def ols_plot(y, x, add_intercept=True, alpha=0.05, xlim=None, ax=None):
"""
Generate a scatter plot with OLS prediction plus confidence intervals
:param y:
:param x:
:param add_intercept:
:param alpha:
:param ax:
:return:
"""
if ax is None:
fig = plt.figure()
ax = fig.add_subplot(111)
try:
x = x.astype(float)
except Exception:
pass
if add_intercept:
X = sm.add_constant(x)
else:
X = x
model = sm.OLS(y, X)
res = model.fit()
# plot data
ax.scatter(x, y, marker='o')
if xlim is None:
xlim = np.array(ax.get_xlim())
xx = np.linspace(xlim[0], xlim[1], 100)
# compute prediction and confidence intervals
if add_intercept:
b0, b1 = res.params
sdev, lower, upper = wls_prediction_std(res,
sm.add_constant(xx),
alpha=alpha)
# b0_min, b0_max = res.conf_int(alpha=alpha)[0]
# b1_min, b1_max = res.conf_int(alpha=alpha)[1]
else:
b1 = res.params[0]
b0 = 0.
sdev, lower, upper = wls_prediction_std(res, xx, alpha=alpha)
# b0 = b0_min = b0_max = 0.
# b1_min, b1_max = res.conf_int(alpha=alpha)[0]
ax.plot(xx, b0 + b1 * xx, 'k-', lw=1.5)
ax.fill_between(xx, lower, upper, edgecolor='b', facecolor='b', alpha=0.4)
# lower = b0_min + b1_min * xlim
# upper = b0_max + b1_max * xlim
# ax.fill_between(xlim, lower, upper, edgecolor='b', facecolor='b', alpha=0.4)
ax.set_xlim(xlim)
return res, ax
def plot_regression(_output):
global analysis
def to_percent(x, position):
s = str(100 * x)
if plt.rcParams['text.usetex'] is True:
return s + r'$\%$'
else:
return s + '%'
mpl.style.use('classic')
fig = plt.figure()
x = np.array(analysis.iloc[:, 1], dtype=float)
y = np.array(analysis.iloc[:, 2], dtype=float) * 100
model_x = sm.add_constant(x)
model = sm.OLS(y, model_x)
fitted = model.fit()
fit = np.polyfit(x, y, 1)
fit_function = np.poly1d(fit)
sdev, lower, upper = wls_prediction_std(fitted, alpha=0.05)
plt.fill_between(x, lower, upper, color='#67e0d7', alpha=0.3)
plt.plot(x, fit_function(x), color='green')
x = np.array(analysis.iloc[:, 4], dtype=float)
y = np.array(analysis.iloc[:, 5], dtype=float) * 100
model_x = sm.add_constant(x)
model = sm.OLS(y, model_x)
fitted = model.fit()
fit = np.polyfit(x, y, 1)
fit_function = np.poly1d(fit)
sdev, lower, upper = wls_prediction_std(fitted, alpha=0.05)
plt.fill_between(x, lower, upper, color='#93e067', alpha=0.3)
plt.plot(x, fit_function(x), color='black')
formatter = FuncFormatter(to_percent)
plt.gca().xaxis.set_major_formatter(formatter)
plt.xticks(fontsize=20)
plt.yticks(fontsize=20)
plt.xlim(0, 1)
plt.ylim(0, 10)
circle1 = mlines.Line2D(
[], [],
color='green',
markerfacecolor="green",
label='AEP Risk (CDC Definition)') # Make a circle for the legend
circle2 = mlines.Line2D(
[], [],
color='black',
markerfacecolor="black",
label='AEP Risk (Actual)') # Make a circle for the legend
plt.legend(handles=[circle1, circle2],
numpoints=1,
prop={'size': 15},
loc=2)
plt.title('Compliance with CDC Recommendation (%)', fontsize=20)
plt.tight_layout()
plt.savefig(_output + '.pdf')
plt.savefig(_output + '.jpg', bbox_inches='tight')
def _regional_prediction(X, X_pred, Y, i):
mod = sm.OLS(np.log(Y[i]), X)
res = mod.fit()
y_pred = res.predict(X_pred)
_, _, std_u = wls_prediction_std(res, exog=X_pred, alpha=1-0.6827) # 1 s.d.
