Logistic_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# To Do"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* improve executive summary\n",
    "\n",
    "\n",
    "* add additional tests (e.g., overdispersion)\n",
    "\n",
    "\n",
    "* add feature with continuous variable\n",
    "\n",
    "\n",
    "* add additional features to improve predictability\n",
    "\n",
    "\n",
    "* cost function, maximizing likelihood, and general logistic regression discussion\n",
    "\n",
    "\n",
    "* improve confusion matrix graphics \n",
    "\n",
    "\n",
    "* add auc metric"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Executive Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[nbviewer](http://nbviewer.jupyter.org/github/nuclth/Python_Statistics/blob/master/Logistic_Regression.ipynb)\n",
    "\n",
    "This is a notebook that implements logistic regression on a dataset. The problem is to predict whether a student will smoke based off whether their parents do or do not smoke. This is a simplest working example of logistic regression where the response variable is binary and the independent variable is either binary (in the first pass) or has three levels. \n",
    "\n",
    "This notebook is based off the notes and problem example in chapter 6.2 of the PSU [Stat 504](https://onlinecourses.science.psu.edu/stat504/node/150) course."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Concepts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* logistic regression\n",
    "* confusion matrix\n",
    "* ROC curve\n",
    "* dummy variables\n",
    "* z statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dataset Creation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "First let's import the relevant modules:\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import third party libraries\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# import sklearn functions\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.metrics import roc_curve\n",
    "\n",
    "# import custom functions\n",
    "from src.logreg_functions import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "Now we can create our dataset. The idea is we want to predict whether a student smokes or not given the information about whether either of their parents smoke. This can be visualized in a 2x2 table as given below. The latin letters `a, b, c, d` correspond to the number of students in a given category. \n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Student Smokes | Student Does Not Smoke\n",
    "---------|--------\n",
    "A Parent Smokes | a | b\n",
    "No Parent Smokes | c | d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we continue, let's take a guess:\n",
    "<br><br>\n",
    "<center>**Hypothesis**: Students with parents who smoke, are more likely to be smokers themselves.</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "We'll see if this hypothesis is justified or not further in. First to create our data, we call a python function, `create_smoking_data (a, b, c, d)` to fill a dataframe with student statistics. Each response will be a Y/N string.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "df = create_smoking_data(816, 3203, 188, 1168)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "For the table above, these numbers would correspond to the following populations (again these numbers are taken from the PSU [Stats 504](https://onlinecourses.science.psu.edu/stat504/node/150) course),"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Student Smokes | Student Does Not Smoke\n",
    "---------|--------\n",
    "A Parent Smokes | 816 | 3203\n",
    "No Parent Smokes | 188 | 1168"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Let's do a quick check through the dataframe to make sure everything looks ok.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>parent_smoking</th>\n",
       "      <th>student_smoking</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Y</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Y</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>N</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Y</td>\n",
       "      <td>Y</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>N</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  parent_smoking student_smoking\n",
       "0              Y               N\n",
       "1              Y               N\n",
       "2              N               N\n",
       "3              Y               Y\n",
       "4              N               N"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>parent_smoking</th>\n",
       "      <th>student_smoking</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5370</th>\n",
       "      <td>Y</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5371</th>\n",
       "      <td>N</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5372</th>\n",
       "      <td>Y</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5373</th>\n",
       "      <td>Y</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5374</th>\n",
       "      <td>Y</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     parent_smoking student_smoking\n",
       "5370              Y               N\n",
       "5371              N               N\n",
       "5372              Y               N\n",
       "5373              Y               N\n",
