Logistic_Regression_Assumptions.ipynb

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   "source": [
    "# Logistic Regression Assumptions\n",
    "___\n",
    "\n",
    "- When the assumptions of logistic regression analysis are not met, problems such as biased coefficient estimates or very large standard errors for the logistic regression coefficients may lead to invalid statistical inferences. \n",
    "- In this demo, we go through each key assumption with code examples (on the Titanic dataset)\n",
    "- Link to TowardsDataScience article: https://towardsdatascience.com/assumptions-of-logistic-regression-clearly-explained-44d85a22b290\n",
    "- Last updated: 29 Jan 2022\n",
    "\n",
    "___\n",
    "### Contents\n",
    "[**Initial Setup**](#initial-setup)\n",
    "\n",
    "[**Assumption 1** - Appropriate outcome type](#assumption-outcome) \n",
    "\n",
    "[**Assumption 2** - Linearity of independent variables and log odds](#assumption-linearity) \n",
    "\n",
    "[**Assumption 3** - No strongly influential outliers](#assumption-outlier)  \n",
    "\n",
    "[**Assumption 4** - Absence of multicollinearity](#assumption-multicollinearity)  \n",
    "\n",
    "[**Assumption 5** - Independence of observations](#assumption-independence)  \n",
    "\n",
    "[**Assumption 6** - Sufficiently large sample size](#assumption-size)  \n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='initial-setup'></a>\n",
    "### Initial Setup\n",
    "- Import and pre-process Titanic dataset (suitable example as it is a classification problem)\n",
    "- Can ignore the details of the data preparation, as the objective here is just to prepare a dataset for the subsequent assumptions testing\n",
    "- Reference: https://www.kaggle.com/mnassrib/titanic-logistic-regression-with-python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import dependencies\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('darkgrid')\n",
    "import math\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.genmod.generalized_linear_model import GLM\n",
    "from statsmodels.genmod import families\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Basic pre-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "      <th>TravelAlone</th>\n",
       "      <th>Pclass_2</th>\n",
       "      <th>Pclass_3</th>\n",
       "      <th>Embarked_Q</th>\n",
       "      <th>Embarked_S</th>\n",
       "      <th>Sex_male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>26.0</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\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>35.0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Survived   Age     Fare  TravelAlone  Pclass_2  Pclass_3  Embarked_Q  \\\n",
       "0         0  22.0   7.2500            0         0         1           0   \n",
       "1         1  38.0  71.2833            0         0         0           0   \n",
       "2         1  26.0   7.9250            1         0         1           0   \n",
       "3         1  35.0  53.1000            0         0         0           0   \n",
       "4         0  35.0   8.0500            1         0         1           0   \n",
       "\n",
       "   Embarked_S  Sex_male  \n",
       "0           1         1  \n",
       "1           0         0  \n",
       "2           1         0  \n",
       "3           1         0  \n",
       "4           1         1  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import Titanic dataset (train.csv)\n",
    "df_raw = pd.read_csv('data/train.csv')\n",
    "\n",
    "# Create categorical variable for traveling alone\n",
    "df_raw['TravelAlone'] = np.where((df_raw[\"SibSp\"] + df_raw[\"Parch\"])>0, 0, 1).astype('uint8')\n",
    "df_raw.drop('SibSp', axis=1, inplace=True)\n",
    "df_raw.drop('Parch', axis=1, inplace=True)\n",
    "df_raw.drop('PassengerId', axis=1, inplace=True)\n",
    "df_raw.drop('Name', axis=1, inplace=True)\n",
    "df_raw.drop('Ticket', axis=1, inplace=True)\n",
    "df_raw.drop('Cabin', axis=1, inplace=True)\n",
    "# df_raw.drop('Fare', axis=1, inplace=True)\n",
    "\n",
    "# Create categorical variables and drop some variables\n",
    "df_titanic = pd.get_dummies(df_raw, columns=[\"Pclass\",\"Embarked\",\"Sex\"], \n",
    "                         drop_first=True) # Remove first variable to prevent collinearity\n",
    "\n",
    "# Fill NaN (median imputation)\n",
    "df_titanic[\"Age\"].fillna(df_titanic[\"Age\"].median(skipna=True), inplace=True)\n",
    "\n",
    "df_titanic.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kenne\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "# Define dependent and independent variables\n",
