# Condition number:
np.linalg.cond(results.model.exog)
# ## Heteroskedasticity tests
#
# Breush-Pagan test:
name = ['Lagrange multiplier statistic', 'p-value',
'f-value', 'f p-value']
test = sms.het_breushpagan(results.resid, results.model.exog)
lzip(name, test)
# Goldfeld-Quandt test
name = ['F statistic', 'p-value']
test = sms.het_goldfeldquandt(results.resid, results.model.exog)
lzip(name, test)
# ## Linearity
#
# Harvey-Collier multiplier test for Null hypothesis that the linear specification is correct:
name = ['t value', 'p value']
test = sms.linear_harvey_collier(results)
lzip(name, test)
# Other plotting options can be found on the [Graphics page.](http://www.statsmodels.org/stable/graphics.html) # ## Multicollinearity # # Condition number: np.linalg.cond(results.model.exog) # ## Heteroskedasticity tests # # Breush-Pagan test: name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value'] test = sms.het_breushpagan(results.resid, results.model.exog) lzip(name, test) # Goldfeld-Quandt test name = ['F statistic', 'p-value'] test = sms.het_goldfeldquandt(results.resid, results.model.exog) lzip(name, test) # ## Linearity # # Harvey-Collier multiplier test for Null hypothesis that the linear specification is correct: name = ['t value', 'p value'] test = sms.linear_harvey_collier(results) lzip(name, test)
# This block creates the objects for each statistic we'd like printed to Excel.<br>
# <br>
# It will report $R^2$, $R^2 adj,$ residuals, the f p-value, aic, the fitted model parameters, normality of the residuals, the Bruesh-Pagan Test for heteroscedasicity and the Harvey-Collier test for linearity.
# <codecell>
r_squared = model.rsquared
r_square_adj = model.rsquared_adj
residuals = model.resid
p = model.f_pvalue
aic = model.aic
pvalues = pd.DataFrame(model.pvalues)
params = pd.DataFrame(model.params)
normality = sms.jarque_bera(model.resid)
breush_pagan_hska = sms.het_breushpagan(model.resid, model.model.exog)
harvey_collier = sms.linear_harvey_collier(model)
# <headingcell level=4>
# Print the regression results to Excel
# <codecell>
Range("Results", "O6").value = "R^2"
Range("Results", "P6").value = r_squared
Range("Results", "O7").value = "R^2 Adjusted"
Range("Results", "P7").value = r_square_adj
Range("Results", "O8").value = "p-value"
Range("Results", "P8").value = p
def check_rmse(df, response, list_of_list):
for item in list_of_list:
cols = item
print('\nUsing scikit:\n')
# instantiate model
lm = LinearRegression()
# fit model
lm.fit(X_train[cols], y_train)
# make predictions
y_pred = lm.predict(X_test[cols])
print('MAE:', mean_absolute_error(y_test, y_pred))
print('RMSE:', np.sqrt(mean_squared_error(y_test, y_pred)))
print('R-Squared:', r2_score(y_test, y_pred))
print('Score', lm.score(X_test[cols], y_test))
# normality check
residual = y_test - y_pred
sm.qqplot(residual, stats.distributions.norm, line='r')
#plt.show()
print('\nUsing statsmodels:\n')
formula = "{0} ~ {1}".format(response, '+'.join(cols))
print(formula)
model = smf.ols(formula, data=df).fit()
y_pred = model.predict(X_test[cols])
print('RMSE:', np.sqrt(mean_squared_error(y_test, y_pred)))
print(model.params)
print(model.summary())
print('\nCHECKING RESIDUALS\n')
residual = y_test - y_pred
fig, ax = plt.subplots(1,2)
# axes are in a two-dimensional array, indexed by [row, col]
ax[0].hist(model.resid_pearson)
ax[0].set_ylabel('Count')
ax[0].set_xlabel('Normalized residuals')
ax[1].scatter(residual, y_pred)
# normality check
res = model.resid
sm.qqplot(res, stats.distributions.norm, line='r')
#plt.show()
# linearity check
##The Harvey-Collier test performs a t-test (with parameter degrees of freedom) on the recursive residuals.
##If the true relationship is not linear but convex or concave the mean of the recursive residuals should differ from 0 significantly.
import statsmodels.stats.api as sms
try:
harvey_collier = sms.linear_harvey_collier(model)
print(harvey_collier)
except np.linalg.linalg.LinAlgError as e:
print(e)
## equal variation check
### violation of homoscedasticity.
### small pvalue = bad
from statsmodels.stats.diagnostic import het_breuschpagan
_, pval, __, f_pval = het_breuschpagan(residual, X_test[cols])
print('Pval', pval)
print('f_pval', f_pval)
## correlation analysis
# Compute matrix of correlation coefficients
corr_matrix = np.corrcoef(df[cols].T)
print(pd.DataFrame(corr_matrix))
### https://matplotlib.org/gallery/images_contours_and_fields/image_annotated_heatmap.html
# Display heat map
fig, ax = plt.subplots(1, 1, figsize=(6, 6))
ax.imshow(corr_matrix)
ax.set_title('Heatmap of correlation matrix')
# Rotate the tick labels and set their alignment.
plt.setp(ax.get_xticklabels(), rotation=45, ha="right",
rotation_mode="anchor")