       "5374              Y               N"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Looks good. How about on a more macroscopic scale?\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 5375 entries, 0 to 5374\n",
      "Data columns (total 2 columns):\n",
      "parent_smoking     5375 non-null object\n",
      "student_smoking    5375 non-null object\n",
      "dtypes: object(2)\n",
      "memory usage: 84.1+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "So we see that we have 5375 total entries with no missing data (as expected given that's how we constructed it). \n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>parent_smoking</th>\n",
       "      <th>student_smoking</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5375</td>\n",
       "      <td>5375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>Y</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>4019</td>\n",
       "      <td>4371</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       parent_smoking student_smoking\n",
       "count            5375            5375\n",
       "unique              2               2\n",
       "top                 Y               N\n",
       "freq             4019            4371"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Our dataframe holds two unique values (Y/N) as expected for a binary variable and response. We can also see from the `top` and `freq` outputs that our dataset is weighted heavily towards parents who smoke and students who don't.\n",
    "\n",
    "Let's reinforce these points with some graphics, first with absolute counts and then with the relative percentage of each population:\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kIrjmmmsASCkxceLEAlckSZIk1Tz7XkmS6o4Bs9TEnHjiifTu3RuA1atXF7ga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\nEZGIlBJVQpAY50MQh6JIKRfiUEwJMQ7ttNNqSV1UVRTpAT3otEaqHed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jmIFtqaoOTXK/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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff1dc37ecf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(20,10))\n",
    "\n",
    "plot_cat (df, ax=ax[0], rel=False)\n",
    "plot_cat (df, ax=ax[1], rel=True)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Again as seen from the absolute counts, our dataset overrepresents students who don't smoke and parents who do. On the relative side, the percentages of the two groups in a given bin should be approximately equal if there is no relationship between the variable and response. However, looking at the distribution above, there is a slight imbalance where students who smoke are more likely to have parents who smoke relative to students who don't. \n",
    "\n",
    "This demonstrates, assuming there was no bias in how the data was drawn and that our statistical sample is large enough, that there exists some correlation between parents smoking and students smoking.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression is a method used for binary classification (student smoking = Y/N). Here we perform it over one categorical variable $x$ which can take values of 0 or 1. The idea behind logistic regression is that we want to retain the advantage of linearity in a model but allow for our target variable to be constrained to be between 0 and 1 (rather than $-\\infty$ to $\\infty$ as in linear regression). This is accomplished in logistic regression using the logistic function. Thus the probability for student $i$ to smoke is $\\pi_i$ and is given by,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\pi_i = \\frac{\\exp(\\beta_0 + \\beta_1 x_i)}{1 + \\exp(\\beta_0 + \\beta_1 x_i)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\text{logit} \\left( \\pi_i \\right) \\equiv \\text{log} \\left( \\frac{\\pi_i}{1 - \\pi_i} \\right) = \\beta_0 + \\beta_1 x_i$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Now we can create our training and validation datasets. First let's map the our Y/N to numerical values 1/0 and split our data into a **training set** and a **validation set** with **80%** in the former and **20%** in the latter:\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Y/N to 1/0 map\n",
    "df['student_smoking'] = df['student_smoking'].map(lambda x: 1 if x == 'Y' else 0)\n",
    "df['parent_smoking'] = df['parent_smoking'].map(lambda x: 1 if x == 'Y' else 0)\n",
    "\n",
    "# number of training samples\n",
    "num = 4300\n",
    "\n",
    "# split into training/validation sets\n",
    "train = df.copy()\n",
    "valid = df.iloc[num:]\n",
    "train = df.drop(train.index[num:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Now pull off the true response for each student into two new series for the training/validation datasets, then drop the same variables for the fit and validation.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.486196\n",
      "         Iterations 6\n"
     ]
    }
   ],
   "source": [
    "# create series for training/validation response\n",
    "train_res = train['student_smoking'].copy()\n",
    "valid_res = valid['student_smoking'].copy()\n",
    "\n",
    "# drop response from training/validation set\n",
    "train = train.drop(['student_smoking'], axis=1)\n",
    "valid = valid.drop(['student_smoking'], axis=1)\n",
    "\n",
    "# add a constant term for the intercept\n",
    "train = sm.tools.tools.add_constant(train, prepend=False, has_constant='skip')\n",
    "valid = sm.tools.tools.add_constant(valid, prepend=False, has_constant='skip')\n",
    "\n",
    "# fit the model\n",
    "logit = sm.Logit(train_res, train)\n",
