwwGLgSGlXDuw4BZKaXZKaV1wCTgjHbHfAC4NqU0ByCl5NxqSZXtzjafoZ5wqjdOkaQ6VMoc6G8Aj6WUWrp57tHA3Db9eRRvyrLBW4A+ETEFGAJ8N6X0q/YnioiLgYsBRo4cyZQpU7oZpWesWLEit/dW73CM68OWjvOQVxdyyKzsP9FaGxp4pO/2rPPnpWL557k+OM61rxLHuMsCujCl4jTgCxGRgGeAH6aUFpVw7o4mBaYO3v8Q4HiyKSEPR8QjKaW/bPSilK4ArgAYP358mjBhQglv3/OmTJlCXu+t3uEY14ctHuef/NebzYbDJ3LUqaf1XCj1OP881wfHufZV4hh3OoUjIo4Gpha6vwJ+XWg/Wti3OfOAXdr0dwYWdHDMbSmllSmlV8k+rPjWUoJLUq9641WYdl+xf/yZuUWRJOWrqyvQ3wLOTCnNaLPt+sJNVH7MptMx2psKjI2I3YH5wLlkc57buh74fkQ0AX0L5/xON/JLUu+456ZsBQ6AsQfAmLH55pEk5aarAnqbdsUzACmlxyNiyOZOnFJaHxGXApOBRuDKlNLTEXFJYf/lKaVnI+I24M9kN2n5aUrpqS36SiSpXNaugftuKfZPfE9+WSRJueuqgI6IGJZSeqPdxu0obf1oUkq3ALe023Z5u/5lwGWlxZWkHDx6D6xYlrWHj4S3HZFvHklSrroqhL8D3B4Rx0bEkMJjAnArTrOQVC9S2vjGKce9Gxoa88sjScpdp1egU0pXRMQC4KvA/mQraDwD/EdK6cZeyidJ+Xr+KZj/16zdtx+8/aRc40iS8tflMnYppZuAm3opiyRVnrZXn488HgYOzi+LJKkilDSXWZLq0uuLs1t3b3Dcu/PLIkmqGBbQktSZe2+G1tasvfdBMHpMrnEkSZVhswV0YR3nzW6TpJrSvA7uu7XY9+qzJKmglCvQ13Sw7eqeDiJJFWXafbB8adYeNhzedmS+eSRJFaPTDxFGxD5kq29sGxFntdm1DdC/3MEkKVd3t1lsaMJp0OjSdZKkTFercOwNnAYMBU5vs3058PEyZpKkfM2eCS/OzNpNfeAdJ+ebR5JUUbpaB/p64PqIODKl9HAvZpKkfN1zQ7F96LEwZGhuUSRJlaeUOdBzI+KPEfFKRCyKiGsiYueyJ5OkPCxbAlPvK/aP98ODkqSNlVJA/xy4ARgFjAZuLGyTpNpz362wvjlr77EPjHlLvnkkSRWnlAJ6h5TSz1NK6wuPXwAjypxLknpfS0u29vMGLl0nSepAKQX04oi4ICIaC48LgNfKHUySet2Mh+CNV7P2kKFwyNtzjSNJqkylFNAfAc4BXgYWAmcXtklSbbm7zYcHjz0V+vTNL4skqWJ1tYwdACmlOYD/jympts2dDX95Mms3NmYFtCRJHejqRir/0sXrUkrpq2XII0n5uKfNjVPGHZ3dfVCSpA50dQV6ZQfbBgEfBbYHLKAl1YaVy+GRu4t9PzwoSepCVzdS+daGdkQMAT4NXARMAr7V2eskqeo8eDusW5u1d9kDxu6fbx5JUkXrcg50RGwHfBY4H/glcHBK6Y3eCCZJvaK1Be65qdifeDpE5JdHklTxupoDfRlwFnAFcGBKaUWvpZKk3vLUNFi8MGsPHAyHT8w3jySp4nW1jN3fk9198MvAgohYVngsj4hlvRNPksrsrjZL1x1zEvTrn18WSVJV6GoOdClrREtS9Xp5Hjw9PWtHwITT8s0jSaoKFsmS6lfbpesOOgxG7JRfFklS1bCAllSf1qyCh+4o9l26TpJUIgtoSfXp4btg9aqsvePOsO+4fPNIkqqGBbSk+pMS3N1m+saE06DBX4eSpNJ0+2+MiLgzIm6NCD9tI6kqDV30Eiyck3X6DYCjT8w3kCSpqnR5I5VOXAjsBBzRw1kkqVeMnvlYsXPU8TBgUH5hJElVp9sFdEppAbAAmN7zcSSpzF57heHzni/2J56eXxZJUlXaokl/EXFrTweRpF5x7y1ESll7n7fBqN1yjSNJqj5d3cr74M52AW8rSxpJKqfmdXBfm3//H+fVZ0lS93U1hWMqcC9Zwdze0LKkkaRymnYfrFiatbcbAW/1oxySpO7rqoB+FviblNLz7XdExNzyRZKkMmm/dF1jY35ZJElVq6s50F/pYv8nez6KJJXR7Jnw4kwAWhsa4ZiTcg4kSapWnV6BTild3cW+68qSRpLK5Z7i1edXxuzLjkOG5pdFklTVvPWWpNq3fAlMvffN7vy9D8kviySp6llAS6p9998G65uz9h77sHz7nfLNI0mqahbQkmpbSwtMubnY98YpkqStVFIBHRH7tH2WpKrxxCPw+uKsPWRbGH9MvnkkSVWv1CvQv233LEnVoe3Sde84Bfr0zS+LJKkmdHcKR0c3VZGkyrTgJXju8azd0ADHvivXOJKk2uAcaEm1q83SdYw7Krv7oCRJW8kCWlJtWrUSHrqz2PfDg5KkHtLdAjqVJYUk9bSH74S1a7L2qN1g74PyzSNJqhmlFtDR7lmSKldrK9x9Q7F/3Lsh/PUlSeoZpRbQx7R7lqTK9ezjsGh+1h4wEI44Ltc4kqTaUlIBnVJa0fZZkiraPW2uPh/9Tug/IL8skqSa44cIJdWWV1+GJx4t9iecll8WSVJNsoCWVFum3Ayp8Hnn/Q+BHXfON48kqeZstoCOiE+Xsk2ScrduLdx/W7F/3LvzyyJJqlmlXIH+UAfbPtzDOSRp6/1pCqxcnrWH7wgHjs81jiSpNjV1tiMizgM+AOweEW0+kcMQ4LVyB5OkbkkJ7ryu2J/wLmhozC2OJKl2dVpAAw8BC4HhwLfabF8O/LmcoSSp22b+Gea9mLX79oNjTs43jySpZnVaQKeUXgJeAo7svTiStIXaXn0+6kQYNCS3KJKk2lbKhwiPiIipEbEiItZFREtELOuNcJJUksUL4YlHiv3jz8gviySp5pXyIcLvA+cBzwMDgI8B3ytnKEnqlrtv2Hjpup12yTePJKmmdTUH+k0ppVkR0ZhSagF+HhEPlTmXJJVmzSp4YHKxf8KZuUWRJNWHUgroVRHRF3g8Iv6b7IOFg8obS5JK9NCdsHpV1t5x5+wKtCRJZVTKFI4PAo3ApcBKYBfgveUMJUklaW2Fu64v9o8/Axq8waokqbw2+zdNSumllNLqlNKylNK/pZQ+m1KaVcrJI+LkiJgZEbMi4otdHHdo4cOJZ3cnvKQ699RUWDQ/aw8YBEeekG8eSVJd6OpGKk8CqbP9KaWDujpxRDQCPwBOBOYBUyPihpTSMx0c91/A5E3PIklduLPN1edjTob+A/LLIkmqG13NgX4fsHorzn0YMCulNBsgIiYBZwDPtDvuk8A1wKFb8V6S6s38v8Izj2XtaIDjTs81jiSpfnRVQP82pXRwRPxfSumDW3Du0cDcNv15wOFtD4iI0cB7gOPoooCOiIuBiwFGjhzJlClTtiDO1luxYkVu763e4RhXj7c8chujCu3FO+/F0089BzxX0msd5/rgONcHx7n2VeIYd1VA942IDwFHRcRZ7XemlK7dzLmjg23tp4T8D/CFlFJLREeHv/leVwBXAIwfPz5NmDBhM29dHlOmTCGv91bvcIyrxIrl8PvvvNkdcd7HmfCWA0t+ueNcHxzn+uA4175KHOOuCuhLgPOBoUD7/xtNwOYK6HlkK3ZssDOwoN0x44FJheJ5OHBqRKxPKV23mXNLqmf33wrr1mbtXfaEsQfkm0eSVFc6LaBTSg8AD0TEtJTSz7bg3FOBsRGxOzAfOBf4QLv32H1DOyJ+Adxk8SypSy0tcM+Nxf4JZ0AX/4MlSVJP2+yNVLaweCaltD4iLiVbXaMRuDKl9HREXFLYf/mWnFdSnZvxILy+OGsP2RYOm5BrHElS/SnpVt5bKqV0C3BLu20dFs4ppQ+XM4ukGnHHH4vtCadBn775ZZEk1SVv2SWpesx6Bl54Nms39YFjT803jySpLpV0BToihgFjgf4btqWU7itXKEnq0OSri+0jJsLQ7fPLIkmqW5stoCPiY8CnyVbReBw4AniYbO1mSeodi+bD4w8X+ydusrqmJEm9opQpHJ8mu8nJSymlicA4YHFZU0lSe3f8EVJhKfkDD4XRY3KNI0mqX6UU0GtSSmsAIqJfSuk5YO/yxpKkNpYvgQdvL/ZPOju3KJIklTIHel5EDAWuA+6IiDfY9IYoklQ+U26G5nVZe9e9YO+D8s0jSaprpawD/Z5C8ysRcQ+wLXBbWVNJ0gbr1sLdNxT7J73XG6dIknLVrXWgU0r3liuIJHXo4btg+dKsvd0OcMgx+eaRJNU914GWVLlaW+H2a4r9E86EprLe/0mSpM2ygJZUuf78aLZ8HcCAQfCOk/PNI0kSFtCSKtnkNlefjz0V+g/ML4skSQWl3EhlOZDabV4KTAP+PqU0uxzBJNW52c/B809l7cZGOP6MfPNIklRQymTCb5MtW/dbIIBzgR2BmcCVwIRyhZNUx9retvuwiTBseH5ZJElqo5QpHCenlH6cUlqeUlqWUroCODWl9DtgWJnzSapHL8+Fxx4s9t/pbbslSZWjlAK6NSLOiYiGwuOcNvvaT+2QpK132x+Kt+0+4FDYZY9880iS1EYpBfT5wAeBV4BFhfYFETEAuLSM2STVo9cXZ2s/b/Cu9+eXRZKkDpRyJ8LZwOmd7H6gZ+NIqnu3XwMtLVl77P4w9oB880iS1E4pq3CMAD4OjGl7fErpI+WLJakuLV8C991a7J96bm5RJEnqTCmrcFwP3A/cCbSUN46kunbX9bBubdbeZU84YHy+eSRJ6kApBfTAlNIXyp5EUn1bvRLuuqHYP/X9EJFfHkmSOlHKhwhviohTy55EUn2bcktWRAOMHA2HHJ1vHkmSOlFKAf1psiJ6dUQsi4jlEbGs3MEk1ZF1a+GOa4v9k98HDY355ZEkqQulrMIxpDeCSKpjD94By97I2sOGw5HH55tHkqQudFpAR8Q+KaXnIuLgjvanlB4rXyxJdWN9M9z6+2L/pLOhqU9+eSRJ2oyurkB/FrgY+FYH+xJwXFkSSaovD94Br7+StYdsC8ecnG8eSZI2o9MCOqV0ceF5Yu/FkVRX1jfDzZOK/ZPfB/3655dHkqQSlLKMHRFxFJveSOVXZcokqV60v/o84bR880iSVIJS7kT4f8CewOMUb6SSAAtoSVtufTPc0ubq80lne/VZklQVSrkCPR7YL6WUyh1GUh156E54rXD1efC2MPH0fPNIklSiUtaBfgrYsdxBJNWR9c1w81XFvlefJUlVpJQr0MOBZyLiT8DaDRtTSu8uWypJtW2Tq8/OfZYkVY9SCuivlDuEpDqyydzn90L/AfnlkSSpm0opoPcE7k8pPV/uMJLqwEN3wquLsvbgbZz7LEmqOqUU0GOACyJiN2A6cD9ZQf14GXNJqkXN6+DG3xT77/TqsySp+mz2Q4QppX9JKR0HHAA8AHyOrJCWpO6550Z449WsPWQoHOdHKSRJ1aeUdaC/DBwNDAZmAP9AdhVakkq3eiXc8rti/7TzvPosSapKpUzhOAtYD9wM3As8klJaU9ZUkmrP7dfCimVZe/sd4B2n5JtHkqQtVMoUjoOB44E/AScCT0bEA+UOJqmGLF+SFdAbnHEh9OmbWxxJkrZGKVM4DgCOAY4luyvhXJzCIak7bvkdrF2dtUftBkdMzDePJElboZQpHP9FNnXjf4GpKaXm8kaSVFNeewXuuanYf8+HoKExvzySJG2lUgro9wJ7AQloBCygJZXuxl9nN08B2GMfeNuR+eaRJGkrdToHOiKaIuK/yaZs/BL4NTA3Iv47Ivr0VkBJVWzhXHjwzmL/rIsgIr88kiT1gK4+RHgZsB2wR0rpkJTSOLK7Eg4FvtkL2SRVu2t+Bqk1a+93MOzz1nzzSJLUA7oqoE8DPp5SWr5hQ0ppGfC3wKnlDiapyj37ODz+SNaOyK4+S5JUA7oqoFNKKXWwsYVsPrQkday1BX7/k2L/yONhzNj88kiS1IO6KqCfiYgL22+MiAuA58oXSVLVe+hOmPtC1u7bD97z4VzjSJLUk7paheMTwLUR8RFgOtlV50OBAcB7eiGbpGq0ZjX88RfF/klnw7DhucWRJKmndVpAp5TmA4dHxHHA/kAAt6aU7uqtcJKq0G1/gKVvZO2h28PJ78s3jyRJPWyz60CnlO4G7u6FLJKq3euL4fZriv33fBj69c8tjiRJ5dDVHGhJ6p5rfw7r1mbtXffKPjwoSVKNsYCW1DNmz4RH2vxn1TkfhwZ/xUiSao9/u0naeq0t8NvvF/vjjvKmKZKkmmUBLWnr3T8Z/vp81m7qk119liSpRllAS9o6K5Zlc583OOUcGLFTfnkkSSozC2hJW+fan8PK5Vl7+I5ZAS1JUg2zgJa05V6cCfffVuyfe0l250FJkmqYBbSkLdPaAr/5PqSU9Q86DN52RL6ZJEnqBRbQkrbM3Tdu/MHBcy/JN48kSb3EAlpS9732CvzxF8X