jkclem

# for the paired t-test for differnce of means
from scipy.stats import ttest_rel

# save and printprint the results of the test on the Ridge estimates
lasso_results = ttest_rel(unbiased_sigma_estimates, lasso_sigma_estimates)
print(f'Test Statistic for the Paired t-test between the True Model and LASSO: {round(lasso_results[0], 4)}')
print(f'p-value for the Paired t-test between the True Model and LASSO: {round(lasso_results[1], 4)}')
print()
# save and printprint the results of the test on the Ridge estimates
ridge_results = ttest_rel(unbiased_sigma_estimates, ridge_sigma_estimates)

jkclem

# suppresses warnings from sklearn
def warn(*args, **kwargs):
    pass
import warnings
warnings.warn = warn

# import LassoCV
from sklearn.linear_model import LassoCV
# import RidgeCV
from sklearn.linear_model import RidgeCV

jkclem

# for linear algebra and random numbers
import numpy as np
# for linear regression
import statsmodels.api as sm
# for visualization
import matplotlib.pyplot as plt
# for generating combinations of explanatory variables for model selection based on AIC
from itertools import combinations

# set a random seed for reproducibility

jkclem

def best_information_criterion_selection(y, X, criterion='AIC'):
    '''
    This function takes in a column numpy array (y) and design matrix (X) (with the first column as all 1s for
    the intercept) which is also a numpy array, and returns the OLS model with the lowest Information 
    Criterion. The default criterion is AIC; and the other option is BIC.
    '''
    
    # check inputs are valid
    assert y.shape[0] == X.shape[0], 'The number of rows in y and X do not match!'
    assert (criterion == 'AIC') or (criterion == 'BIC'), 'Valid criterions are AIC and BIC!'

jkclem

from statsmodels.discrete.discrete_model import Logit

# add an intercept since statsmodels does not
my_data['Intercept'] = 1

# fit the logistic regression model using MLE
mle_mod = Logit(my_data[target], my_data[['Intercept'] + vars_of_interest])
mle_mod_fit = mle_mod.fit(disp=False)

# print the summary

jkclem

plt.figure(figsize=(12, 5), dpi= 80, facecolor='w', edgecolor='k')

plt.subplot(1, 2, 1)
plt.plot(mcmc_log_mod.raw_beta_distr[0], mcmc_log_mod.raw_beta_distr[1])
plt.title('Simulated Raw Joint Distribution of the Coefficients', fontsize=12)
plt.xlabel('Intercept', fontsize=10)
plt.ylabel('Coefficient of Price Percentile', fontsize=10)

plt.subplot(1, 2, 2)
plt.plot(mcmc_log_mod.beta_distr[0], mcmc_log_mod.beta_distr[1])

jkclem

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

# load in field goal data
all_data = pd.read_csv('candy-data.csv')

# list of independent variables in the model
vars_of_interest = ['pricepercent']
# name of dependent variable

jkclem

class mcmc_logistic_reg:
    
    import numpy as np
    
    def __init__self(self):
        self.raw_beta_distr = np.empty(1)
        self.beta_distr = np.empty(1)
        self.beta_hat = np.empty(1)
        self.cred_ints = np.empty(1)
    

jkclem

jkclem