    "result = logit.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Let's see how we did.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>  <td>student_smoking</td> <th>  No. Observations:  </th>  <td>  4300</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>  4298</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Fri, 17 Nov 2017</td> <th>  Pseudo R-squ.:     </th> <td>0.004868</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>14:52:49</td>     <th>  Log-Likelihood:    </th> <td> -2090.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -2100.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>6.107e-06</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>parent_smoking</th> <td>    0.4214</td> <td>    0.096</td> <td>    4.399</td> <td> 0.000</td> <td>    0.234</td> <td>    0.609</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>          <td>   -1.7634</td> <td>    0.085</td> <td>  -20.673</td> <td> 0.000</td> <td>   -1.931</td> <td>   -1.596</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:        student_smoking   No. Observations:                 4300\n",
       "Model:                          Logit   Df Residuals:                     4298\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Fri, 17 Nov 2017   Pseudo R-squ.:                0.004868\n",
       "Time:                        14:52:49   Log-Likelihood:                -2090.6\n",
       "converged:                       True   LL-Null:                       -2100.9\n",
       "                                        LLR p-value:                 6.107e-06\n",
       "==================================================================================\n",
       "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------\n",
       "parent_smoking     0.4214      0.096      4.399      0.000       0.234       0.609\n",
       "const             -1.7634      0.085    -20.673      0.000      -1.931      -1.596\n",
       "==================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "There's a lot to unpack here so let's focus on just a few crucial points:\n",
    "\n",
    "* Our constant coefficient is approximately $\\beta_0 \\approx -1.8$. This means that the probability for a student to smoke without smoking parents is $\\pi \\approx 14\\%$. \n",
    "\n",
    "\n",
    "* The parental smoking coefficient is approximately $\\beta_1 \\approx 0.45$. The means that with a smoking parent, a student's probability to smoke is $\\pi \\approx 20\\%$, a risk increase of around 1.5 times. Note that since the coefficient is positive, the correlation is positive.\n",
    "\n",
    "\n",
    "* Our z value for $\\beta_0$ is large while the the value for $\\beta_1$ is somewhat smaller but still large. Given the sizes, we can say that the coefficients are statistically meaningful. For more information on z values, see the appendix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the course page for the [Stat 504](https://onlinecourses.science.psu.edu/stat504/node/150) course, we see that our values for the training set are quite close to the expected values: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\beta_0 = -1.827 \\ , \\qquad \\beta_1 = 0.459$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "So we seem to have a decent fit indicating some meaningful relationship between our variable and response. But how predictive is our model? Putting in our validation set, we see that we get our two possible probability outputs as outlined above,\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.14636364,  0.2071875 ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = result.predict(valid)\n",
    "predictions.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "But what threshold do we set? That is, what probability cutoff do we use to decide which student goes in which bin? Note that here we only have one possible threshold (a value between 0.14 and 0.2) as any threshold would put alll students into one bin or the other. A way to assess a given threshold choice is to look at a confusion matrix. A confusion matrix is a table showing predicted responses on one table axis and true reponses on the other. If the model we are using is perfect, the confusion matrix should be diagonal.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[229, 666],\n",
       "       [ 27, 153]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# map prediction to 1/0 for a threshold = 0.17\n",
    "pred_map = predictions.map(lambda x: 1 if x > 0.17 else 0)\n",
    "\n",
    "confusion_matrix (valid_res, pred_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Documentation for the confusion matrix output is given [here](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.confusion_matrix.html). In short: \n",
    "\n",
    "* $C_{0,0}$ are true negatives\n",
    "* $C_{1,0}$ are false negatives\n",
    "* $C_{0,1}$ are false positives\n",
    "* $C_{1,1}$ are true positives\n",
    "\n",
    "With information from this table, we can also construct two important metrics to assess a binary classification model: the true positive rate (TPR) and false positive rate (FPR). Their formulas are given by:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\text{TPR} = \\frac{\\text{TP}}{\\text{TP + FN}} \\enspace ,  \\qquad \\text{FPR} \\equiv \\frac{\\text{FP}}{\\text{FP + TN}} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where\n",
    "\n",
    "* TP is the number of true positives\n",