    "X_cols = df_titanic.columns.to_list()[1:]\n",
    "X = df_titanic[X_cols]\n",
    "y = df_titanic['Survived']\n",
    "\n",
    "# Add constant\n",
    "X_constant = sm.add_constant(X, prepend=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "<a name='assumption-outcome'></a>\n",
    "### Assumption 1 - Appropriate outcome type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "print(y.nunique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    549\n",
       "1    342\n",
       "Name: Survived, dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- There are only two outcomes (i.e. binary classification of survived or did not survive), so we will be using Binary Logistic Regression (which is the default method we use when we specify family=Binomial in our logit models earlier)\n",
    "- Other types of Logistic Regression (where outcomes > 2) include:\n",
    "    - Multinomial Logistic Regression: Target variable has three or more nominal categories such as predicting the type of Wine\n",
    "    - Ordinal Logistic Regression: Target variable has three or more ordinal categories such as restaurant or product rating from 1 to 5.\n",
    "- More info: https://www.datacamp.com/community/tutorials/understanding-logistic-regression-python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "<a name='assumption-linearity'></a>\n",
    "### Assumption 2 - Linearity of independent variables and log odds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Box-Tidwell Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- One of the important assumptions of logistic regression is the linearity of the logit over the continuous covariates. This assumption means that relationships between the continuous predictors and the logit (log odds) is linear. \n",
    "- The **Box-Tidwell transformation (test)** can be used to test the linearity in the logit assumption when performing logistic regression.\n",
    "- It checks whether the logit transform is a linear function of the predictor, effectively adding the non-linear transform of the original predictor as an interaction term to test if this addition made no better prediction.\n",
    "- A **statistically significant** p-value of the interaction term in the Box-Tidwell transformation means that the linearity assumption is violated\n",
    "- If one variable is indeed found to be non-linear, then we can resolve it by incorporating higher order polynomial terms for that variable in the regression analysis to capture the non-linearity (e.g. x^2) .- Another solution to this problem is the categorization of the independent variables. That is transforming metric variables to ordinal level and then including them in the model. \n",
    "\n",
    "___\n",
    "- Details on R implementation of Box-Tidwell test in R, please refer to the `Box-Tidwell-Test-in-R.ipynb` notebook\n",
    "- There is no native Python package to run the Box Tidwell test (unlike in R), so we will be coding the test below manually"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "      <th>TravelAlone</th>\n",
       "      <th>Pclass_2</th>\n",
       "      <th>Pclass_3</th>\n",
       "      <th>Embarked_Q</th>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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      ],
      "text/plain": [
       "   Survived   Age     Fare  TravelAlone  Pclass_2  Pclass_3  Embarked_Q  \\\n",
       "0         0  22.0   7.2500            0         0         1           0   \n",
       "1         1  38.0  71.2833            0         0         0           0   \n",
       "2         1  26.0   7.9250            1         0         1           0   \n",
       "3         1  35.0  53.1000            0         0         0           0   \n",
       "4         0  35.0   8.0500            1         0         1           0   \n",
       "\n",
       "   Embarked_S  Sex_male  \n",
       "0           1         1  \n",
       "1           0         0  \n",
       "2           1         0  \n",
       "3           1         0  \n",
       "4           1         1  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Box Tidwell only works for positive values. Hence, drop values where x = 0\n",
    "df_titanic_2 = df_titanic.drop(df_titanic[df_titanic.Age == 0].index)\n",
    "df_titanic_2 = df_titanic_2.drop(df_titanic[df_titanic.Fare == 0].index)\n",
    "\n",
    "# Export processed df_titanic for separate R notebook: `Box-Tidwell-Test-in-R.ipynb`\n",
    "# df_titanic_2.to_csv('data/train_processed.csv', index=False)\n",
    "\n",