_, ci_l, ci_u = wls_prediction_std(res, exog=X_pred, alpha=1-0.95) # 95% CI
return y_pred, std_u, ci_l, ci_u, res.params[1]
def predict(self, ID, ALPHA=0.5):
list1 = get_data(ID)
vector = self.vectorizer.transform([list1[0]])
vector = self.lsa.transform(vector)
array = np.array([list1[1:4]])**2.0 / self.sum
array = array**0.5
vector = np.hstack([vector, array])
length = vector.shape[1]
'''
for i in range(length):
tmp = vector[0][i] * vector[0][i]
tmp = np.array([[tmp]])
vector = np.hstack([vector, tmp])
'''
for i in range(length):
for j in range(i, length):
tmp = vector[0][i] * vector[0][j]
tmp = np.array([[tmp]])
vector = np.hstack([vector, tmp])
vector = del_vector(vector, self.dellist)
estimated = self.results.predict(vector)
prstdn, infa, supa = wls_prediction_std(self.results,
vector,
alpha=ALPHA)
if infa[0] < 0:
infa[0] = 0
return estimated[0]**2.0, infa[0]**2.0, supa[0]**2.0
def visualize_linear_regression(data,
fit,
stock,
benchmark,
axis_low=-0.1,
axis_high=0.1,
show_std=False):
"""Create a scatter plot and linear model of the stock returns vs. the benchmark returns.
Arguments:
data -- a tidy DataFrame, with columns stock_ret, bench_ret, and const
fit -- a linear regression result
stock -- name of the stock
benchmark -- name of the benchmark index
axis_low -- lowest value for x and y axes (defult -0.1)
axis_high -- highest value for x and y axes (defult 0.1)
show_std -- whether to show upper and lower bands around answer (default False)
"""
ax = data.plot(kind='scatter',
x='bench_ret',
y='stock_ret',
title='1-Day Returns',
xlim=(axis_low, axis_high),
ylim=(axis_low, axis_high))
X_new = pd.DataFrame({'bench_ret': [axis_low, axis_high]})
X_new['const'] = 1
preds = fit.predict(X_new)
plt.plot(X_new['bench_ret'], preds, 'r-')
if show_std:
_, lower, upper = wls_prediction_std(fit, X_new)
plt.plot(X_new['bench_ret'], lower, 'r--', X_new['bench_ret'], upper,
'r--')
ax.set_xlabel(benchmark)
ax.set_ylabel(stock)
ax.set_aspect(1)
def get_predicted_y_PI(self, x_pred, alpha=0.05):
""" :returns prediction interval of the y at the provided x values """
X_pred = self.f.get_X(x_pred)
sdev, lower, upper = wls_prediction_std(self.fitted,
exog=X_pred,
alpha=alpha)
return lower, upper
def try_prod24h_before(
columns=['Tout', 'vWind', 'vWindavg24', 'prod24h_before'],
add_const=False,
y=y):
plt.close('all')
X = all_data[columns]
res = mlin_regression(y, X, add_const=add_const)
timesteps = ens.gen_hourly_timesteps(dt.datetime(2015, 12, 17, 1),
dt.datetime(2016, 1, 15, 0))
plt.subplot(2, 1, 1)
plt.plot_date(timesteps, y, 'b', label='Actual prodution')
plt.plot_date(timesteps, res.fittedvalues, 'r', label='Weather model')
prstd, iv_l, iv_u = wls_prediction_std(res)
plt.plot_date(timesteps, iv_u, 'r--', label='95% conf. int.')