+u86FHUblFkeSpN5kAS2pe1LKpm6sXZP1R+3qBwclSXWlrAV0RJwcETMjYlZEfLGD/edHxJ8Lj4ciwjsvSJVu2v3w5z8V+xd+JpvCIUlSnShbAR0RjcAPgFOA/YDzImK/doe9CBybUjoI+CpwRbnySOoBK5fDVT8q9iecBnu1/2MtSVJtK+cV6MOAWSml2SmldcAk4Iy2B6SUHkopvVHoPgLsXMY8krbW738Cywp/ZIduD2ddlG8eSZJyEGnDElQ9feKIs4GTU0ofK/Q/CByeUrq0k+P/Adhnw/Ht9l0MXAwwcuTIQyZNmlSWzJuzYsUKBg8enMt7q3c4xp3bbt4sDppy9Zv9p97xHl7dde8cE205x7k+OM71wXGufXmO8cSJE6enlMa3395UxveMDrZ1WK1HxETgo8DbO9qfUrqCwvSO8ePHpwkTJvRQxO6ZMmUKeb23eodj3IkVy+HGNjOsDj2WAy78m/zybCXHuT44zvXBca59lTjG5Syg5wG7tOnvDCxof1BEHAT8FDglpfRaGfNI2lKTfgRLX8/a2wyD8z+Rbx5JknJUzjnQU4GxEbF7RPQFzgVuaHtAROwKXAt8MKX0lzJmkbSlZjwEj9xd7H/wUzB4m/zySJKUs7JdgU4prY+IS4HJQCNwZUrp6Yi4pLD/cuBfgO2BH0YEwPqO5plIysnyJfCr/y32jzwexh2ZWxxJkipBOadwkFK6Bbil3bbL27Q/BmzyoUFJFSAl+MV3siIaslU3vF23JEneiVBSJ6bcBE88Wux/6DMwaEhucSRJqhQW0JI2Nf+v2ZrPG5xwJhx4aF5pJEmqKBbQkjbWvA6u+Eb2DLDz7vDej+SbSZKkCmIBLWljf/hpdgUaoE9fuPiL2bMkSQIsoCW1Ne0+uLvNapPv/xsYtVt+eSRJqkAW0JIyL8+Fn3+n2B93FBx7an55JEmqUBbQkmDtGvjR12Dt6qw/Yie46LOQrc8uSZLasICW6l1K8OvvFec9N/WBv/0yDBycayxJkiqVBbRU7+69BR6+q9g//xOw65755ZEkqcJZQEv17Lkn4KofFvtHnQhvPym/PJIkVQELaKleLX4ZLv8atLRk/V33zK4+O+9ZkqQuWUBL9WjNKvj+V2DFsqy/zTC49CvQr3+eqSRJqgoW0FK9aW2Fn31z4w8NfuKfYbsRucaSJKlaWEBL9eYPP4EZDxX7H/wk7LlffnkkSaoyFtBSPbn9Wrjjj8X+iWfB0e/ML48kSVXIAlqqF9Puy64+b3Dw0fC+j+aXR5KkKmUBLdWDvzwFP70su2kKwF77wcc+Dw2N+eaSJKkKWUBLte6l5+F7/wLrm7P+jjtnK2707ZdrLEmSqpUFtFTL5v8VvvNPsHpV1t9mGHz6P2DwNrnGkiSpmllAS7Vq0QL49j8W13oeOBj+7mswYsd8c0mSVOUsoKVa9Nor8O0vwtLXs36/AfCZr8Eue+SbS5KkGmABLdWaxS/DZZ/LimiAPn3hU/8Ge+ydby5JkmpEU94BJPWgRfPhW1+E1xdn/cYm+MS/wN4H5ZtLkqQaYgEt1YoFc7LiecO0jaY+WfF8wPh8c0mSVGMsoKVa8NLz8D//DMuXZP2+/eDSf4X9Ds41liRJtcgCWqp2zzwGP/gqrF2d9fv1h0/9u9M2JEkqEwtoqZo9eg9c+S1oWZ/1Bw7Oiue99ss3lyRJNcwCWqpGKcHt18IfflLcNmw4fOY/YPSY3GJJklQPLKClatO8Dn7zfXjg9uK2Ubtm6zxvNyK/XJIk1QkLaKmaLF8CP/wqPP90cdvY/eETX4HBQ/JKJUlSXbGAlqrFnBfgh/8Ory4qbjvyBLjwU9nNUiRJUq+wgJYqXUpw/23w2x/C+uZsWwSc/VF453uztiRJ6jUW0FIlW7smm+/80J3Fbf0Hwse/AG89PL9ckiTVMQtoqVLNnQ0/+S9Y8FJx2+gx8Lf/BDvuklssSZLqnQW0VGlaW+HOP8K1vyhO2QA46gQ4/9LsRimSJCk3FtBSJXl9cXZjlOceL27r2w/OvQSOOdn5zpIkVQALaKkStLbCvbfANVfCmlXF7buNhY99HnZyyoYkSZXCAlrK28tz4ZffheefKm6LBjj1HDj9fGjqk182SZK0CQtoKS9r18Ctv4Pbrt54rvPI0fDhz2Y3SJEkSRXHAlrqbSnB1HvhDz+FN14tbm9ogJPPgdM/4I1RJEmqYBbQUm+aMwuuunzj6RoAY8bChZ+BXffMJZYkSSqdBbTUGxbNh+v/L7vynFJx+5Ch8N6L4KgTsyvQkiSp4llAS+X02iK48bfw0B3ZShsbNDbC8WfCaR+AgYNyiydJkrrPAloqh8Uvw+1Xw/2TN/6AIGS34D77Yy5NJ0lSlbKAlnrSS8/D5Kth6v2QWjfet+/b4MwPwZ775hJNkiT1DAtoaWu1tsLT0+H2a+DZxzfdv+e+8J4Pwz5v7e1kkiSpDCygpS219A148Ha471Z49eVN9+87Dk4+G/Y72FtwS5JUQyygpe5obYHnnsjmNj/2ILSs33h/NMChx8BJZ2e34ZYkSTXHAlranJRg3ovwyF3w6BRY8tqmxwwcDEefCMedASN27PWIkiSp91hASx1JCRa8BDMegqn3wfy/dnzcnvvChHfBIcdA3369GlGSJOXDAlraoLWVbRbPh6t/lhXOi+Z3fNyQbeHQY+GYk2GXPXo3oyRJyp0FtOrbkteyFTSeng7PzODgFcs6Pq5vPxh3FBxxXPbhwCb/6EiSVK+sAlRfViyHF56BmX/OiubOpmYA9OsPBx6aFc5vPRz6D+y1mJIkqXJZQKt2pQSvL4bnn4Lnn4ZZT3ddMAPr+g+k78FHw8FHw37jnNcsSZI2YQGt2pBSNh3jpefhpVnZ81+fh2VvdP26xiYYuz/sfwjsfwgPvTCHCRMn9k5mSZJUlSygVX1Wr4QFc7JVMjY85r2Y3dhkcxoaYNe9sqJ537fBWw6C/gOK+2fPLVtsSZJUGyygVZnWN8Ori7I7/L2yABYvhIVzs2L59cWln6ffgGypubH7w177wx77ZHObJUmStpAFtPLRvA7eeDWbdvHGq1lRvHghvLIQFi+A11+F1Nq9c/YbALvumd0BcMzY7Hnk6OyqsyRJUg+xgFbPaW2FVSth+RJYvjR7XrYEViwtFspvvApvvJZt21KNTVlhPGo3GL1b9jxqNxg5Choae+iLkSRJ6pgFtDbVvA5WrciK4VUrsjnHbftvPlbCyuWFgnkJrFgGLS09kyEChg2HETtljx12gh1GZYXyDqNdh1mSJOWmrFVIRJwMfBdoBH6aUvpGu/1R2H8qsAr4cErpsXJmqlopZcXp+ubio3kdNDe329YMzWth7ZrssW5De3WbbWuK7bbb1qyBNauy85RbQwMM3T4rkoduD8NGwIgdC49RMHwk9Olb/hySJEndVLYCOiIagR8AJwLzgKkRcUNK6Zk2h50CjC08Dgd+VHiuLFPvg9UrGfWXZ6FlaVbIthYeLS3Z1IWWtv127ZbW0va1NBcL4uZ2hfL65qyIrnQDBsLgbWGboTBkaHbb6yFDs/52I7KCedhwrnthFZfd8TwLlqxmVAzgc0fszZnjRpc93peve5KrHp1LS0o0RnDe4bvwH2ce2Onx182Yz2WTZ2Y5hw7gcydtPmdnr6m07b2hu9/vzuT5NUjl4s+1VL3KeQX6MGBWSmk2QERMAs4A2hbQZwC/Sikl4JGIGBoRO6WUFpYxV/dd/VN47RXeAvCnvMP0gsYmGDgYBg4qPg8YzNRX1jJ9cTPLol/2aOjH0ujHYW/dnU+cPj4rlku4anzdjPl86bqnWd2cTfeYv2Q1X7r2SYCy/uXx5eue5NePzHmz35LSm/2OirrrZsznS9c+2a2cnb1m2kuvc830+RWzvauvoad09/vdmS0ZB6nS+XMtVbdyFtCjgbaL6s5j06vLHR0zGqisArpSPpjW0ABNfbJHnz5Zsbqh39Sm36dPtiJFv37Qt3+2bFu//lm7/4Biu1+/wr4BG+/v2y+bg9zOuV+6hZZBm14Ff+C5xCc+NKLkL+OyyTPf/Etjg9XNLVw2eWZZ/+K46tGO13i+6tG5HRZ0W5Kzs9dsuApbKdvL/b2G7n+/O5PXz4tUTv5cS9UtUpmmBUTE+4CTUkofK/Q/CByWUvpkm2NuBr6eUnqg0L8L+HxKaXq7c10MXAwwcuTIQyZNmlSWzJ3ZfcYU+qxdzbr1LTT160uKhuzR0NFzFPsdHhNdvr61sZHWhiZS4bm1sZHWxkZSQxMp5+XYnpzf+coZB47ettfP012lvO+KFSsYPHhwycd35z0qTTm/11DZPy9tx1m1q5LHOa/fg7WoksdZPSPPMZ44ceL0lNL49tvLWUAfCXwlpXRSof8lgJTS19sc82NgSkrpqkJ/JjChqykc48ePT9OmTStL5s2ZMmUKEyZMyOW9K8GeX7plk6uZAI0RvPD1U0s+z9HfuJv5S1Zvsn300AE8+MXjtipjV0rJ33aMtyRnZ69pjOj0vfPYXu7vNVT2z0u9/1muF5U8znn9HqxFlTzO6hl5jnFEdFhAl/OS5lRgbETsHhF9gXOBG9odcwNwYWSOAJZW3Pxnvem8w3fp1vbOfO6kvRnQZ+NpMQP6NPK5k/be4myl6G7+LcnZ2WvOO3yXitpe7u81VP/Pi1RO/lxL1a1sc6BTSusj4lJgMtkydlemlJ6OiEsK+y8HbiFbwm4W2TJ2F5Urj7behnmrW7uqwob5fb396fPu5t+SnF29Zvxu21XU9nKr9p8XqZz8uZaqW9mmcJSLUzhUTo5xfXCc64PjXB8c59pXb1M4JEmSpJpjAS1JkiR1gwW0JEmS1A0W0JIkSVI3WEBLkiRJ3WABLUmSJHWDBbQkSZLUDRbQkiRJUjdYQEuSJEndYAEtSZIkdYMFtCRJktQNFtCSJElSN0RKKe8M3RIRi4GXcnr74cCrOb23eodjXB8c5/rgONcHx7n25TnGu6WURrTfWHUFdJ4iYlpKaXzeOVQ+jnF9cJzrg+NcHxzn2leJY+wUDkmSJKkbLKAlSZKkbrCA7p4r8g6gsnOM64PjXB8c5/rgONe+ihtj50BLkiRJ3eAVaEmSJKkbLKAlSZKkbrCALkFEnBwRMyNiVkR8Me886hkRsUtE3BMRz0bE0xHx6cL27SLijoh4vvA8LO+s2joR0RgRMyLipkLfMa4xETE0Iq6OiOcKf6aPdJxrT0T8XeH39VMRcVVE9Hecq19EXBkRr0TEU222dTquEfGlQk02MyJOyiOzBfRmREQj8APgFGA/4LyI2C/fVOoh64G/TyntCxwBfKIwtl8E7kopjQXuKvRV3T4NPNum7xjXnu8Ct6WU9gHeSjbejnMNiYjRwKeA8SmlA4BG4Fwc51rwC+Dkdts6HNfC39PnAvsXXvPDQq3WqyygN+8wYFZKaXZKaR0wCTgj50zqASmlhSmlxwrt5WR/4Y4mG99fFg77JXBmLgHVIyJiZ+BdwE/bbHaMa0hEbAO8A/gZQEppXUppCY5zLWoCBkREEzAQWIDjXPVSSvcBr7fb3Nm4ngFMSimtTSm9CMwiq9V6lQX05o0G5rbpzytsUw2JiDHAOOBRYGRKaSFkRTawQ47RtPX+B/g80Npmm2NcW/YAFgM/L0zV+WlEDMJxrikppfnAN4E5wEJgaUrpdhznWtXZuFZEXWYBvXnRwTbX/qshETEYuAb4TEppWd551HMi4jTglZTS9LyzqKyagIOBH6WUxgEr8b/xa05hDuwZwO7AKGBQRFyQbyrloCLqMgvozZsH7NKmvzPZfxmpBkREH7Li+TcppWsLmxdFxE6F/TsBr+SVT1vtaODdEfFXsulXx0XEr3GMa808YF5K6dFC/2qygtpxri0nAC+mlBanlJqBa4GjcJxrVWfjWhF1mQX05k0FxkbE7hHRl2zi+g05Z1IPiIggmzP5bErp22123QB8qND+EHB9b2dTz0gpfSmltHNKaQzZn927U0oX4BjXlJTSy8DciNi7sOl44Bkc51ozBzgiIgYWfn8fT/bZFce5NnU2rjcA50ZEv4jYHRgL/Km3w3knwhJExKlk8ygbgStTSl/LN5F6QkS8HbgfeJLi/Nh/JJsH/XtgV7Jf2O9LKbX/cIOqTERMAP4hpXRaRGyPY1xTIuJtZB8U7QvMBi4iu0jkONeQiPg34P1kqyjNAD4GDMZxrmoRcRUwARgOLAL+FbiOTsY1Iv4J+AjZz8FnUkq39npmC2hJkiSpdE7hkCRJkrrBAlqSJEnqBgtoSZIkqRssoCVJkqRusICWJEmSusECWpIqXESsyDuDJKnIAlqSJEnqBgtoSaoSETEhIqZExNUR8VxE/KZwRzYi4tCIeCginoiIP0XEkIjoHxE/j4gnI2JGREwsHPvhiLguIm6MiBcj4tKI+GzhmEciYrvCcXtGxG0RMT0i7o+IffL8+iWpUjTlHUCS1C3jgP2BBcCDwNER8Sfgd8D7U0pTI2IbYDXwaYCU0oGF4vf2iHhL4TwHFM7VH5gFfCGlNC4ivgNcSHb31SuAS1JKz0fE4cAPgeN66euUpIplAS1J1eVPKaV5ABHxODAGWAosTClNBUgpLSvsfzvwvcK25yLiJWBDAX1PSmk5sDwilgI3FrY/CRwUEYOBo4A/FC5yA/Qr75cmSdXBAlqSqsvaNu0Wst/jAaQOjo0OtnV0ntY2/dbCORuAJSmlt21xUkmqUc6BlqTq9xwwKiIOBSjMf24C7gPOL2x7C7ArMLOUExauYr8YEe8rvD4i4q3lCC9J1cYCWpKqXEppHfB+4HsR8QRwB9nc5h8CjRHxJNkc6Q+nlNZ2fqZNnA98tHDOp4Ezeja5JFWnSKmj//WTJEmS1BGvQEuSJEndYAEtSZIkdYMFtCRJktQNFtCSJElSN1hAS5IkSd1gAS1JkiR1gwW0JEmS1A3/H4GX0GKJRZ+kAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0, 100, 500)\n",