    "df_titanic_2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic Regression with statsmodel - Inclusion of interaction term (logit transform) as part of Box-Tidwell test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "      <th>Fare</th>\n",
       "      <th>TravelAlone</th>\n",
       "      <th>Pclass_2</th>\n",
       "      <th>Pclass_3</th>\n",
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       "      <td>0</td>\n",
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       "      <td>1</td>\n",
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      ],
      "text/plain": [
       "   Survived   Age     Fare  TravelAlone  Pclass_2  Pclass_3  Embarked_Q  \\\n",
       "0         0  22.0   7.2500            0         0         1           0   \n",
       "1         1  38.0  71.2833            0         0         0           0   \n",
       "2         1  26.0   7.9250            1         0         1           0   \n",
       "3         1  35.0  53.1000            0         0         0           0   \n",
       "4         0  35.0   8.0500            1         0         1           0   \n",
       "\n",
       "   Embarked_S  Sex_male  Age:Log_Age  Fare:Log_Fare  \n",
       "0           1         1    68.002934      14.362261  \n",
       "1           0         0   138.228274     304.141753  \n",
       "2           1         0    84.710510      16.404927  \n",
       "3           1         0   124.437182     210.922595  \n",
       "4           1         1   124.437182      16.789660  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
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    }
   ],
   "source": [
    "df_titanic_lt = df_titanic_2.copy()  # lt = logit transform\n",
    "\n",
    "# Define continuous variables\n",
    "continuous_var = ['Age', 'Fare']\n",
    "\n",
    "# Add logit transform interaction terms (natural log) for continuous variables e.g. Age * Log(Age)\n",
    "for var in continuous_var:\n",
    "    df_titanic_lt[f'{var}:Log_{var}'] = df_titanic_lt[var].apply(lambda x: x * np.log(x)) #np.log = natural log\n",
    "\n",
    "df_titanic_lt.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Age', 'Fare', 'Age:Log_Age', 'Fare:Log_Fare']"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Keep columns related to continuous variables\n",
    "cols_to_keep = continuous_var + df_titanic_lt.columns.tolist()[-len(continuous_var):]\n",
    "cols_to_keep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:               Survived   No. Observations:                  876\n",
      "Model:                            GLM   Df Residuals:                      871\n",
      "Model Family:                Binomial   Df Model:                            4\n",
      "Link Function:                  logit   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:                -536.19\n",
      "Date:                Sat, 29 Jan 2022   Deviance:                       1072.4\n",
      "Time:                        22:39:39   Pearson chi2:                     881.\n",
      "No. Iterations:                     4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=================================================================================\n",
      "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "Age              -0.1123      0.058     -1.948      0.051      -0.225       0.001\n",
      "Fare              0.0785      0.013      6.057      0.000       0.053       0.104\n",
      "Age:Log_Age       0.0218      0.013      1.640      0.101      -0.004       0.048\n",
      "Fare:Log_Fare    -0.0119      0.002     -5.251      0.000      -0.016      -0.007\n",
      "const            -0.3764      0.402     -0.937      0.349      -1.164       0.411\n",
      "=================================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kenne\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "# Redefine independent variables to include interaction terms\n",
    "X_lt = df_titanic_lt[cols_to_keep]\n",
    "y_lt = df_titanic_lt['Survived']\n",
    "\n",
    "# Add constant\n",
    "X_lt_constant = sm.add_constant(X_lt, prepend=False)\n",
    "  \n",
    "# Build model and fit the data (using statsmodel's Logit)\n",
    "logit_results = GLM(y_lt, X_lt_constant, family=families.Binomial()).fit()\n",
    "\n",
    "# Display summary results\n",
    "print(logit_results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We are interested in the p-values for the logit transformed interaction terms of  `Age:Log_Age` and `Fare:Log_Fare`\n",
    "- From the summary table above, we can see that the p value for `Fare:Log_Fare` is <0.001, which is statistically significant, whereas `Age:Log_Age` is not\n",
    "- This means that there is non-linearity in the `Fare` feature, and the assumption has been violated\n",