    "* FN is the number of false negatives\n",
    "* FP is the number of false positives\n",
    "* TN is the number of true negatives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The denominators in each correspond to the number of actual positives and actual negatives for the TPR and FPR respectively. For the table above, the TPR and FPR are given by:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\text{TPR} = \\frac{153}{180} = 0.85 \\enspace , \\qquad \\text{FPR} = \\frac{666}{895} = 0.74 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to access this same information is using a receiver operating characteristic (ROC) curve. This will come in handy as it will allows us to explore the same information for all thresholds simulatenously. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fpr</th>\n",
       "      <th>thres</th>\n",
       "      <th>tpr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.207187</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.744134</td>\n",
       "      <td>0.207187</td>\n",
       "      <td>0.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.146364</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        fpr     thres   tpr\n",
       "0  0.000000  1.207187  0.00\n",
       "1  0.744134  0.207187  0.85\n",
       "2  1.000000  0.146364  1.00"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpr, tpr, thres = roc_curve (valid_res, predictions)\n",
    "\n",
    "rocdf = pd.DataFrame(dict(fpr=fpr, tpr=tpr, thres=thres))\n",
    "rocdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "And we can see for our threshold choice (really threshold choice in the same range) we exactly reproduce the expected TPR and FPR values. \n",
    "\n",
    "Now let's plot the ROC curve,\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IhauxfLpsF7Nu0TFs2NPVqVXO9R3D0mvz5s00aNCAqKgoAJo2bcrcuXNp0qSJ13LKjrSA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\nJAV4kiRJkkwgKcCTJEmSZAL5H7jc9i1I1C78AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff1dc2382b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_roc (rocdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "and we see that our model isn't particularly great. The dashed line above is a baseline that corresponds to just randomly guessing whether a student smokes or not and the blue line connects points of different TPR/FPR values for different threshold choices. As discussed previously, there is only one threshold value where we can actually make a prediction other than grouping everyone into one bin. With this choice, we get back a false positive rate of 73% and a true positive rate of 82%. This is better than random guessing though not by much. Clearly our model needs improving.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding a New Variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Our previous model is likely too simplistic. Let's try adding a new variable by splitting up the parent smoking variable into two groups, one where both parents of the student smoke and another where only one smokes:\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Student Smokes | Student Does Not Smoke\n",
    "---------|--------\n",
    "Both Parents Smoke | a | b\n",
    "One Parent Smokes | c | d\n",
    "No Parent Smokes | e | f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "This requires a new logistic regression function where our probability $\\pi_i$ for student $i$ now has two possible binary inputs $x_{1,i}$ and $x_{2,i}$,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\pi_i = \\frac{\\exp(\\beta_0 + \\beta_1 x_{1,i} + \\beta_2 x_{2,i})}{1 + \\exp(\\beta_0 + \\beta_1 x_{1,i} + \\beta_2 x_{2,i})}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\text{logit} \\left( \\pi_i \\right) \\equiv \\text{log} \\left( \\frac{\\pi_i}{1 - \\pi_i} \\right) = \\beta_0 + \\beta_1 x_{1,i} + \\beta_2 x_{2,i}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Above, $x_1$ is 1 when *only one* parent smokes and zero otherwise. $x_2$ is 1 when *both* parents smoke and zero otherwise. Therefore with only two variables, we cover all three possibilities. \n",
    "\n",
    "We again call a previously defined python function, `create_smoking_data_mod (a, b, c, d, e, f)` to fill a dataframe with the values as specified in the [Stat 504](https://onlinecourses.science.psu.edu/stat504/node/150) course. \n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = create_smoking_data_mod (400, 1380, 416, 1823, 188, 1168)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "This would fill the preceding table in the following way,\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Student Smokes | Student Does Not Smoke\n",
    "---------|--------\n",
    "Both Parents Smoke | 400 | 1380\n",
    "One Parent Smokes | 416 | 1823\n",
    "No Parent Smokes | 188 | 1168"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "And like before, let's make a quick plot to see what this data looks like in absolute and relative terms:\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AJ554otr6N1erVq22+J2Abdu2Lb0br3xwsaXsueeeFBcXM2/evArH5s2bx8aNG0v/7uV9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\nBmZJkiRJkiRJUi82MEuSJEmSJEmSevn/9/6S3uhKER0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff1dc108a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(20,10))\n",
    "\n",
    "plot_cat_mod (df, ax=ax[0], rel=False)\n",