    "P_hat = 1/(1 + np.exp(-log_reg.params[0]-log_reg.params[1]*X))\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (12, 7))\n",
    "ax.scatter(df['Annual_Family_Income'], df['Own_House'])\n",
    "ax.plot(X, P_hat, color = 'tomato', lw = 3)\n",
    "ax.grid()\n",
    "ax.set_xlabel('Income')\n",
    "ax.set_ylabel('Owning a flat = 1, Not Owning = 0')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b4562a1-d3ec-42f5-b9e5-46005bdefea3",
   "metadata": {},
   "source": [
    "To interpret estimated coefficients, we can calculate the marginal effect by taking derivative w.r.t certain $\\beta$, in this case $\\beta_1$.\n",
    "$$\n",
    "\\frac{dP_i}{d X_i} = \\frac{dP_i}{dZ_i}\\frac{dZ_i}{dX_i}=\\frac{e^{-Z_i}}{(1+e^{-Z_i})^2}\\beta_2\n",
    "$$\n",
    "Plot both accumulative and marginal effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "3a56cd37-cf4a-4da6-8a67-f09058eeb09a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta1_hat, beta2_hat = log_reg.params[0], log_reg.params[1]\n",
    "X = np.linspace(0, 100, 500)\n",
    "\n",
    "Z = beta1_hat + beta2_hat*X\n",
    "dPdX = np.exp(-Z)/(1+np.exp(-Z))**2*beta2_hat\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize = (12, 7))\n",
    "ax1.scatter(df['Annual_Family_Income'], df['Own_House'])\n",
    "ax1.plot(X, P_hat, color = 'tomato', lw = 3, label='Accumulative Effect')\n",
    "ax1.legend(loc ='center left')\n",
    "\n",
    "ax2 = ax1.twinx() \n",
    "ax2.plot(X, dPdX, lw = 3, color = 'Gold', label = 'Marginal Effect')\n",
    "ax2.legend(loc='center right')\n",
    "ax2.set_title('Accumulative and Marginal Effect of Family Income on Owning a House')\n",
    "ax2.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d22484f-81f9-4c0b-a2e2-ec5f520dcab6",
   "metadata": {},
   "source": [
    "As family income raises, the marginal probability will reach maximum around $40000$ pounds, to summarize the effect, we calculate the marginal effect at the mean value of the independent variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "8aee3923-548b-448d-ab30-193a6e3abe5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03297676614392626"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_mean = np.mean(df['Annual_Family_Income'])\n",
    "Z_mean_effect = beta1_hat + beta2_hat*X_mean\n",
    "dPdX = np.exp(-Z_mean_effect)/(1+np.exp(-Z_mean_effect))**2*beta2_hat; dPdX"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ee4701f-f876-4246-a110-02280df28a81",
   "metadata": {},
   "source": [
    "At the sample mean, $1000$ pounds increase in family income increases the probability of owning a house by $3.2 \\%$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f46c537-b4cf-46d2-bec6-06a1f3676b80",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> More Than One Variable</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "cf5d81fc-3eaf-473b-b26c-17cdd394b294",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.247296\n",
      "         Iterations 8\n",
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:               admitted   No. Observations:                   30\n",
      "Model:                          Logit   Df Residuals:                       26\n",
      "Method:                           MLE   Df Model:                            3\n",
      "Date:                Thu, 09 Sep 2021   Pseudo R-squ.:                  0.6432\n",
      "Time:                        12:16:41   Log-Likelihood:                -7.4189\n",
      "converged:                       True   LL-Null:                       -20.794\n",
      "Covariance Type:            nonrobust   LLR p-value:                 6.639e-06\n",
      "===================================================================================\n",
      "                      coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "const             -16.3315      8.601     -1.899      0.058     -33.189       0.526\n",
      "gmat                0.0025      0.018      0.141      0.888      -0.032       0.037\n",
      "gpa                 3.3208      2.397      1.385      0.166      -1.378       8.020\n",
      "work_experience     0.9975      0.585      1.704      0.088      -0.150       2.145\n",
      "===================================================================================\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_excel('Basic_Econometrics_practice_data.xlsx', sheet_name = 'GMAT_Work_Quali_Resp'); df.head()\n",
    "\n",
    "Y = df[['admitted']]\n",
    "X = df[['gmat', 'gpa', 'work_experience']]\n",
    "X = sm.add_constant(X)\n",
    "log_reg_house = sm.Logit(Y, X).fit()\n",
    "print(log_reg_house.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b597b6b-ee22-4e90-9e26-6ba747c8104e",
   "metadata": {},
   "source": [
    "The estimated model is\n",
    "$$\n",
    "\\hat{P_i} = \\frac{1}{1+e^{-(-16.3315+0.0025 X_{2i} + 3.3208 X_{3i}+.9975 X_{4i})}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "b3038355-3619-43f5-9be2-87a350195b4c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Marginal effect of GMAT, GPA and Working Exp are 0.0005751109753324387, 0.7627645112662916 and 0.22911309163038573 accordingly.\n"
     ]
    }
   ],
   "source": [
    "beta1_hat, beta2_hat, beta3_hat, beta4_hat = log_reg.params[0], log_reg.params[1], log_reg.params[2], log_reg.params[3]\n",
    "X2_mean = np.mean(df['gmat'])\n",
    "X3_mean = np.mean(df['gpa'])\n",
    "X4_mean = np.mean(df['work_experience'])\n",
    "Z_mean_effect = beta1_hat + beta2_hat*X2_mean + + beta3_hat*X3_mean + beta4_hat*X4_mean\n",
    "dPdX2 = np.exp(-Z_mean_effect)/(1+np.exp(-Z_mean_effect))**2*beta2_hat\n",
    "dPdX3 = np.exp(-Z_mean_effect)/(1+np.exp(-Z_mean_effect))**2*beta3_hat\n",
    "dPdX4 = np.exp(-Z_mean_effect)/(1+np.exp(-Z_mean_effect))**2*beta4_hat\n",