    "- We can resolve this by including a polynomial term (e.g. `Fare^2`) to account for the non-linearity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visual Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Re-run logistic regression on original set of X and y variables\n",
    "logit_results = GLM(y, X_constant, family=families.Binomial()).fit()\n",
    "predicted = logit_results.predict(X_constant)\n",
    "\n",
    "# Get log odds values\n",
    "log_odds = np.log(predicted / (1 - predicted))\n",
    "\n",
    "# Visualize predictor continuous variable vs logit values (Age)\n",
    "plt.scatter(x=X_constant['Age'].values, y=log_odds);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confirming that there is logit linearity for the `Age` variable (Recall earlier that p value for `Age:Log Age` is 0.101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize predictor variable vs logit values for Fare\n",
    "plt.scatter(x=X_constant['Fare'].values, y=log_odds);\n",
    "plt.xlabel(\"Fare\")\n",
    "plt.ylabel(\"Log-odds\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confirming that there is logit NON-linearity for the `Fare` variable (Recall earlier that p value for `Fare:Log Fare` is <0.001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "<a name='assumption-outlier'></a>\n",
    "### Assumption 3 - No strongly influential outliers\n",
    "- Influential values are extreme individual data points that can alter the quality of the logistic regression model.\n",
    "- Cook’s Distance is an estimate of the influence of a data point. It takes into account both the leverage and residual of each observation. Cook’s Distance is a summary of how much a regression model changes when the **i**th observation is removed.\n",
    "- A general rule of thumb is that any observation with a Cook’s distance greater than 4/n (where n = total observations) is considered to be influential (https://www.statology.org/cooks-distance-python/ and https://www.scikit-yb.org/en/latest/api/regressor/influence.html?highlight=cook#module-yellowbrick.regressor.influence), though there are even more generic cutoff values of >0.5-1.0.\n",
    "- For outliers, we can use the absolute standardized residuals to identify them (std resid > 3)\n",
    "- Reference: https://www.statsmodels.org/dev/examples/notebooks/generated/influence_glm_logit.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:               Survived   No. Observations:                  891\n",
      "Model:                            GLM   Df Residuals:                      882\n",
      "Model Family:                Binomial   Df Model:                            8\n",
      "Link Function:                  logit   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:                -398.95\n",
      "Date:                Sat, 29 Jan 2022   Deviance:                       797.91\n",
      "Time:                        22:39:40   Pearson chi2:                     933.\n",
      "No. Iterations:                     5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "Age            -0.0333      0.008     -4.397      0.000      -0.048      -0.018\n",
      "Fare            0.0004      0.002      0.164      0.870      -0.004       0.005\n",
      "TravelAlone     0.0695      0.196      0.354      0.723      -0.315       0.454\n",
      "Pclass_2       -0.9406      0.291     -3.236      0.001      -1.510      -0.371\n",
      "Pclass_3       -2.2737      0.289     -7.870      0.000      -2.840      -1.707\n",
      "Embarked_Q     -0.0337      0.373     -0.091      0.928      -0.764       0.697\n",
      "Embarked_S     -0.5540      0.235     -2.353      0.019      -1.015      -0.093\n",
      "Sex_male       -2.5918      0.196    -13.206      0.000      -2.977      -2.207\n",
      "const           3.7977      0.456      8.326      0.000       2.904       4.692\n",
      "===============================================================================\n"
     ]
    }
   ],
   "source": [
    "# Use GLM method for logreg here so that we can retrieve the influence measures\n",
    "logit_model = GLM(y, X_constant, family=families.Binomial())\n",
    "logit_results = logit_model.fit()\n",
    "print(logit_results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "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>cooks_d</th>\n",
       "      <th>std_resid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000041</td>\n",
       "      <td>0.330871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000046</td>\n",
       "      <td>0.243040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.001006</td>\n",