plt.plot_date(timesteps, iv_l, 'r--')
plt.ylabel('MW')
plt.legend(loc=2)
plt.subplot(2, 1, 2)
plt.plot_date(timesteps, res.resid, '-', label='Residual')
plt.ylabel('MW')
plt.legend()
print "MAE = " + str(mae(res.resid))
print "MAPE = " + str(mape(res.resid, y))
print "RMSE = " + str(rmse(res.resid))
print res.summary()
return res
def plot_locality_regression(snps, cob, gene_limit=10):
# Get degree and bootstrap degree
log('Fetching Empirical Degree')
degree = cob.locality(
cob.refgen.candidate_genes(snps, gene_limit=gene_limit,
chain=True)).sort('local')
log('Fetching BS Degree')
#bsdegree = pd.concat([cob.locality(cob.refgen.bootstrap_candidate_genes(snps,gene_limit=gene_limit,chain=True)) for x in range(50)]).sort('local')
# get OLS for the bootstrapped degree
log('Fitting models')
model = sm.OLS(degree['global'], degree.local)
res = model.fit()
std, iv_l, iv_u = wls_prediction_std(res)
# plot the bootstrapped data
fig, ax = pylab.subplots(figsize=(8, 6))
fig.hold(True)
ax.set_xlim(0, max(degree.local))
ax.set_ylim(0, max(degree['global']))
# plot the bootstraps std
# plot the true data
log('Plotting Empirical')
ax.plot(degree.local, degree['global'], 'o', label='Empirical')
log('Plotting Residuals')
ax.plot(degree.local, res.fittedvalues, '--')
ax.plot(degree.local, res.fittedvalues + 2.5 * std, 'r--')
ax.plot(degree.local, res.fittedvalues - 2.5 * std, 'r--')
ax.set_xlabel('Number Local Interactions')
ax.set_ylabel('Number Global Interactions')
log('Saving Figure')
fig.savefig('{}_locality.png'.format(cob.name))
def linreg_stock(stock_ticker='AAPL', start_date = '2019-12-01',
end_date = '2020-02-05', visualize=False):
"""
Defines an ordinary linear regression, between time and
stock price. The function returns the 95% confidence interval
of the slope beta
"""
this_stock = Stock(stock_ticker)
panel_data = this_stock.get_price_history(
start_date=start_date, end_date=end_date)
if panel_data.shape[0] == 0:
return [np.nan, np.nan]
panel_data['x_val'] = list(range(panel_data.shape[0]))
X = panel_data['x_val']
y = panel_data['Open'].values/panel_data['Open'].values[0]
X = sm.add_constant(X)
model = sm.OLS(y, X)
results = model.fit()
A = results.conf_int(alpha=0.05, cols=None)
beta_lower = A[0]['x_val']
beta_upper = A[1]['x_val']
if visualize:
prstd, iv_l, iv_u = wls_prediction_std(results)
plt.plot(panel_data['x_val'], y, 'ro')
plt.plot(panel_data['x_val'], results.fittedvalues, 'r--.', label="OLS")
plt.plot(panel_data['x_val'], iv_l, 'b--.')
plt.plot(panel_data['x_val'], iv_u, 'b--.')
return [beta_lower, beta_upper]
def LR(df, options):
origsize = len(df)
ldf = df.copy()
if 'divisor' in options:
ldf = df.tail(int(origsize / options['divisor']))
x = np.arange(len(ldf))
X = sm.add_constant(x)
res = sm.OLS(ldf, X).fit()
print(res.summary())
std, lower, upper = wls_prediction_std(res)
middle = res.predict()
nfill = origsize - len(ldf)
if nfill < origsize:
empty = np.full_like(np.arange(nfill), np.nan, dtype=np.double)
std = np.append(empty, std)
lower = np.append(empty, lower)
upper = np.append(empty, upper)
middle = np.append(empty, middle)
return std, middle, lower, upper
def user_model(data):
"""
This function allows the user to enter their own linear regression
model formula, which is then run in the statsmodels package and
returns model results.