    "print('Marginal effect of GMAT, GPA and Working Exp are {}, {} and {} accordingly.'.format(dPdX2, dPdX3, dPdX4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f137a00b-8f62-4cb6-92d6-f91e7a123cbf",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Goodness of Fit</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f128c30-2e12-4c1f-94ef-f31929e23579",
   "metadata": {},
   "source": [
    "You might be wondering why log-likelihood is a negative number as in the report, recall that any likelihood is a joint distribution which must lie between $[0, 1]$, so the log likelihood must be negative, the plot below is a reminder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "6abb2172-52eb-43d7-8665-0fe96ca02ffa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RwG9TAIiBvuFR7Wv0aXejbzz4nl6SzBhpYXGWNiws0orZuVpRkatls3LOCrx1dScJwAAQRfxGBYAoGwmOqb6lX7sbe7X7lE+7G3t1rGNANrxIg+YUZGjNnDz90buqtHJ2rpZX5CozlV/HABBL/NYFgCmwNrzxxK5TvXqzoVe7TvXqQHOfAmPhXdaKslK1ujJXd6yapZWVeVpZkav8zBSHqwYAEIIB4BL0DY9qdyTwvtnQo92NPnUPBiRJ6cmJWjE7V/ddW6VVlXlaVZmnWblpbDoBAC5ECAaA8wiFrI52DGjnyZ5w6D3VoyPt4WkNp+fx3ri0RKsr87W6Mk/VpVlKSkxwumwAwCQQggEgon94VLtP+bTjZI92NPTozYYe9Q8HJUl5GclaU5mn21bO0to5+VpZmcvSZAAwgxGCAXiStVaNPUPacbJH2092a/uJHh1q6x8f5V1cmq33rwoH3rVz8jSvKJNpDQAQRwjBADwhOBbSwZZ+bTvRrR2R0Ht617Ws1CStmZOnW5aXad3cfK2qzGOUFwDiHCEYQFzyB4La1dCrN0706I0T3drZ0CN/YEySVJGXrmsWFKpmbr7WzS3Q4rJsJSYwygsAXkIIBhAXfP5RbT/ZrW1vdev1t7q1r8mnYMjKGGlJWY7uWjdbV1YVqKYqX+W56U6XCwBwGCEYwIzUOTASDrzHu7TtRI/qW/tkrZSSmKBVlbnafN18XTmvQOvm5jO1AQDwDoRgADNCe/+wXj/erdff6tLrx7t1pH1AUnht3nVz8/W5G6u1fl6BVlfmKS050eFqAQBuRwgG4EpdAyN67Xi3Xj3eqVePdelYx6AkKTMlUTVVBbpzbYWunl+oFRW5SmZtXgDAJSIEA3AFn39Ur73VpVePhT8OtfVLCofeK+cV6EM1lbp6fqGWz8phQwoAwJQRggE4Yigwpu0nu/W7o136/bFO7WvyKWSltOQEXVlVoNtXz9I1CxjpBQBMD0IwgJgYC1ntbfLplSMdeuVop3ae7FVgLKSkBKM1c/L06U2LdO3CIq2uzFNKEqEXADC9CMEAps3JrkFtPdKpV4506vfHOtUX2YJ4WXmO/ujaKr1rQaGurCpQZiq/igAAscW/PACipm94VK8e69LWIx16+XCnGrr9kqRZuWm6ZXmZ3r2oWNcuKFRhVqrDlQIAvI4QDOCyhUJW+5p9eulQh14+0qGdDb0aC1llpiTqmgWF+pN3z9OGRUWaV5QpY9iRDQDgHoRgAJeka2BEW4906qXDHXr5cIe6BgOSpBUVubr/+vnasKhYa+fkM68XAOBqUQnBxphbJP0fSYmS/p+19h+j8b4AnBeK3ND2m/p21R1q154mn6yVCjJTdN2iItUuLtGGRUVMcQAAzChTDsHGmERJD0q6SVKjpDeMMT+31h6Y6nsDcIZvaFRbj3Tot/UdeulwuzoHAjJGWl2Zp8/dWK3rq4u1oiJXCQlMcQAAzEzRGAleL+motfa4JBljtki6QxIhGJhB3uoc1IsH2/TTbUM68tzzGgtZ5aYn6/rqYm1cUqzrq0tUkJnidJkAAESFsdZO7Q2MuUvSLdbaP408/rikq6y1n5pw3GZJmyWptLR03ZYtW6Z03ksxMDCgrKysmJ0Pk0NfnDUWsjraG9Kb7WPa1RFU62D4d0F5htXa0hStKknUgtwEJTLa6wpcL+5EX9yHnriTk33ZuHHjDmttzcTnozESfK5/Id+RrK2135H0HUmqqamxtbW1UTj15NTV1SmW58Pk0JfY8weCevlwp5470Krf1rerxz+q5ESjq+cX6v4lJbphaamO7dlGX1yI68Wd6Iv70BN3cmNfohGCGyVVnvF4tqTmKLwvgCjoHBjRiwfb9Nz+Nr1ytFMjwZBy05O1aUmJblpWqg2LipSdljx+/DEHawUAIFaiEYLfkLTIGDNPUpOkj0q6OwrvC+AyNfb49ez+Nj27v1VvnOiWtdLs/HTdfdUc3bSsVFdWFSg5kSXMAADeNeUQbK0NGmM+JelZhZdIe9hau3/KlQG4JEfbB/Ts/lb9el+r9jb5JElLyrL1mU2LdPMVZVpans2GFQAARERlnWBr7TOSnonGewGYvCNt/frl3hY9s7dFh9sGJElr5uTpi7cu0c1XlKmqKNPhCgEAcCd2jANmmEOtbwffo+0DMka6cm6B/ub9y3Tz8jKV56Y7XSIAAK5HCAZmgOMdA3p6T4ue3tOsw23h4Lu+qkD33nGFbrmiTCU5aU6XCADAjEIIBlyqscevX+5p0S/2NGtfU5+kcPD9uzuu0C3Ly1SSTfAFAOByEYIBF+keDOiXe1v01JtN2n6yR1J4q+K/ft9SvW9lOVMdAACIEkIw4DB/IKjnD7TpqV3Nevlwh4Ihq+rSLP3lzYt1+6pZqizIcLpEAADiDiEYcMBYyOq14116fEejfr2/Vf7AmMpz0/QnG+bpA6srtKSM5cwAAJhOhGAgho629+vxnU168s0mtfiGlZ2WpNtXzdIH1lRofVWBEhIIvgAAxAIhGJhmPv+ontrdpJ/uaNSeRp8SE4yury7WA+9bqhuXliotOdHpEgEA8BxCMDANxkJWvzvaqcd2NOrZ/a0KBENaVp6jL9+2TLevmqXi7FSnSwQAwNMIwUAUner267Htp/TTHY1q9g0rNz1Zd6+fo7vWzdbyilynywMAABGEYGCKAsGQXjjYpke2NWjrkU4ZI21YVKwvMd0BAADXIgQDl+lE56C2vHFKP91xSp0DAc3KTdNnb1ykD9dUalYe6/kCAOBmhGDgEgTHwqO+P3jtpH53tEuJCUablpTo7vVzdF11sRJZ3QEAgBmBEAxMQnvfsB7ZdkqPbGtQa9+wZuWm6fM3VevDV1aqNIftiwEAmGkIwcB5WGv12vFu/fC1k3p2f6uCIavrqov19x9Yrk1LShj1BQBgBiMEAxMMj47pqV1N+o/fnVB9a79y05N137VVuuequaoqynS6PAAAEAWEYCCixTekH7x6Uo9sa1CPf1RLyrL1vz64QrevqlB6Cis8AAAQTwjB8Lxdp3r1/7Ye16/2tSpkrW5aWqr7rp2nq+cXyBimPAAAEI8IwfCkUMjqxfp2fffl49p2olvZqUn642urdO81VaosyHC6PAAAMM0IwfCU4dExPb6zUQ9tfUvHOwdVkZeuL9+2TB+5slJZqVwOAAB4Bf/qwxN8/lF9/9UT+t7vT6hrMKCVs3P19Y+t0a3Ly5SUmOB0eQAAIMYIwYhr7f3DeuiVt/Sj1xo0MBLUpiUl+uR187V+HvN9AQDwMkIw4lJDl1/ffvmYHtvRqOBYSLetnKU/q12gpeU5TpcGAABcgBCMuPJW56C+/psjempXsxKN0QfXzdYnr5vP+r4AAOAshGDEheMdA/rGb47qyV1NSklK0H3vqtInrpvPlsYAAOCcCMGY0Y5Fwu9TkfD7pxvm6xMb5qs4O9Xp0gAAgIsRgjEjNXT59b9fOKwndzUpNSlRn9gwX5+4br6Ksgi/AADg4gjBmFHa+ob19d8c0ZZtp5SYYPSnG+ZrM+EXAABcIkIwZoSewYC+9dIxfe/3JzQWsvro+kp9etMi5vwCAIDLQgiGq/kDQT209S19++XjGgwEdeeaCn32hmrNKWRrYwAAcPkIwXClsZDV4zsb9a/PHVJb34jes6xUX7h5sapLs50uDQAAxAFCMFxn65EO/cMvD6q+tV+rK/P04N1rVVNV4HRZAAAgjhCC4RqHWvv11WcO6qXDHaosSNc37l6j960oZ3tjAAAQdYRgOK7XH9C/PX9YP3jtpLLTkvXX71uqj18zV6lJiU6XBgAA4hQhGI4JWasfvX5S//LsIfmGRvXxq+fqczdVKy8jxenSAABAnCMEwxFvnOjW3/x+WA39+3T1/AJ95f1XaGl5jtNlAQAAjyAEI6ba+4f11V8e1JO7mlWQZvTg3Wv13hVlzPsFAAAxRQhGTIRCVj/e1qD/9et6jYyG9OlNC7U8oVk3ryx3ujQAAOBBhGBMu/rWPn3pZ3u1s6FX18wv1P+8c7kWFGeprq7F6dIAAIBHEYIxbfyBoP7Pi0f00Na3lJOerK99eJXuXFPB1AcAAOA4QjCmxe+Oduq/P75HjT1D+nDNbH3x1qXKz2TVBwAA4A6EYETVwEhQX33moH78eoPmF2XqJ5uv1lXzC50uCwAA4CyEYETNK0fCo7/NviF9YsM8ff49i5WWzIYXAADAfQjBmLL+4VF99Zl6PbItPPr70/uv0bq5BU6XBQAAcF6EYEzJq8e69IXHdqvFN6TN183Xf72pmtFfAADgeoRgXJZAMKR/e+GwvvXSMVUVZuqx+9+ldXPznS4LAABgUgjBuGTHOwb02Z/s0p5Gnz56ZaW+fNsyZabyVwkAAMwcJBdMmrVWj24/pb/5+QGlJCXo3+9Zq1tXsOMbAACYeQjBmBSff1R/9bM9+tW+Vr1rQaH+9cOrVJ6b7nRZAAAAl4UQjIva09irP//RTrX1Deuvbl2izRvmKyGBXd8AAMDMRQjGeVlr9eNtDfrbnx9QUVaKHv3kNVozh5vfAADAzJcwlW82xnzIGLPfGBMyxtREqyg4bygwps8/ulsPPLFPVy8o1NOf2UAABgAAcWOqI8H7JP2BpG9HoRa4xPGOAf3ZD3fqcHu/PnvjIn160yIlMv0BAADEkSmFYGvtQUkyhoAUL369r1VfeGy3khONvnffel1fXex0SQAAAFHHnGBICs//ffC3R/Uvzx3Wqso8ffOetarIY/UHAAAQn4y19sIHGPOCpLJzvPSAtfapyDF1kr5grd1+gffZLGmzJJWWlq7bsmXL5dZ8yQYGBpSVlRWz8800gTGr/9g3oldbxnR1eaL+eHmqUhKnf3SfvrgTfXEn+uJO9MV96Ik7OdmXjRs37rDWvuPetYuOBFtrb4xGAdba70j6jiTV1NTY2traaLztpNTV1SmW55tJ2vuHtfn7O7Srxa+/vHmx/rx2Qcymt9AXd6Iv7kRf3Im+uA89cSc39oXpEB62v9mnT/zndvX4R/Wt/7JWtyxn9zcAAOANU10i7U5jTKOkayT90hjzbHTKwnR7bn+r7vr3V2UlPXb/NQRgAADgKVNdHeIJSU9EqRbEyCPbGvTAE3u1oiJX3723RiU5aU6XBAAAEFNMh/CQM1eAqF1crG/es1YZKfwVAAAA3kMC8ohQyOrvnj6g7/3+hO5cU6F/umulkhOnNBsGAABgxiIEe0AgGNLnH9utX+xu1ic2zNMXb12qBHaAAwAAHkYIjnODI0Hd/8Md2nqkU1+8dYk+ef0Cp0sCAABwHCE4jvmGRvWHD2/T3iaf/vmulfpQTaXTJQEAALgCIThO9Q2P6t6Ht+lAs0//fs9aveeKc236BwAA4E2E4DjUNzyqex86HYDX6cZlpU6XBAAA4CosDxBn+ofDUyD2N/v0TQIwAADAORGC40h/ZArE3kafHrx7rW4iAAMAAJwTIThOnB4B3tvo04PMAQYAALggQnAc8AeCuu8/3tCeRp++cfda3UwABgAAuCBC8AwXHAvp0z9+UzsbevT1j63RLcsJwAAAABfD6hAzmLVWDzyxTy/Wt+sf7lyuW1eUO10SAADAjMBI8Az2by8c0U+2n9JnNi3UPVfNdbocAACAGYMQPEP96PWT+r8vHtFHair1uZuqnS4HAABgRiEEz0DP7W/Vl5/cp01LSvQPdy6XMcbpkgAAAGYUQvAMs+Nktz79yJtaMTtP37h7jZISaSEAAMClIkHNICe7BvUn/7lds/LS9fAf1igjhfsaAQAALgcheIbwB4L65A92SJL+8771KsxKdbgiAACAmYsQPANYa/XffrpHh9v69fWPrdGcwgynSwIAAJjRCMEzwHe3HtfTe1r0lzcv0YZFxU6XAwAAMOMRgl3ud0c79Y+/qtd7V5Tp/uvnO10OAABAXCAEu1hjj1+f+vFOLSjO0j/dtYql0AAAAKKEEOxSw6Njuv+HOxQcs/r2x9cpK5WVIAAAAKKFZOVC1lo98MQ+7Wvq00N/WKP5xVlOlwQAABBXGAl2oce2N+rxnY36ixsW6YalpU6XAwAAEHcIwS7T0OXX3/5iv66ZX6i/uGGR0+UAAADEJUKwi4yFrD7/2C4lGKN/+fAqJSRwIxwAAMB0YE6wi3x363G9caJH//qhVarIS3e6HAAAgLjFSLBLHGzp09eeO6xbrijTH6ytcLocAACAuEYIdoGR4Jg+95NdyklP1lf/YAXrAQMAAEwzpkO4wNeeP6z61n49/Ec1KshMcbocAACAuMdIsMPeONGt77x8XB9bX6lNS1gODQAAIBYIwQ4aGAnqvz66S5X5Gfrr9y1zuhwAAADPYDqEg/7l2UNq6hnSo5+8RplsiwwAABAzjAQ7pL61Tz947aTuuWquaqoKnC4HAADAUwjBDrDW6itP7VdOWpI+/55qp8sBAADwHEKwA57e06LX3+rWF25erLwMVoMAAACINUJwjPkDQX31mYO6YlaOPnrlHKfLAQAA8CTuxoqxB397VC2+YX39Y2uUmMCmGAAAAE5gJDiGTnQO6rsvv6U711RwMxwAAICDCMEx9PdPH1ByotEXb13idCkAAACeRgiOkd/Wt+vF+nZ95oZFKslJc7ocAAAATyMEx8BIcEx/+4v9ml+cqfuuned0OQAAAJ5HCI6B//jdCZ3o8usr779CKUn8kQMAADiNRDbNBkeC+vZLx3R9dbGury52uhwAAACIEDztfvjaSfX4R/UXNy5yuhQAAABEEIKn0VBgTN/delzvXliktXPynS4HAAAAEYTgafTItgZ1DgT06U0LnS4FAAAAZyAET5Ph0TF9++VjWj+vQFfNL3S6HAAAAJyBEDxNHtvRqLa+EX1mE3OBAQAA3IYQPA0CwZC+VXdMa+bk6dqFjAIDAAC4zZRCsDHmn40x9caYPcaYJ4wxeVGqa0Z78s0mNfUO6TObFskY43Q5AAAAmGCqI8HPS1purV0p6bCkL069pJktOBbSg3VHtaIiV7WLWRcYAADAjaYUgq21z1lrg5GHr0maPfWSZrZf7GnWyS6/PrVpIaPAAAAALhXNOcF/LOlXUXy/GWcsZPWN3xzVkrJs3bS01OlyAAAAcB7GWnvhA4x5QVLZOV56wFr7VOSYByTVSPoDe543NMZslrRZkkpLS9dt2bJlKnVfkoGBAWVlZU37eba1BPXN3SP681WpWl+eNO3nm+li1RdcGvriTvTFneiL+9ATd3KyLxs3btxhra2Z+PxFQ/DFGGP+UNL9km6w1von8z01NTV2+/btUzrvpairq1Ntbe20n+f9X39F/kBQz33ueiUmMBXiYmLVF1wa+uJO9MWd6Iv70BN3crIvxphzhuCprg5xi6T/Lun2yQbgeLW/2ae9TT7de00VARgAAMDlpjon+BuSsiU9b4zZZYz5VhRqmpEefeOUUpISdMfqWU6XAgAAgIuY0sRVa+3CaBUykw2PjunJXc26+Yoy5WWkOF0OAAAALoId46Lg2f2t8g2N6iM1lU6XAgAAgEkgBEfBY9sbNTs/Xe9awBbJAAAAMwEheIpOdfv1ytFOfWhdpRK4IQ4AAGBGIARP0WM7GmWMdFeN5zfLAwAAmDEIwVMwFrL66fZT2rCoWBV56U6XAwAAgEkiBE/BK0c71ewb5oY4AACAGYYQPAWPvnFK+RnJunFZidOlAAAA4BIQgi9T92BAzx1o1QfWVCg1KdHpcgAAAHAJCMGX6ck3mzQ6ZvWRK5kKAQAAMNMQgi+DtVaPbj+lVbNztaQsx+lyAAAAcIkIwZdhT6NP9a39+jCjwAAAADMSIfgy/GT7KaUlJ+j9q2Y5XQoAAAAuAyH4EgXHQnp6d7NuXV6unLRkp8sBAADAZSAEX6KdDb3qGw7qPctKnS4FAAAAl4kQfInqDrUrKcHo2kVFTpcCAACAy0QIvkR1hzq0dm4+UyEAAABmMELwJWjvG9aBlj5dX13sdCkAAACYAkLwJXjpcIckqXYxIRgAAGAmIwRfgrrDHSrJTtWycjbIAAAAmMkIwZMUHAvplSOdur66WMYYp8sBAADAFBCCJ2l3Y698Q6O6nqkQAAAAMx4heJLqDnUowUgbFhKCAQAAZjpC8CTVHerQ2jn5ys1gaTQAAICZjhA8CZ0DI9rb5GNpNAAAgDhBCJ6El8eXRitxuBIAAABEAyF4EuoOdagoK0VXzGJpNAAAgHhACL6IsZDV1iMdum5RsRISWBoNAAAgHhCCL2JPY696/CyNBgAAEE8IwRdxemm06xYRggEAAOIFIfgiXjrcoVWVecrPTHG6FAAAAEQJIfgCugcD2t3Yy9JoAAAAcYYQfAFbj3TIWpZGAwAAiDeE4AuoO9ShgswUrazIdboUAAAARBEh+DxCIauXD3dow6IilkYDAACIM4Tg8zjRNaiuwYCuXVDkdCkAAACIMkLwedS39kuSlrFLHAAAQNwhBJ9HfUufEoy0sCTL6VIAAAAQZYTg8zjQ0q/5xVlKS050uhQAAABEGSH4POpb+7SkLNvpMgAAADANCMHn0Dc8qsaeIS0tZz4wAABAPCIEn8OhyE1xS8sZCQYAAIhHhOBzqG/pkyQtKWMkGAAAIB4Rgs/hYGu/ctOTVZ6b5nQpAAAAmAaE4HOobwnfFGcMO8UBAADEI0LwBKGQVX1rPzfFAQAAxDFC8ASnevzyB8a4KQ4AACCOEYInONgSXhmCm+IAAADiFyF4goMtfTJGqi5lJBgAACBeEYInqG/t07zCTKWnsF0yAABAvCIET8BNcQAAAPGPEHyGgZGgTnb5taSMqRAAAADxjBB8htPbJS9hJBgAACCuTSkEG2P+3hizxxizyxjznDFmVrQKc0J9a3i7ZJZHAwAAiG9THQn+Z2vtSmvtaklPS/ofUy/JOQdb+pSdmqSKvHSnSwEAAMA0mlIIttb2nfEwU5KdWjnOqm/p15JytksGAACId8baqeVWY8w/SLpXkk/SRmttx3mO2yxpsySVlpau27Jly5TOeykGBgaUlZV1wWOstfqzF/y6tiJJH1+WGqPKvG0yfUHs0Rd3oi/uRF/ch564k5N92bhx4w5rbc3E5y8ago0xL0gqO8dLD1hrnzrjuC9KSrPWfuVixdTU1Njt27dfvOooqaurU21t7QWPOdXt14Z/+q2+eucK3X3VnNgU5nGT6Qtij764E31xJ/riPvTEnZzsizHmnCE46WLfaK29cZLn+LGkX0q6aAh2o4Mt4ZkdS7gpDgAAIO5NdXWIRWc8vF1S/dTKcU59a7+MkRazXTIAAEDcu+hI8EX8ozFmsaSQpJOS7p96Sc442NKnuQUZykyd6h8JAAAA3G5Kic9a+8FoFeK0+tZ+LSljkwwAAAAvYMc4Sf5AUCe6BpkPDAAA4BGEYEmH2wZkrbSU7ZIBAAA8gRCst1eGWMp0CAAAAE8gBEuqb+lTZkqiZuezXTIAAIAXEIIlHWzt15LyHCUksF0yAACAF3g+BFtrdbClT0vKuCkOAADAKzwfgpt9w+ofDmoJN8UBAAB4hudDcEOXX5I0rzDT4UoAAAAQK54Pwb3+gCQpPzPZ4UoAAAAQK4TgoVFJUn5GisOVAAAAIFY8H4J7IiPBeRmMBAMAAHiF50Nwr39UKUkJSk9OdLoUAAAAxAgh2B9QfkayjGGNYAAAAK/wfAju8Y8qL535wAAAAF7i+RDs848yHxgAAMBjPB+Ce/wBVoYAAADwGEIwI8EAAACe4+kQbK2VbyigPEaCAQAAPMXTIXgwMKbRMat8RoIBAAA8xdMhuGeQjTIAAAC8yNMh2BfZMpnpEAAAAN7i6RB8estkVocAAADwFo+H4NMjwUyHAAAA8BJPh2CfnznBAAAAXuTpEDw+Esy2yQAAAJ7i8RAcUGZKolKSPP3HAAAA4DmeTn8+/ygrQwAAAHiQp0Nwjz+g/EzmAwMAAHiNx0PwKPOBAQAAPMjTIdg3NMrKEAAAAB7k6RDc4w+wUQYAAIAHeTYEj4UsI8EAAAAe5dkQ3D88KmvF6hAAAAAe5NkQfHqjjHxGggEAADzHwyGYLZMBAAC8yrMh2Hd6y2SmQwAAAHiOZ0Pw6ZFgVocAAADwHg+H4MhIcDrTIQAAALzGsyHY5w/IGCmHEAwAAOA5ng3BPf5R5aYnKzHBOF0KAAAAYsyzIbh3aJSpEAAAAB7l3RDsD7AyBAAAgEd5NgT3+ANslAEAAOBRng3Bvf5RRoIBAAA8yuMhmJFgAAAAL/JkCA4EQxoYCbJRBgAAgEd5MgT7hk5vmcxIMAAAgBd5MgT3RrZMZk4wAACAN3kyBJ/eMpnVIQAAALzJkyF4fCQ4nZFgAAAAL/JoCGZOMAAAgJdFJQQbY75gjLHGmKJovN9064mMBOdnMhIMAADgRVMOwcaYSkk3SWqYejmx0Ts0qqQEo8yURKdLAQAAgAOiMRL8b5L+myQbhfeKiV5/QHkZKTLGOF0KAAAAHDClEGyMuV1Sk7V2d5TqiYmewVFWhgAAAPAwY+2FB3CNMS9IKjvHSw9I+pKk91hrfcaYE5JqrLWd53mfzZI2S1Jpaem6LVu2TKXuSzIwMKCsrKzxx/+4bUghK33pqvSY1YB3mtgXuAN9cSf64k70xX3oiTs52ZeNGzfusNbWTHz+oiH4fIwxKyS9KMkfeWq2pGZJ6621rRf63pqaGrt9+/bLOu/lqKurU21t7fjjW/73y6osyNB3733HnwdiaGJf4A70xZ3oizvRF/ehJ+7kZF+MMecMwUmX+4bW2r2SSs44wQldYCTYTXr8Aa2cnet0GQAAAHCIZ9cJZstkAAAA77rskeCJrLVV0Xqv6TQUGNNIMMRGGQAAAB7muZHg8Y0yGAkGAADwLM+F4PEtk9MZCQYAAPAqD4bg8Egwc4IBAAC8y3MhuCcyEpyfyUgwAACAV3kuBPcORUaC0xkJBgAA8CrvheDTc4JZHQIAAMCzPBeCewYDSk9OVFpyotOlAAAAwCGeC8G9Q6OMAgMAAHic90KwP8DKEAAAAB7nwRA8qnxGggEAADzNcyG4xx9gOgQAAIDHeS4E9/pHmQ4BAADgcZ4KwdZa9Q4xHQIAAMDrPBWC+0eCGgtZNsoAAADwOE+F4N5BNsoAAACA10JwZMvkfOYEAwAAeJqnQnAPWyYDAABAHgvBvf7wSDCrQwAAAHibx0JweCSY1SEAAAC8zVMhuCcyEpybTggGAADwMk+F4F7/qLLTkpSU6KkfGwAAABN4Kg32+gOsDAEAAABvheAe/ygrQwAAAMBbIbjXH2BlCAAAAHgsBA+NsjIEAAAAvBWCewYDymNlCAAAAM/zTAgOjoXUNxxkOgQAAAC8E4L7hoOS2CgDAAAAHgrBPWyZDAAAgAjPhODe8RDMSDAAAIDXeSgEj0piJBgAAAAeCsE9kRDMnGAAAAB4JgRfX12sH/3pVSrLTXO6FAAAADgsyekCYqU4O1XF2alOlwEAAAAX8MxIMAAAAHAaIRgAAACeQwgGAACA5xCCAQAA4DmEYAAAAHgOIRgAAACeQwgGAACA5xCCAQAA4DmEYAAAAHgOIRgAAACeQwgGAACA5xCCAQAA4DmEYAAAAHgOIRgAAACeQwgGAACA5xhrbexPakyHpJMxPGWRpM4Yng+TQ1/cib64E31xJ/riPvTEnZzsy1xrbfHEJx0JwbFmjNlura1xug6cjb64E31xJ/riTvTFfeiJO7mxL0yHAAAAgOcQggEAAOA5XgnB33G6AJwTfXEn+uJO9MWd6Iv70BN3cl1fPDEnGAAAADiTV0aCAQAAgHFxFYKNMbcYYw4ZY44aY/7qHK8bY8z/jby+xxiz1ok6vWYSfak1xviMMbsiH//DiTq9xBjzsDGm3Riz7zyvc604YBJ94VqJMWNMpTHmt8aYg8aY/caYvzjHMVwvMTbJvnC9xJgxJs0Ys80YszvSl789xzGuuV6SnDpxtBljEiU9KOkmSY2S3jDG/Nxae+CMw26VtCjycZWkf498xjSZZF8kaau19raYF+hd35P0DUnfP8/rXCvO+J4u3BeJayXWgpI+b63daYzJlrTDGPM8/7Y4bjJ9kbheYm1E0iZr7YAxJlnSK8aYX1lrXzvjGNdcL/E0Erxe0lFr7XFrbUDSFkl3TDjmDknft2GvScozxpTHulCPmUxfEGPW2pcldV/gEK4VB0yiL4gxa22LtXZn5Ot+SQclVUw4jOslxibZF8RY5BoYiDxMjnxMvPnMNddLPIXgCkmnznjcqHdeEJM5BtE12T/zayL/++RXxpgrYlMaLoBrxb24VhxijKmStEbS6xNe4npx0AX6InG9xJwxJtEYs0tSu6TnrbWuvV7iZjqEJHOO5yb+18dkjkF0TebPfKfCWxoOGGPeK+lJhf83CZzDteJOXCsOMcZkSXpc0mettX0TXz7Ht3C9xMBF+sL14gBr7Zik1caYPElPGGOWW2vPvM/BNddLPI0EN0qqPOPxbEnNl3EMouuif+bW2r7T//vEWvuMpGRjTFHsSsQ5cK24ENeKMyJzGx+X9CNr7c/OcQjXiwMu1heuF2dZa3sl1Um6ZcJLrrle4ikEvyFpkTFmnjEmRdJHJf18wjE/l3Rv5M7EqyX5rLUtsS7UYy7aF2NMmTHGRL5er/Dfy66YV4ozca24ENdK7EX+vB+SdNBa+7XzHMb1EmOT6QvXS+wZY4ojI8AyxqRLulFS/YTDXHO9xM10CGtt0BjzKUnPSkqU9LC1dr8x5v7I69+S9Iyk90o6Kskv6T6n6vWKSfblLkl/ZowJShqS9FHLLi7TyhjziKRaSUXGmEZJX1H4BgauFQdNoi9cK7F3raSPS9obmecoSV+SNEfienHQZPrC9RJ75ZL+M7IyVIKkR621T7s1i7FjHAAAADwnnqZDAAAAAJNCCAYAAIDnEIIBAADgOYRgAAAAeA4hGAAAAJ5DCAYAAIDnEIIBAADgOYRgAAAAeM7/BxAjItFufjs+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0.01, 3, 100)\n",