       "      <td>0.866265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000091</td>\n",
       "      <td>0.313547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000017</td>\n",
       "      <td>0.280754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>886</th>\n",
       "      <td>0.000292</td>\n",
       "      <td>0.589428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>887</th>\n",
       "      <td>0.000049</td>\n",
       "      <td>0.225427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>888</th>\n",
       "      <td>0.001102</td>\n",
       "      <td>1.029623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>889</th>\n",
       "      <td>0.001417</td>\n",
       "      <td>0.763489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>890</th>\n",
       "      <td>0.000133</td>\n",
       "      <td>0.372182</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>891 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      cooks_d  std_resid\n",
       "0    0.000041   0.330871\n",
       "1    0.000046   0.243040\n",
       "2    0.001006   0.866265\n",
       "3    0.000091   0.313547\n",
       "4    0.000017   0.280754\n",
       "..        ...        ...\n",
       "886  0.000292   0.589428\n",
       "887  0.000049   0.225427\n",
       "888  0.001102   1.029623\n",
       "889  0.001417   0.763489\n",
       "890  0.000133   0.372182\n",
       "\n",
       "[891 rows x 2 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "# Get influence measures\n",
    "influence = logit_results.get_influence()\n",
    "\n",
    "# Obtain summary df of influence measures\n",
    "summ_df = influence.summary_frame()\n",
    "\n",
    "# Filter summary df to Cook distance\n",
    "diagnosis_df = summ_df.loc[:,['cooks_d']]\n",
    "\n",
    "# Append absolute standardized residual values\n",
    "diagnosis_df['std_resid'] = stats.zscore(logit_results.resid_pearson)\n",
    "diagnosis_df['std_resid'] = diagnosis_df.loc[:,'std_resid'].apply(lambda x: np.abs(x))\n",
    "\n",
    "# Sort by Cook's Distance\n",
    "diagnosis_df.sort_values(\"cooks_d\", ascending=False)\n",
    "diagnosis_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Threshold for Cook Distance = 0.004489337822671156\n"
     ]
    }
   ],
   "source": [
    "# Set Cook's distance threshold\n",
    "cook_threshold = 4 / len(X)\n",
    "print(f\"Threshold for Cook Distance = {cook_threshold}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot influence measures (Cook's distance)\n",
    "fig = influence.plot_index(y_var=\"cooks\", threshold=cook_threshold)\n",
    "plt.axhline(y=cook_threshold, ls=\"--\", color='red')\n",
    "fig.tight_layout(pad=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion of data points that are highly influential = 6.1%\n"
     ]
    }
   ],
   "source": [
    "# Find number of observations that exceed Cook's distance threshold\n",
    "outliers = diagnosis_df[diagnosis_df['cooks_d'] > cook_threshold]\n",
    "prop_outliers = round(100*(len(outliers) / len(X)),1)\n",
    "print(f'Proportion of data points that are highly influential = {prop_outliers}%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion of highly influential outliers = 1.3%\n"
     ]
    }
   ],
   "source": [
    "# Find number of observations which are BOTH outlier (std dev > 3) and highly influential\n",
    "extreme = diagnosis_df[(diagnosis_df['cooks_d'] > cook_threshold) & \n",
    "                       (diagnosis_df['std_resid'] > 3)]\n",
    "prop_extreme = round(100*(len(extreme) / len(X)),1)\n",
    "print(f'Proportion of highly influential outliers = {prop_extreme}%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>cooks_d</th>\n",
       "      <th>std_resid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>297</th>\n",
       "      <td>0.015636</td>\n",
       "      <td>4.951289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>570</th>\n",
       "      <td>0.009277</td>\n",
       "      <td>3.030644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>0.008687</td>\n",
       "      <td>3.384369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>338</th>\n",
       "      <td>0.005917</td>\n",
       "      <td>4.461842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>414</th>\n",
       "      <td>0.005666</td>\n",
       "      <td>4.387731</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      cooks_d  std_resid\n",
       "297  0.015636   4.951289\n",
       "570  0.009277   3.030644\n",
       "498  0.008687   3.384369\n",
       "338  0.005917   4.461842\n",
       "414  0.005666   4.387731"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display top 5 most influential outliers\n",