    "plot_cat_mod (df, ax=ax[1], rel=True)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Note that since our categorical variable now has three possible values, we need to create some dummy variables to represent the different possibilities: \n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# map response Y/N to 1/0\n",
    "df['student_smoking'] = df['student_smoking'].map(lambda x: 1 if x == 'Y' else 0)\n",
    "\n",
    "# create/add dummy variables and drop superfluous terms\n",
    "dum_var = pd.get_dummies(df['parent_smoking'], prefix='#_smoke_par')\n",
    "df = pd.concat([df, dum_var], axis=1)\n",
    "df = df.drop(['parent_smoking', '#_smoke_par_0'], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "As before we map student Y/N responses to 1/0. We also drop the original parent smoking variable as it is replaced by our dummy variables. We also drop one of the dummy variable columns as it is superfluous, i.e., [0,0], [0,1], and [1,0] exhaust our 3 possibilities for the remaining two dummy variables. After these operations, our data now looks like this:\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>student_smoking</th>\n",
       "      <th>#_smoke_par_1</th>\n",
       "      <th>#_smoke_par_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   student_smoking  #_smoke_par_1  #_smoke_par_2\n",
       "0                0              0              1\n",
       "1                0              1              0\n",
       "2                0              0              0\n",
       "3                0              1              0\n",
       "4                0              0              0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Finally, let's do exactly what we did before in splitting off our data into a training/validation dataset in an 80/20 ratio.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.485034\n",
      "         Iterations 6\n"
     ]
    }
   ],
   "source": [
    "# number of training samples\n",
    "num = 4300\n",
    "\n",
    "# split into training/validation sets\n",
    "train = df.copy()\n",
    "valid = df.iloc[num:]\n",
    "train = df.drop(train.index[num:])\n",
    "\n",
    "# create response series\n",
    "train_res = train['student_smoking'].copy()\n",
    "valid_res = valid['student_smoking'].copy()\n",
    "\n",
    "# drop response from training/validation set\n",
    "train = train.drop(['student_smoking'], axis=1)\n",
    "valid = valid.drop(['student_smoking'], axis=1)\n",
    "\n",
    "# add an intercept term\n",
    "train = sm.tools.tools.add_constant(train, prepend=False, has_constant='skip')\n",
    "valid = sm.tools.tools.add_constant(valid, prepend=False, has_constant='skip')\n",
    "\n",
    "# fit the model\n",
    "logit = sm.Logit(train_res, train)\n",
    "result = logit.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>  <td>student_smoking</td> <th>  No. Observations:  </th>  <td>  4300</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>  4297</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>Fri, 17 Nov 2017</td> <th>  Pseudo R-squ.:     </th> <td>0.005883</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>14:52:55</td>     <th>  Log-Likelihood:    </th> <td> -2085.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -2098.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>4.358e-06</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>#_smoke_par_1</th> <td>    0.3212</td> <td>    0.105</td> <td>    3.062</td> <td> 0.002</td> <td>    0.116</td> <td>    0.527</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>#_smoke_par_2</th> <td>    0.5230</td> <td>    0.107</td> <td>    4.886</td> <td> 0.000</td> <td>    0.313</td> <td>    0.733</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>         <td>   -1.7618</td> <td>    0.086</td> <td>  -20.458</td> <td> 0.000</td> <td>   -1.931</td> <td>   -1.593</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:        student_smoking   No. Observations:                 4300\n",
       "Model:                          Logit   Df Residuals:                     4297\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Fri, 17 Nov 2017   Pseudo R-squ.:                0.005883\n",
       "Time:                        14:52:55   Log-Likelihood:                -2085.6\n",
       "converged:                       True   LL-Null:                       -2098.0\n",
       "                                        LLR p-value:                 4.358e-06\n",
       "=================================================================================\n",
       "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "#_smoke_par_1     0.3212      0.105      3.062      0.002       0.116       0.527\n",
       "#_smoke_par_2     0.5230      0.107      4.886      0.000       0.313       0.733\n",
       "const            -1.7618      0.086    -20.458      0.000      -1.931      -1.593\n",
       "=================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "As before we touch on a few points\n",
    "\n",
    "* Our coefficients found are: $\\beta_0 \\approx -1.8$, $\\enspace \\beta_1 \\approx 0.37$, $\\enspace \\beta_2 \\approx 0.55$.\n",
    "\n",
    "\n",
    "* The baseline probability for a student to smoke without smoking parents is still $\\pi \\approx 14\\%$. \n",
    "\n",
    "\n",
    "* There is a positive correlation with having one parent smoke and a student smoking. One parent smoking raises the probability to $\\pi \\approx 19\\%$.\n",
    "\n",
    "\n",