    "Y = np.log(X)\n",
    "fig, ax = plt.subplots(figsize = (12, 7))\n",
    "ax.plot(X, Y)\n",
    "ax.grid()\n",
    "ax.set_title('$Y = e^X$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66f4222e-720d-49e2-a5cb-7ad2e0761b9e",
   "metadata": {},
   "source": [
    "Because the estimation method is MLE, which means we are not seeking to minimize $RSS$, then it would be meaningless to report $R^2$. So the proper replacement is pseudo-$R^2$ as in report.\n",
    "\n",
    "Pseudo-$R^2$ is comparing the log-likelihood $\\ln{L}$ of the original model with log-likelihood $\\ln{L_0}$ that would have been obtained with only the intercept in the regression.\n",
    "$$\n",
    "\\text{pseudo-}R^2=1-\\frac{\\ln{L}}{\\ln{L_0}}\n",
    "$$\n",
    "Compare with $R^2$ in OLS, conceptually, $\\ln{L}$ is equivalent to $RSS$ and $\\ln{L_0}$ is equivalent to $TSS$ of the linear regression model.\n",
    "$$\n",
    "R^2 =1-\\frac{RSS}{TSS}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1f1b23b-9c3f-437a-b53d-da0b7d97fea6",
   "metadata": {},
   "source": [
    "The results object has those data encapsulated, we just call the properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "2f016611-443c-42a7-9fe3-81b8bcf4c269",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pseudo-R2: 0.6432266516492773\n"
     ]
    }
   ],
   "source": [
    "Pseudo_R2 = 1- log_reg_house.llf/log_reg_house.llnull\n",
    "print('Pseudo-R2: {}'.format(Pseudo_R2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01916e25-baf5-4f55-a11d-15601bba1109",
   "metadata": {},
   "source": [
    "The equivalent $F$-test in linear regression model is **likelihood ratio** (LR)\n",
    "$$\n",
    "2\\ln{(L/L_0)} = 2(\\ln{L}-\\ln{L_0})\n",
    "$$\n",
    "which follows $\\chi^2$ with $k-1$ degree of freedom, $k-1$ is the number of independent variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "4df10d4b-61fd-45f4-bf7a-c4ec227099e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Likelihood Ratio: 26.75104440310262\n"
     ]
    }
   ],
   "source": [
    "LR = 2*(log_reg_house.llf-log_reg_house.llnull)\n",
    "print('Likelihood Ratio: {}'.format(LR))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba9beee0-3e0e-4710-8531-c31dfdf6891c",
   "metadata": {},
   "source": [
    "Keep in mind, with qualitative response models, goodness of fit is not a main concern. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8117ddc1-286f-4955-82e0-87662dcb2531",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Probit Model</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5faae836-eaf9-4b19-ae1f-23982f7dd975",
   "metadata": {},
   "source": [
    "The **probit model** provides an alternative but similar approach to qualitative response model. We also start by defining variable $Z_i$\n",
    "$$\n",
    "Z_i = \\beta_1 + \\beta_2X_2+...+\\beta_k X_k\n",
    "$$\n",
    "But the sigmoid function is a accumulative standard normal distribution\n",
    "$$\n",
    "P_i = F(Z_i)\n",
    "$$\n",
    "The marginal effect of $X_i$ is \n",
    "$$\n",
    "\\frac{\\partial P_i}{\\partial X_i}=\\frac{dP_i}{dZ_i}\\frac{\\partial Z}{\\partial X_i}=f(Z)\\beta_i\n",
    "$$\n",
    "where $f(Z) = F'(Z)$, is the PDF function of standard normal distribution\n",
    "$$\n",
    "f(Z) = \\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{1}{2}Z^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "c2607a1f-a36f-4523-b260-03013db47459",
   "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",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pregnancies</th>\n",
       "      <th>Glucose</th>\n",
       "      <th>BloodPressure</th>\n",
       "      <th>SkinThickness</th>\n",
       "      <th>Insulin</th>\n",
       "      <th>BMI</th>\n",
       "      <th>DiabetesPedigreeFunction</th>\n",
       "      <th>Age</th>\n",
       "      <th>Outcome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>148</td>\n",
       "      <td>72</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>33.6</td>\n",
       "      <td>0.627</td>\n",
       "      <td>50</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>85</td>\n",
       "      <td>66</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>26.6</td>\n",
       "      <td>0.351</td>\n",
       "      <td>31</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>183</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23.3</td>\n",
       "      <td>0.672</td>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>89</td>\n",
       "      <td>66</td>\n",
       "      <td>23</td>\n",
       "      <td>94</td>\n",
       "      <td>28.1</td>\n",
       "      <td>0.167</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>137</td>\n",
       "      <td>40</td>\n",
       "      <td>35</td>\n",
       "      <td>168</td>\n",
       "      <td>43.1</td>\n",
       "      <td>2.288</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "0            6      148             72             35        0  33.6   \n",
       "1            1       85             66             29        0  26.6   \n",
       "2            8      183             64              0        0  23.3   \n",
       "3            1       89             66             23       94  28.1   \n",
       "4            0      137             40             35      168  43.1   \n",
       "\n",
       "   DiabetesPedigreeFunction  Age  Outcome  \n",
       "0                     0.627   50        1  \n",
       "1                     0.351   31        0  \n",
       "2                     0.672   32        1  \n",
       "3                     0.167   21        0  \n",
       "4                     2.288   33        1  "
