4.4.2 Example: South African Heart Disease

%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

df = pd.read_csv('../data/SAheart/SAheart.data', index_col = 0)
df['famhist'] = df['famhist'].map({'Present': 1, 'Absent': 0})

# These columns are not used in the book.
df.pop('adiposity')
df.pop('typea')

df_y = df.pop('chd')
df.head()

	sbp	tobacco	ldl	famhist	obesity	alcohol	age
row.names
1	160	12.00	5.73	1	25.30	97.20	52
2	144	0.01	4.41	0	28.87	2.06	63
3	118	0.08	3.48	1	29.14	3.81	46
4	170	7.50	6.41	1	31.99	24.26	58
5	134	13.60	3.50	1	25.99	57.34	49

pd.plotting.scatter_matrix(df, marker='O',
                           facecolors = 'none', 
                           edgecolors = df_y.map({0: 'blue', 1: 'red'}),
                           figsize = (10, 10))
plt.show()

class LogisticRegression:
    def predict(X):
        X = np.c_[np.ones((X.shape[0], 1)), X]
        return self._sigmoid(X @ self.beta)
    
    def fit(self, X, y):
        X = np.c_[np.ones((X.shape[0], 1)), X]
        self.beta = np.zeros(X.shape[1])
        
        while True:
            p = self._sigmoid(X @ self.beta)
            W = np.diag(p * (1 - p)) 
            derivative = X.T @ (y - p)
            hessian = -X.T @ W @ X

            if np.allclose(derivative, 0):
                break    
            self.beta -= np.linalg.inv(hessian) @ derivative
        
        self.stderr = np.sqrt(np.diag(np.linalg.inv(-hessian)))
        self.z_score = self.beta / self.stderr
        return self
    
    def _sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

model = LogisticRegression().fit(df.values, df_y.values)

pd.options.display.float_format = '{0:.3f}'.format

pd.DataFrame(data = {'Coefficient': model.beta, 
                     'Std. Error': model.stderr,
                     'Z Score' : model.z_score}, 
             index = ["Intercept", *df.columns.tolist()])

	Coefficient	Std. Error	Z Score
Intercept	-4.130	0.964	-4.283
sbp	0.006	0.006	1.023
tobacco	0.080	0.026	3.034
ldl	0.185	0.057	3.218
famhist	0.939	0.225	4.177
obesity	-0.035	0.029	-1.187
alcohol	0.001	0.004	0.136
age	0.043	0.010	4.181