    "* There is a positive correlation with having both parents smoke and a student smoking. Both parents smoking raises the probability to $\\pi \\approx 22\\%$.\n",
    "\n",
    "\n",
    "* Our z values are again large enough to say that our variables are statistically significant.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expected values from the Stat 504 course are:\n",
    "\n",
    "$$\\beta_0 = -1.826 \\enspace , \\qquad \\beta_1 = 0.351 \\enspace , \\qquad \\beta_2 = 0.588 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "and we can see that our coefficients are quite close to the expected values. But again, how does our model do in predicting our validation set?\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.19145394  0.22464789  0.14656772]\n"
     ]
    }
   ],
   "source": [
    "preds = result.predict(valid)\n",
    "\n",
    "print (preds.unique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fpr</th>\n",
       "      <th>thres</th>\n",
       "      <th>tpr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.224648</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.312430</td>\n",
       "      <td>0.224648</td>\n",
       "      <td>0.445055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.722284</td>\n",
       "      <td>0.191454</td>\n",
       "      <td>0.835165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.146568</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        fpr     thres       tpr\n",
       "0  0.000000  1.224648  0.000000\n",
       "1  0.312430  0.224648  0.445055\n",
       "2  0.722284  0.191454  0.835165\n",
       "3  1.000000  0.146568  1.000000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpr, tpr, thres = roc_curve (valid_res, preds)\n",
    "\n",
    "rocdf = pd.DataFrame(dict(fpr=fpr, tpr=tpr, thres=thres))\n",
    "rocdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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5+lx5Btu2ExWRooAjDauwxR9fCPA1xpxLT3NKKZVdft55ij7TNxCdKLwHP1yD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff1dbdda358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_roc (rocdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Again our model is not working that well although it is better than before. Likely it is still too simplistic as our model only allows for two possible threshold choices. That is, we can choose to place every student with a smoking parent into the smoking bin, or alternatively only place those with two smoking parents in the smoking bin. \n",
    "\n",
    "This classification scheme is likely too simplistic to account for the complexities of human behavior and would require additional features to increase predictive power. Some features that could potentially be included are:\n",
    "\n",
    "* Household income\n",
    "* Student grades\n",
    "* Parental employment and/or education\n",
    "* Student disciplinary history\n",
    "* Student age\n",
    "* Student friends' smoking status\n",
    "* Other parental identifiers \n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Business Decisions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So assuming we can't improve our model with new features, how would we go about using it? We have two possible thresholds to consider but which one to use is situational:\n",
    "\n",
    "1. Supposing we want to discourage student smoking in a low cost and minimal way, say by distributing an informational pamplet to all students the model classifies as smoking. In that case, we might opt for the higher TPR values (81%). As the method is low cost and not invasive, we might not care that we also give pamphlets to students who aren't currently smoking (FPR = 73%).\n",
    "<br><br>\n",
    "2. In contrast, suppose we wanted to discourage student smoking using a higher time/cost method such as scheduled counseling sessions. Just to start, this would probably be inadvisable with our current model due to the small predictive power. But supposing we went ahead anyway, we would probably opt for a method with a lower FPR (31%) since we would be concerned about wasting resources. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Appendix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Z Values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more on z values see the PSU [Stat 414](https://onlinecourses.science.psu.edu/stat414/node/269) course."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$Z = \\left(\\bar{X} - \\mu\\right) \\frac{\\sqrt{N}}{\\sigma}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* $\\bar{X}$ is the found mean\n",
    "* $\\mu$ is the expected mean\n",
    "* $\\sigma$ is the standard deviation\n",
    "* $N$ is the total number of samples\n",
    "\n",
    "This is to say that $Z$ is the difference between the found mean ($\\bar{X}$) and the expected mean ($\\mu$) weighted by the standard error $\\sigma / \\sqrt{N}$. So when testing a variable for significance, the found mean will be the coefficient value and $\\mu$ will be 0 (mean of a normal distribution). So the larger the coefficient is divided it's standard error, the larger it's z value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resources"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* PSU [Stat 414](https://onlinecourses.science.psu.edu/stat414/node/269) course on z statistics\n",
    "* PSU [Stat 504](https://onlinecourses.science.psu.edu/stat504/node/150) course on logistic regression"
   ]
  }
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