"""
# List available covariates in the data set
print('The data set contains the following covariates: \n')
print(list(data.columns), '\n')
# Prompt user to input model formula, in R type syntax
userFormula = choose_data = input('Enter your regression model formula, using syntax as shown: \n \n dependent_variable ~ covariate1 + covariate 2 + ... \n \n')
# Run the user-defined model as a statsmodels linear regression
userModel = smf.ols(formula=userFormula, data=data).fit()
print('\n', userModel.summary(), '\n')
# Retrieve y variable and time variable for plotting
yvar = userModel.model.endog_names
y = data[yvar]
timeVar = list(data.columns[data.dtypes == 'datetime64[ns]'])
x = data[timeVar]
# covars = list(userModel.params.keys())
# Plot dependent variable data and model fitted values vs time
prstd, iv_l, iv_u = wls_prediction_std(userModel)
fig = plt.figure(figsize=(12,6))
plt.plot(x, userModel.fittedvalues, 'r.', alpha=0.2, label='Fitted Values')
plt.plot(x, y, 'b.', alpha=0.2, label='%s data' % yvar)
plt.legend(loc='upper left')
plt.title('%s actual data and model fitted values' % yvar, fontsize='x-large')
def get_prediction(res, x):
"""
得到模型的预测结果以及结果的上下限
"""
prstd, ci_low, ci_up = wls_prediction_std(res, alpha=0.05)
pred = res.predict(x)
return pd.DataFrame({"ci_low": ci_low, "pred": pred, "ci_up": ci_up})
def dataframe_ordinary_least_squares(dataframe_in,
x_col_name,
y_col_name,
showplot=False):
x = dataframe_in[x_col_name].to_numpy()
X = sm.add_constant(x)
X = np.array(X, dtype=float)
y = dataframe_in[y_col_name].to_numpy()
model = sm.OLS(y, X)
results = model.fit()
prstd, iv_l, iv_u = wls_prediction_std(results)
dataframe_in['OLS Values'] = results.fittedvalues
dataframe_in['Confidence Upper'] = iv_u
dataframe_in['Confidence Lower'] = iv_l
if (showplot == True):
print(results.summary())
fig, ax = plt.subplots()
ax.scatter(x, y, color="#778899", label="Test Volume")
ax.plot(x,
dataframe_in['OLS Values'],
".--",
color="#4682B4",
label="Ordinary Least Squares Regression")
ax.plot(x, iv_u, color="#F08080", ls=":")
ax.plot(x, iv_l, color="#F08080", ls=":")
plt.show()
def plot_locality_regression(snps,cob,gene_limit=10):
# Get degree and bootstrap degree
log('Fetching Empirical Degree')
degree = cob.locality(cob.refgen.candidate_genes(snps,gene_limit=gene_limit,chain=True)).sort('local')
log('Fetching BS Degree')
#bsdegree = pd.concat([cob.locality(cob.refgen.bootstrap_candidate_genes(snps,gene_limit=gene_limit,chain=True)) for x in range(50)]).sort('local')
# get OLS for the bootstrapped degree
log('Fitting models')
model = sm.OLS(degree['global'],degree.local)
res = model.fit()
std, iv_l, iv_u = wls_prediction_std(res)
# plot the bootstrapped data
fig,ax = pylab.subplots(figsize=(8,6))
fig.hold(True)
ax.set_xlim(0,max(degree.local))
ax.set_ylim(0,max(degree['global']))
# plot the bootstraps std
# plot the true data
log('Plotting Empirical')
ax.plot(degree.local,degree['global'],'o',label='Empirical')
log('Plotting Residuals')
ax.plot(degree.local,res.fittedvalues,'--')
ax.plot(degree.local,res.fittedvalues+2.5*std,'r--')
ax.plot(degree.local,res.fittedvalues-2.5*std,'r--')
ax.set_xlabel('Number Local Interactions')
ax.set_ylabel('Number Global Interactions')
log('Saving Figure')
fig.savefig('{}_locality.png'.format(cob.name))
def PlotFit(res, x):
prstd, iv_l, iv_u = wls_prediction_std(res)
fig, ax = plt.subplots(figsize=(8, 6))
ax.plot(x, 'o', label='data')