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel('Basic_Econometrics_practice_data.xlsx', sheet_name = 'Diabetes_Quali_Resp'); df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dd3102c-e68b-403d-9a03-f4ec2787495c",
   "metadata": {},
   "source": [
    "Here is the data explanation\n",
    "<ul>\n",
    "<li><em>Pregnancies</em>: Number of times pregnant</li>\n",
    "<li><em>Glucose</em>: Plasma glucose concentration over 2 hours in an oral glucose tolerance test</li>\n",
    "<li><em>BloodPressure</em>: Diastolic blood pressure (mm Hg)</li>\n",
    "<li><em>SkinThickness</em>: Triceps skin fold thickness (mm)</li>\n",
    "<li><em>Insulin</em>: 2-Hour serum insulin (mu U/ml)</li>\n",
    "<li><em>BMI</em>: Body mass index (weight in kg/(height in m)2)</li>\n",
    "<li><em>DiabetesPedigreeFunction</em>: Diabetes pedigree function (a function which scores likelihood of diabetes based on family history)</li>\n",
    "<li><em>Age</em>: Age (years)</li>\n",
    "<li><em>Outcome</em>: Class variable (0 if non-diabetic, 1 if diabetic)</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "6f4cc417-bca8-4b3c-a2ce-d45ce0826115",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.472380\n",
      "         Iterations 6\n",
      "                          Probit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   No. Observations:                  768\n",
      "Model:                         Probit   Df Residuals:                      759\n",
      "Method:                           MLE   Df Model:                            8\n",
      "Date:                Fri, 10 Sep 2021   Pseudo R-squ.:                  0.2697\n",
      "Time:                        07:31:05   Log-Likelihood:                -362.79\n",
      "converged:                       True   LL-Null:                       -496.74\n",
      "Covariance Type:            nonrobust   LLR p-value:                 2.736e-53\n",
      "============================================================================================\n",
      "                               coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------------\n",
      "const                       -4.8638      0.384    -12.653      0.000      -5.617      -4.110\n",
      "Pregnancies                  0.0723      0.018      3.972      0.000       0.037       0.108\n",
      "Glucose                      0.0199      0.002      9.968      0.000       0.016       0.024\n",
      "BloodPressure               -0.0079      0.003     -2.585      0.010      -0.014      -0.002\n",
      "SkinThickness                0.0012      0.004      0.307      0.758      -0.007       0.009\n",
      "Insulin                     -0.0007      0.001     -1.423      0.155      -0.002       0.000\n",
      "BMI                          0.0523      0.008      6.250      0.000       0.036       0.069\n",
      "DiabetesPedigreeFunction     0.4982      0.164      3.036      0.002       0.177       0.820\n",
      "Age                          0.0102      0.005      1.887      0.059      -0.000       0.021\n",
      "============================================================================================\n"
     ]
    }
   ],
   "source": [
    "Y = df[['Outcome']]\n",
    "X = df[['Pregnancies', 'Glucose', 'BloodPressure', 'SkinThickness', 'Insulin', 'BMI', 'DiabetesPedigreeFunction', 'Age']]\n",
    "X = sm.add_constant(X)\n",
    "log_reg_diabetes = sm.Probit(Y, X).fit()\n",
    "print(log_reg_diabetes.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cbe5ec5-c052-4e35-b1f4-85be211ad847",
   "metadata": {},
   "source": [
    "Because marginal effect of any independent variables will not be constant, we summarize the effect as the same procedure in logit model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "038e89f7-6014-4924-b390-3ad6ded3dc23",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pregnancies:        0.02524786219145608\n",
      "Glucose:            0.006945036190111587\n",
      "BloodPressure:      -0.0027682789498052994\n",
      "SkinThickness:      0.0004320865302513722\n",
      "Insulin:            -0.00025900523552337313\n",
      "BMI:                0.01827361273755261\n",
      "DiabetesPedigreeFunction: 0.17402664547779725\n",
      "Age:                0.0035618676260187995\n"
     ]
    }
   ],
   "source": [
    "beta1_hat, beta2_hat, beta3_hat, beta4_hat = log_reg_diabetes.params[0], log_reg_diabetes.params[1], log_reg_diabetes.params[2], log_reg_diabetes.params[3]\n",
    "beta5_hat, beta6_hat, beta7_hat, beta8_hat = log_reg_diabetes.params[4], log_reg_diabetes.params[5], log_reg_diabetes.params[6], log_reg_diabetes.params[7]\n",
    "beta9_hat = log_reg_diabetes.params[8]\n",
    "\n",
    "X2_mean = np.mean(df['Pregnancies'])\n",
    "X3_mean = np.mean(df['Glucose'])\n",
    "X4_mean = np.mean(df['BloodPressure'])\n",
    "X5_mean = np.mean(df['SkinThickness'])\n",
    "X6_mean = np.mean(df['Insulin'])\n",
    "X7_mean = np.mean(df['BMI'])\n",
    "X8_mean = np.mean(df['DiabetesPedigreeFunction'])\n",
    "X9_mean = np.mean(df['Age'])\n",
    "\n",
    "Z_mean_effect = beta1_hat + beta2_hat*X2_mean + + beta3_hat*X3_mean + beta4_hat*X4_mean + beta5_hat*X5_mean +  beta6_hat*X6_mean + beta7_hat*X7_mean + beta8_hat*X8_mean + beta9_hat*X9_mean\n",
    "                      \n",
    "def f_norm(Z):\n",
    "    return 1/np.sqrt(2*np.pi)*np.exp(-1/2*Z**2)\n",
    "\n",
    "dPdX2 = f_norm(Z_mean_effect)*beta2_hat\n",
    "dPdX3 = f_norm(Z_mean_effect)*beta3_hat\n",
    "dPdX4 = f_norm(Z_mean_effect)*beta4_hat\n",
    "dPdX5 = f_norm(Z_mean_effect)*beta5_hat\n",
    "dPdX6 = f_norm(Z_mean_effect)*beta6_hat\n",
    "dPdX7 = f_norm(Z_mean_effect)*beta7_hat\n",
    "dPdX8 = f_norm(Z_mean_effect)*beta8_hat\n",
    "dPdX9 = f_norm(Z_mean_effect)*beta9_hat\n",
    "\n",
    "print('Pregnancies:        {}'.format(dPdX2))\n",
    "print('Glucose:            {}'.format(dPdX3))\n",
    "print('BloodPressure:      {}'.format(dPdX4))\n",
    "print('SkinThickness:      {}'.format(dPdX5))\n",
    "print('Insulin:            {}'.format(dPdX6))\n",
    "print('BMI:                {}'.format(dPdX7))\n",
    "print('DiabetesPedigreeFunction: {}'.format(dPdX8))\n",
    "print('Age:                {}'.format(dPdX9))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ff75094-dd75-41ea-8d0c-f54582339ad1",
   "metadata": {},
   "source": [
    "However, if you are familiar with the data structure in Pandas, just two lines of codes, the marginal effects are printed below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "7169172e-43c5-4d6b-9a3b-e564f781bdef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pregnancies                 0.025248\n",