# We want to show all ticks...
ax.set_xticks(np.arange(len(cols)))
ax.set_yticks(np.arange(len(cols)))
# ... and label them with the respective list entries
ax.set_xticklabels(cols)
ax.set_yticklabels(cols)
# Loop over data dimensions and create text annotations.
for i in range(len(cols)):
for j in range(len(cols)):
text = ax.text(j, i, round(corr_matrix[i, j], 2),
ha="center", va="center", color="black")
plt.show()
print("\nCross validation using scikit:\n")
# check cross validation predictions, 10 splits
cv_predictions = cross_val_predict(lm, df[cols], df[response], cv=10)
# check errors
print('MAE:', mean_absolute_error(df[response], cv_predictions))
print('RMSE:', np.sqrt(mean_squared_error(df[response], cv_predictions)))
print('R-Squared:', r2_score(df[response],cv_predictions))
#print('Score', accuracy_score(df[response], cv_predictions))
# plot actual vs predicted
fig3 = plt.figure(figsize=(6,6))
plt.scatter(x=cv_predictions, y=df[response])
plt.xlabel('Predictions')
plt.ylabel('Appliances')
df['predictions'] = cv_predictions
# plotting fit results
fig4, ax = plt.subplots()
df.Appliances.plot(ax=ax, style='b-')
# same ax as above since it's automatically added on the right
df.predictions.plot(ax=ax, style='r-')
ax.set_xlabel('Predictions')
ax.set_ylabel('Appliances')
#print(df.head())
#df.plot(y=cv_predictions, color='red', linewidth=1)
#fig4.tight_layout()
#plt.show()
print('\nCHECKING RESIDUALS\n')
residual = df[response] - y_pred
# axes are in a two-dimensional array, indexed by [row, col]
fig4 = plt.figure(figsize=(6,6))
plt.scatter(df.predictions, residual)
plt.hlines(y = 0, xmin = 0, xmax = 250)
plt.title('Residual Plot')
plt.ylabel('Residuals')
plt.show()
name3 = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value']
test3 = sms.het_breuschpagan(lr.resid, lr.model.exog)
lzip(name3, test3)
#======================Goldfeld-Quandt test:
name5 = ['F statistic', 'p-value']
test5 = sms.het_goldfeldquandt(lr.resid, lr.model.exog)
lzip(name5, test5)
#================================================
#================================================
#==================================Linearity test
#======================Harvey-Collier:
name6 = ['t value', 'p value']
test6 = sms.linear_harvey_collier(lr)
lzip(name6, test6)
import statsmodels.stats.diagnostic as ssd
name6 = ['t value', 'p value']
test6 = ssd.acorr_linear_rainbow(lr)
lzip(name6, test6)
#================================================
#================================================
#====Serial correlation (or) Autocorrelation test
#======================Durbin_watson:
#Durbin-Watson test for no autocorrelation of residuals
#printed with summary()
from statsmodels.stats.stattools import durbin_watson
print("Durbin-Watson: ", durbin_watson(lr.resid))
def harveyCollier(results):
name = ['t value', 'p value']
test = sms.linear_harvey_collier(results)
lzip(name, test)
def diagnostic_plots(self, linear_model):
"""
:param linear_model: Linear Model Fit on the Data
:return: None
This method validates the assumptions of Linear Model
"""
diagnostic_result = {}
summary = linear_model.summary()
#diagnostic_result['summary'] = str(summary)
# fitted values
fitted_y = linear_model.fittedvalues
# model residuals
residuals = linear_model.resid
# normalized residuals
residuals_normalized = linear_model.get_influence().resid_studentized_internal
# absolute squared normalized residuals
model_norm_residuals_abs_sqrt = np.sqrt(np.abs(residuals_normalized))
# leverage, from statsmodels internals
leverage = linear_model.get_influence().hat_matrix_diag
# cook's distance, from statsmodels internals
cooks = linear_model.get_influence().cooks_distance[0]
self.check_linearity_assumption(fitted_y, residuals)
self.check_residual_normality(residuals_normalized)
self.check_homoscedacticity(fitted_y, model_norm_residuals_abs_sqrt)
self.check_influcence(leverage, cooks, residuals_normalized)
# 1. Non-Linearity Test
try:
name = ['F value', 'p value']
test = sms.linear_harvey_collier(linear_model)
linear_test_result = lzip(name, test)
except Exception as e:
linear_test_result = str(e)
diagnostic_result['Non_Linearity_Test'] = linear_test_result
# 2. Hetroskedasticity Test
name = ['Lagrange multiplier statistic', 'p-value',
'f-value', 'f p-value']
test = sms.het_breuschpagan(linear_model.resid, linear_model.model.exog)
test_val = lzip(name, test)
diagnostic_result['Hetroskedasticity_Test'] = test_val
# 3. Normality of Residuals
name = ['Jarque-Bera', 'Chi^2 two-tail prob.', 'Skew', 'Kurtosis']
test = sms.jarque_bera(linear_model.resid)
test_val = lzip(name, test)
diagnostic_result['Residual_Normality_Test'] = test_val
# 4. MultiCollnearity Test
test = np.linalg.cond(linear_model.model.exog)
test_val = [('condition no',test)]
diagnostic_result['MultiCollnearity_Test'] = test_val
# 5. Residuals Auto-Correlation Tests
test = sms.durbin_watson(linear_model.resid)
test_val = [('p value', test)]
diagnostic_result['Residual_AutoCorrelation_Test'] = test_val
json_result = json.dumps(diagnostic_result)
return summary, json_result