#ax.plot(x, y_true, 'b-', label="True")
ax.plot(x.index, res.fittedvalues, 'r--.', label="OLS")
ax.plot(x.index, iv_u, 'r--')
ax.plot(x.index, iv_l, 'r--')
# Draw the predictions for one year into the future
time_today = np.datetime64(datetime.today())
#print((time_today-x.index.values[-1])/np.timedelta64(5724000, 's'))
dtRange = np.linspace(
pd.Timestamp(time_today).value,
pd.Timestamp(time_today + np.timedelta64(31536000, 's')).value, 4)
dtRange = pd.to_datetime(dtRange)
Xnew = np.ones((x.shape[0] + 4, 2)) # adding the constant
Xnew[:, 1] = np.arange(x.shape[0] + 4)
Xnew = sm1.add_constant(Xnew)
#print(Xnew)
ynewpred = res.predict(Xnew)
#print(ynewpred)
ax.plot(x.index.union(dtRange), ynewpred, 'r', label="OLS prediction")
ax.legend(loc='best')
if draw: plt.show()
def mcp_model(df_sector, sector, thres_v):
# print('Check the correlation between site and satellite:')
# corr_sit_sat=pearsonr(df_regression['speed_sit'],df_regression['speed_sat'])
# if corr_sit_sat[0]<threshold_satcorr or corr_sit_sat[1]>threshold_p:
# print("Pearson's test p-value is %f %s %f, correlation between valuables is %f %s %f, therefore this satellite data should be rejected."%(corr_sit_sat[1],'>' if corr_sit_sat[1]>threshold_p else '<=',threshold_p,corr_sit_sat[0],'<' if corr_sit_sat[0]<threshold_satcorr else '>=',threshold_satcorr))
# sys.exit()
# else:
# print("Pearson's test p-value is %f <= %f, and the correlation between valuables is %f >= %f"%(corr_sit_sat[1],threshold_p,corr_sit_sat[0],threshold_satcorr))
# corr3_sit_sat=pearsonr(df_regression['speed3_sit'],df_regression['speed3_sat'])
# if corr3_sit_sat[0]<threshold_satcorr or corr3_sit_sat[1]>threshold_p:
# print("Pearson's test p-value is %f %s %f, correlation between valuables is %f %s %f, therefore this satellite data should be rejected."%(corr3_sit_sat[1],'>' if corr3_sit_sat[1]>threshold_p else '<=',threshold_p,corr3_sit_sat[0],'<' if corr3_sit_sat[0]<threshold_satcorr else '>=',threshold_satcorr))
# sys.exit()
# else:
# print("Pearson's test p-value is %f <= %f, and the correlation between valuables is %f >= %f"%(corr3_sit_sat[1],threshold_p,corr3_sit_sat[0],threshold_satcorr))
#
# print('Linear regression (speed_sit, veer) ~ speed_sat:')
# print('Cross validation process.')
# df_train,df_test=mcpprocess.holdout(df_regression,0.75)
# mcpmodel=lrm(df_train['speed_sat'],df_train['speed_sit'])
# print(mcpmodel.summary2())
df_regression = df_sector[df_sector.speed_sit > thres_v].reset_index(
drop=True)
#train:test=4:1
df_train, df_test = mcpprocess.holdout(df_regression, 0.2)
pre_std, Y_l, Y_u = wls_prediction_std(mcpmodel_v)
descriptive.rl_fit(df_regression.speed_sat, df_regression.speed_sit,
mcpmodel_v.fittedvalues, Y_l, Y_u, sector, True, False,
1)
descriptive.rl_residu(df_regression.speed_sat, mcpmodel_v.resid, sector,
True, False, 1)
descriptive.rl_qqplot(resid_norm, sector, True, False, 1)
def try_prod24h_before(columns=['Tout', 'vWind', 'vWindavg24', 'prod24h_before'], add_const=False, y=y):
plt.close('all')
X = all_data[columns]
res = mlin_regression(y, X, add_const=add_const)
timesteps = ens.gen_hourly_timesteps(dt.datetime(2015,12,17,1), dt.datetime(2016,1,15,0))
plt.subplot(2,1,1)
plt.plot_date(timesteps, y, 'b', label='Actual prodution')
plt.plot_date(timesteps, res.fittedvalues, 'r', label='Weather model')
prstd, iv_l, iv_u = wls_prediction_std(res)
plt.plot_date(timesteps, iv_u, 'r--', label='95% conf. int.')