       "Glucose                     0.006945\n",
       "BloodPressure              -0.002768\n",
       "SkinThickness               0.000432\n",
       "Insulin                    -0.000259\n",
       "BMI                         0.018274\n",
       "DiabetesPedigreeFunction    0.174027\n",
       "Age                         0.003562\n",
       "dtype: float64"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_mean_effect = log_reg_diabetes.params[0] + np.sum(log_reg_diabetes.params[1:] * df.mean()[:8])\n",
    "f_norm(Z_mean_effect)*log_reg_diabetes.params[1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdc77c27-0050-4b9a-8683-3288f6b0d12b",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Logit Or Probit?</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37d6ef77-5e00-459e-b707-74913775edb7",
   "metadata": {},
   "source": [
    "Let's use the same data to compare the estimation results between logit and probit model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "id": "e6b190dc-5d27-403d-8961-ee314120a5ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.470993\n",
      "         Iterations 6\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.472380\n",
      "         Iterations 6\n",
      "\n",
      "\n",
      "Logit estimation results:\n",
      "const                      -8.404696\n",
      "Pregnancies                 0.123182\n",
      "Glucose                     0.035164\n",
      "BloodPressure              -0.013296\n",
      "SkinThickness               0.000619\n",
      "Insulin                    -0.001192\n",
      "BMI                         0.089701\n",
      "DiabetesPedigreeFunction    0.945180\n",
      "Age                         0.014869\n",
      "dtype: float64\n",
      "\n",
      "\n",
      "Probit estimation results:\n",
      "const                      -4.863753\n",
      "Pregnancies                 0.072285\n",
      "Glucose                     0.019884\n",
      "BloodPressure              -0.007926\n",
      "SkinThickness               0.001237\n",
      "Insulin                    -0.000742\n",
      "BMI                         0.052317\n",
      "DiabetesPedigreeFunction    0.498238\n",
      "Age                         0.010198\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_excel('Basic_Econometrics_practice_data.xlsx', sheet_name = 'Diabetes_Quali_Resp')\n",
    "Y = df[['Outcome']]\n",
    "X = df[['Pregnancies', 'Glucose', 'BloodPressure', 'SkinThickness', 'Insulin', 'BMI', 'DiabetesPedigreeFunction', 'Age']]\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "logit_reg = sm.Logit(Y, X).fit()\n",
    "probit_reg = sm.Probit(Y, X).fit()\n",
    "\n",
    "print('')\n",
    "print('')\n",
    "print('Logit estimation results:')\n",
    "print(logit_reg.params)\n",
    "print('')\n",
    "print('')\n",
    "print('Probit estimation results:')\n",
    "print(probit_reg.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36dc2ecb-ede9-441d-9ca2-d1340f113878",
   "metadata": {},
   "source": [
    "We have seen both logit and profit, they seem yield similar results, which one is preferable? In practice, more researchers choose Logit due its mathematical simplicity. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60f54934-12e8-4298-941c-61304e5a1c68",
   "metadata": {},
   "source": [
    "Visually, we can also see the difference, that logit is flatter than probit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "id": "b39d3a16-59fa-4793-b993-78e157a36ee2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = np.linspace(-5, 5)\n",
    "Y_probit = sp.stats.norm.cdf(Z, loc = 0, scale = 1)\n",
    "Y_logit = 1/(1+np.exp(-Z))\n",
    "fig, ax = plt.subplots(figsize = (12, 7))\n",
    "ax.plot(Z, Y_probit, lw =3, label = 'Probit')\n",
    "ax.plot(Z, Y_logit, lw = 3, label = 'Logit')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "477de4d9-90a2-4b0c-b280-abd2b877e202",
   "metadata": {},
   "source": [
    "T. Amemiya suggests multiplying a logit estimate by $0.625$ to get a better estimate of the corresponding probit estimate. You can try with the results above."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84e0f9d3-be5a-446e-a662-fcc5b0273fc3",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Tobit Model</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2eec636d-c62c-4733-83d7-c02d4f12556f",
   "metadata": {},
   "source": [
    "The **tobit model** was introduced by James Tobin, that the dependent variable are censored. It would be more straightforward to take a look at a simulated censored data set. Assume the true relationship is\n",
    "$$\n",
    "Y_i = -40 + 5X_i +u_i\n",
    "$$\n",
    "\n",
    "The blue circles are uncensored, or unconstrained data, the red dots are constrained to be non-negative. Apparently, OLS estimation with constrained data will yield erratic results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "id": "c6d1d40f-58d1-468c-91ba-879f821fd5e8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta1, beta2 = -40, 5\n",
    "n = 300\n",
    "X = np.linspace(0, 30, n)\n",
    "u = 10* np.random.randn(n)\n",
    "Y = beta1 + beta2*X + u\n",
    "Y_censored = Y.clip(min = 0)\n",
    "fig, ax = plt.subplots(figsize = (18, 9))\n",
    "ax.scatter(X, Y, s = 50,edgecolors='b', facecolors='none')\n",
    "ax.scatter(X, Y_censored, s = 10, color='r')\n",
    "\n",
    "ax.axhline(y = 0, color = 'k', alpha = .7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72b66110-6ccf-4166-b03f-b01fd88c0900",
   "metadata": {},
   "source": [
    "What about only use the on constrained subsample? i.e. $Y_i>0$ then \n",
    "$$\n",
    "-40 + 5X_i + u_i >0\n",
    "$$\n",
    "It shows a relationship of $u_i$ and $X_i$\n",
    "$$\n",
    "u_i>40-5X_i\n",
    "$$\n",
    "We have assumed that $u_i \\sim N(0, 10)$ in the simulation, this inequality truncated the distribution. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "008138f2-09f2-478b-b4bb-aa463dd57187",
   "metadata": {},
   "source": [
    "However the ```statsmodel``` doesn't have tobit estimation procedure yet. We'll update the tutorial notes if any concise procedure are introduced in ```statsmodel```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6246b78-cb81-4017-90f5-b80a4fb10513",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}