    "extreme.sort_values(\"cooks_d\", ascending=False).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Age              2.00\n",
       "Fare           151.55\n",
       "TravelAlone      0.00\n",
       "Pclass_2         0.00\n",
       "Pclass_3         0.00\n",
       "Embarked_Q       0.00\n",
       "Embarked_S       1.00\n",
       "Sex_male         0.00\n",
       "Name: 297, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Deep dive into index 297 (extreme outlier)\n",
    "X.iloc[297]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.iloc[297]  # 0 = Did not survive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- It is important to note that for data points with relative high Cook's distances, it does **not** automatically mean that it should be immediately removed from the dataset. It is essentially an indicator to highlight which data points are worth looking deeper into, to understand whether they are true anomalies or not\n",
    "- In practice, an assessment of “large” values is a judgement call based on experience and the particular set of data being analyzed.\n",
    "- In addition, based on our pre-defined threshold (4/N), only 5% (51/891) of the points are in the outlier zone, which is small as well. The issue comes when there is a significant number of data points classified as outliers.\n",
    "- The management of outliers is outside the scope of this demo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "<a name='assumption-multicollinearity'></a>\n",
    "### Assumption 4 - Absence of multicollinearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "corrMatrix = X.corr()\n",
    "plt.subplots(figsize=(10, 6))\n",
    "sns.heatmap(corrMatrix, annot=True, cmap=\"RdYlGn\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Correlation matrix can be difficult to interpret when there are many independent variables\n",
    "- Furthermore, not all collinearity problems can be detected by inspection of the correlation matrix: it is possible for collinearity to exist between three or more variables even if no pair of variables has a particularly high correlation. \n",
    "- As such, we use Variance Inflation Factor (VIF) instead"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Variance Inflation Factor (VIF)\n",
    "- Include constant in VIF calculation. Reference: https://stackoverflow.com/questions/42658379/variance-inflation-factor-in-python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>variables</th>\n",
       "      <th>VIF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Age</td>\n",
       "      <td>1.214763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Fare</td>\n",
       "      <td>1.690016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>TravelAlone</td>\n",
       "      <td>1.218899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Pclass_2</td>\n",
       "      <td>2.067296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pclass_3</td>\n",
       "      <td>2.696852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Embarked_Q</td>\n",
       "      <td>1.491371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Embarked_S</td>\n",
       "      <td>1.484453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Sex_male</td>\n",
       "      <td>1.151131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>const</td>\n",
       "      <td>24.218135</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     variables        VIF\n",
       "0          Age   1.214763\n",
       "1         Fare   1.690016\n",
       "2  TravelAlone   1.218899\n",
       "3     Pclass_2   2.067296\n",
       "4     Pclass_3   2.696852\n",
       "5   Embarked_Q   1.491371\n",
       "6   Embarked_S   1.484453\n",
       "7     Sex_male   1.151131\n",
       "8        const  24.218135"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use variance inflation factor to identify any significant multi-collinearity\n",
    "def calc_vif(df):\n",
    "    vif = pd.DataFrame()\n",
    "    vif[\"variables\"] = df.columns\n",
    "    vif[\"VIF\"] = [variance_inflation_factor(df.values, i) for i in range(df.shape[1])]\n",
    "    return(vif)\n",
    "\n",
    "calc_vif(X_constant) # Include constant in VIF calculation in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The threshold for VIF is usually 5 (i.e. values above 5 means there is presence of multicollinearity)\n",
    "- Since all the variables have VIF <5,  it means that there is no multicollinearity, and this assumption is satisfied\n",