plt.plot_date(timesteps, iv_l, 'r--')
plt.ylabel('MW')
plt.legend(loc=2)
plt.subplot(2,1,2)
plt.plot_date(timesteps, res.resid, '-', label='Residual')
plt.ylabel('MW')
plt.legend()
print "MAE = " + str(mae(res.resid))
print "MAPE = " + str(mape(res.resid, y))
print "RMSE = " + str(rmse(res.resid))
print res.summary()
return res
def plot_best_model():
plt.close('all')
columns = ['Tout', 'Toutavg24', 'vWind', 'vWindavg24']#, 'hours', 'hours2','hours3', 'hours4','hours5', 'hours6']#, 'hours7', 'hours8']#,'hours5', 'hours6']
X = all_data[columns]
res = mlin_regression(y, X)
timesteps = ens.gen_hourly_timesteps(dt.datetime(2015,12,17,1), dt.datetime(2016,1,15,0))
plt.subplot(2,1,1)
plt.plot_date(timesteps, y, 'b', label='Actual prodution')
plt.plot_date(timesteps, res.fittedvalues, 'r', label='Weather model')
prstd, iv_l, iv_u = wls_prediction_std(res)
plt.plot_date(timesteps, iv_u, 'r--', label='95% conf. int.')
plt.plot_date(timesteps, iv_l, 'r--')
mean_day_resid = [res.resid[i::24].mean() for i in range(24)]
mean_resid_series = np.tile(mean_day_resid, 29)
plt.plot_date(timesteps, res.fittedvalues + mean_resid_series, 'g', label='Weather model + avg daily profile')
plt.ylabel('MW')
plt.legend(loc=2)
plt.subplot(2,1,2)
plt.plot_date(timesteps, res.resid, '-', label='Residual')
plt.plot_date(timesteps, mean_resid_series)
plt.ylabel('MW')
plt.legend()
mape = np.mean(np.abs((res.fittedvalues + mean_resid_series-y)/y))
mape2 = np.mean(np.abs((res.resid)/y))
mae = np.mean(np.abs((res.fittedvalues + mean_resid_series-y)))
print mape, mape2, mae
res.summary()
return res
def _predict(self, fit, df, **kwargs):
"""
Return a df with predictions and confidence interval
The df will contain the following columns:
- 'predicted': the model output
- 'interval_u', 'interval_l': upper and lower confidence bounds.
Parameters
----------
fit : Statsmodels fit
df : pandas DataFrame or None (default)
If None, use self.df
confint : float (default=0.05)
Confidence level for two-sided hypothesis, if given, overrides the default one.
Returns
-------
df : pandas DataFrame
same as df with additional columns 'predicted', 'interval_u' and 'interval_l'
"""
confint = kwargs.get('confint', self.confint)
# Add model results to data as column 'predictions'
if 'Intercept' in fit.model.exog_names:
df['Intercept'] = 1.0
df['predicted'] = fit.predict(df)
if not self.allow_negative_predictions:
df.loc[df['predicted'] < 0, 'predicted'] = 0
prstd, interval_l, interval_u = wls_prediction_std(
fit, df[fit.model.exog_names])
df['interval_l'] = interval_l
df['interval_u'] = interval_u
return df
def plot_vol_surface(self, x, y, contract, put_call):
"""Plot surface using Ordinary Least Square Fit."""
df = pd.DataFrame(columns=['x', 'y'])
df['x'] = x
df['y'] = y
degree = 3
try:
weights = np.polyfit(x, y, degree)
model = np.poly1d(weights)
results = smf.ols(formula='y ~ model(x)', data=df).fit()
prstd, iv_l, iv_u = wls_prediction_std(results)
fig, ax = plt.subplots(figsize=(8, 6))
plt.title(
"Implied Vol for NG European Options = {0}, moneyness plot= log(K/F): tradeDate: {1}"
.format(contract, self.tradeDate))
ax.plot(x, y, 'o', label="{0} Implied Vol".format(put_call))
ax.plot(x, results.fittedvalues, 'r--.', label="OLS")
ax.plot(x, iv_u, 'r--')
ax.plot(x, iv_l, 'r--')
ax.legend(loc='best')
plt.xlabel("Moneyness: log(K/F)")
plt.ylabel("Implied Vol.")
plt.axvline(0, color='k')
plt.show()
print(prstd)
except ValueError:
logging.info("ValueError!")
def visualize_linear_regression(data,
fit,
response_name,
predictor_name,
show_std=False):
"""Create a scatter plot and linear model of the response variable (column 1) vs. predictor variable (column 2).