    "- Let's have a look at the situation where we did **not** drop the first variable upon getting dummies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kenne\\anaconda3\\lib\\site-packages\\statsmodels\\stats\\outliers_influence.py:193: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  vif = 1. / (1. - r_squared_i)\n",
      "C:\\Users\\kenne\\anaconda3\\lib\\site-packages\\statsmodels\\regression\\linear_model.py:1715: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1 - self.ssr/self.centered_tss\n"
     ]
    },
    {
     "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>variables</th>\n",
       "      <th>VIF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Age</td>\n",
       "      <td>1.217824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Fare</td>\n",
       "      <td>1.690035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>TravelAlone</td>\n",
       "      <td>1.223104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Pclass_1</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pclass_2</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Pclass_3</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Embarked_C</td>\n",
       "      <td>69.925063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Embarked_Q</td>\n",
       "      <td>36.785122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Embarked_S</td>\n",
       "      <td>91.277323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Sex_male</td>\n",
       "      <td>1.157472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>const</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      variables        VIF\n",
       "0           Age   1.217824\n",
       "1          Fare   1.690035\n",
       "2   TravelAlone   1.223104\n",
       "3      Pclass_1        inf\n",
       "4      Pclass_2        inf\n",
       "5      Pclass_3        inf\n",
       "6    Embarked_C  69.925063\n",
       "7    Embarked_Q  36.785122\n",
       "8    Embarked_S  91.277323\n",
       "9      Sex_male   1.157472\n",
       "10        const   0.000000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Avoid dropping first variables upon get_dummies\n",
    "df_test = pd.get_dummies(df_raw, \n",
    "                         columns=[\"Pclass\",\"Embarked\",\"Sex\"], \n",
    "                         drop_first=False)\n",
    "df_test.drop('Sex_female', axis=1, inplace=True)\n",
    "df_test.drop('Survived', axis=1, inplace=True) # Remove dependent variable from VIF calculation\n",
    "df_test[\"Age\"].fillna(df_test[\"Age\"].median(skipna=True), inplace=True)\n",
    "df_test = df_test.assign(const=1)  # Add constant\n",
    "calc_vif(df_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From the above results, we can see that there are numerous VIF values way above the threshold of 5 when we do not drop at least 1 category from the dummy categories we generated\n",
    "- This is a clear sign of multicollinearity IF we do not drop first"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "<a name='assumption-independence'></a>\n",
    "### Assumption 5 - Independence of observations\n",
    "- Error terms need to be independent. That is that the data-points should not be from any dependent samples design, e.g., before-after measurements, or matched pairings. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:               Survived   No. Observations:                  891\n",
      "Model:                            GLM   Df Residuals:                      882\n",
      "Model Family:                Binomial   Df Model:                            8\n",
      "Link Function:                  logit   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:                -398.95\n",
      "Date:                Sat, 29 Jan 2022   Deviance:                       797.91\n",
      "Time:                        22:39:42   Pearson chi2:                     933.\n",
      "No. Iterations:                     5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "Age            -0.0333      0.008     -4.397      0.000      -0.048      -0.018\n",
      "Fare            0.0004      0.002      0.164      0.870      -0.004       0.005\n",
      "TravelAlone     0.0695      0.196      0.354      0.723      -0.315       0.454\n",
      "Pclass_2       -0.9406      0.291     -3.236      0.001      -1.510      -0.371\n",
      "Pclass_3       -2.2737      0.289     -7.870      0.000      -2.840      -1.707\n",
      "Embarked_Q     -0.0337      0.373     -0.091      0.928      -0.764       0.697\n",
      "Embarked_S     -0.5540      0.235     -2.353      0.019      -1.015      -0.093\n",
      "Sex_male       -2.5918      0.196    -13.206      0.000      -2.977      -2.207\n",
      "const           3.7977      0.456      8.326      0.000       2.904       4.692\n",
      "===============================================================================\n"
     ]
    }
   ],
   "source": [
    "# Setup logistic regression model (using GLM method so that we can retrieve residuals)\n",
    "logit_model = GLM(y, X_constant, family=families.Binomial())\n",
    "logit_results = logit_model.fit()\n",
    "print(logit_results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Check residuals series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate residual series plot\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "ax = fig.add_subplot(111, title=\"Residual Series Plot\",\n",
    "                    xlabel=\"Index Number\", ylabel=\"Deviance Residuals\")\n",
    "\n",
    "# ax.plot(X.index.tolist(), stats.zscore(logit_results.resid_pearson))\n",
    "ax.plot(X.index.tolist(), stats.zscore(logit_results.resid_deviance))\n",
    "plt.axhline(y=0, ls=\"--\", color='red');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From the above Deviance residuals versus index number plot, we can see that the assumption of independence of errors is satisfied"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Further investigation on residual dependence plots (Optional)\n",
    "- This is additional investigation. The above check on residuals series (based on index numbers) is sufficient\n",
    "- Reference: https://freakonometrics.hypotheses.org/8210"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 5))\n",
    "ax = fig.add_subplot(\n",
    "            111,\n",
    "            title=\"Residual Dependence Plot\",\n",
    "            xlabel=\"Fitted Values\",\n",
    "            ylabel=\"Pearson Residuals\")\n",
    "\n",
    "# ax.scatter(logit_results.mu, stats.zscore(logit_results.resid_pearson))\n",
    "ax.scatter(logit_results.mu, stats.zscore(logit_results.resid_deviance))\n",
    "ax.axis(\"tight\")\n",
    "ax.plot([0.0, 1.0], [0.0, 0.0], \"k-\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Add a Locally Weighted Scatterplot Smoothing (LOWESS) line to better visualize independence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Setup LOWESS function\n",
    "lowess = sm.nonparametric.lowess\n",
    "\n",
    "# Get y-values from LOWESS (set return_sorted=False)\n",
    "y_hat_lowess = lowess(logit_results.resid_pearson, logit_results.mu, \n",
    "                      return_sorted = False,\n",
    "                      frac=2/3)\n",
    "\n",
    "fig = plt.figure(figsize=(8, 5))\n",
    "ax = fig.add_subplot(111,\n",
    "    title=\"Residual Dependence Plot\",\n",
    "    xlabel=\"Fitted Values\",\n",
    "    ylabel=\"Pearson Residuals\")\n",
    "\n",
    "# ax.scatter(logit_results.mu, stats.zscore(logit_results.resid_pearson))\n",
    "ax.scatter(logit_results.mu, stats.zscore(logit_results.resid_deviance))\n",
    "ax.scatter(logit_results.mu, y_hat_lowess)\n",
    "ax.axis(\"tight\")\n",
    "ax.plot([0.0, 1.0], [0.0, 0.0], \"k-\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "<a name='assumption-size'></a>\n",
    "### Assumption 6 - Sufficiently large sample size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "891"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find total number of observations\n",
    "len(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1    537\n",
      "0    354\n",
      "Name: TravelAlone, dtype: int64\n",
      "0    707\n",
      "1    184\n",
      "Name: Pclass_2, dtype: int64\n",
      "1    491\n",
      "0    400\n",
      "Name: Pclass_3, dtype: int64\n",
      "0    814\n",
      "1     77\n",
      "Name: Embarked_Q, dtype: int64\n",
      "1    644\n",
      "0    247\n",
      "Name: Embarked_S, dtype: int64\n",
      "1    577\n",
      "0    314\n",
      "Name: Sex_male, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# Get value counts for independent variables (mainly focus on categorical)\n",
    "for col in X.columns.to_list()[1:]:\n",
    "    if X.dtypes[col] == 'uint8': # Keep categorical variables only\n",
    "        print(X[col].value_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Rule of thumb is to have at least 10-20 instances of the least frequent outcome for each predictor variable in your model\n",
    "- From the value counts above, we can see that this assumption is satisfied\n",
    "\n",
    "- Another rule of thumb is to have at least 500 observations in the entire dataset\n",
    "- Overall, we have 891 observations, which is a decent dataset size to work with"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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