Arguments:
data -- a tidy DataFrame, with response in column 1, predictor in column 2, and constant in column 3
fit -- a linear regression result
response_name -- name of the response variable
predictor_name -- name of the predictor variable
show_std -- whether to show upper and lower bands around answer (default False)
"""
ax = data.plot(
kind='scatter',
x=1,
y=0,
title=('Relationship of %s vs. %s' % (response_name, predictor_name)),
#xlim=(axis_low, axis_high), ylim=(axis_low, axis_high)
)
X_new = pd.DataFrame({'predictor': ax.get_xlim()})
X_new['const'] = 1
preds = fit.predict(X_new)
plt.plot(X_new['predictor'], preds, 'r-')
if show_std:
_, lower, upper = wls_prediction_std(fit, X_new)
plt.plot(X_new['predictor'], lower, 'r--', X_new['predictor'], upper,
'r--')
ax.set_xlabel(predictor_name)
ax.set_ylabel(response_name)
def test_ci(self):
res_wls = self.res_wls
prstd, iv_l, iv_u = wls_prediction_std(res_wls)
pred_res = get_prediction(res_wls)
ci = pred_res.conf_int(obs=True)
assert_allclose(pred_res.se_obs, prstd, rtol=1e-13)
assert_allclose(ci, np.column_stack((iv_l, iv_u)), rtol=1e-13)
sf = pred_res.summary_frame()
col_names = [
'mean', 'mean_se', 'mean_ci_lower', 'mean_ci_upper',
'obs_ci_lower', 'obs_ci_upper'
]
assert_equal(sf.columns.tolist(), col_names)
pred_res2 = res_wls.get_prediction()
ci2 = pred_res2.conf_int(obs=True)
assert_allclose(pred_res2.se_obs, prstd, rtol=1e-13)
assert_allclose(ci2, np.column_stack((iv_l, iv_u)), rtol=1e-13)
sf2 = pred_res2.summary_frame()
assert_equal(sf2.columns.tolist(), col_names)
def visualizeModel(re, data, features, labels):
"""
模型可视化
"""
# 计算预测结果的标准差，预测下界，预测上界
prstd, preLow, preUp = wls_prediction_std(re, alpha=0.05)
# 为在Matplotlib中显示中文，设置特殊字体
plt.rcParams['font.sans-serif'] = ['SimHei']
# 创建一个图形框
fig = plt.figure(figsize=(6, 6), dpi=80)
# 在图形框里只画一幅图
ax = fig.add_subplot(111)
# 在Matplotlib中显示中文，需要使用unicode
ax.set_title(u'%s' % "线性回归统计分析示例")
# 画点图，用蓝色圆点表示原始数据
ax.scatter(data[features],
data[labels],
color='b',
label=u'%s: $y = x + \epsilon$' % "真实值")
# 画线图，用红色虚线表示95%置信区间
ax.plot(data[features], preUp, "r--", label=u'%s' % "95%置信区间")
ax.plot(data[features], re.predict(data[features]), color='r',
label=u'%s: $y = %.3fx$'\
% ("预测值", re.params[features]))
ax.plot(data[features], preLow, "r--")
legend = plt.legend(shadow=True)
legend.get_frame().set_facecolor('#6F93AE')
plt.show()
def loess_normative_model(self):
""" Compute classical normative model."""
if self.bins is None:
self._create_bins()
# format data
data = self.data[[self.conf, self.score]].to_numpy(dtype=np.float64)
# take the controls
ctr_mask, _ = self._get_masks()
ctr = data[ctr_mask]
self.zm = np.zeros(self.bins.shape[0]) # mean
self.zstd = np.zeros(self.bins.shape[0]) # standard deviation
self.zci = np.zeros([self.bins.shape[0], 2]) # confidence interval
for i, bin_center in enumerate(self.bins):
mu = np.array(bin_center) # bin_center value (age or conf)
bin_mask = (abs(ctr[:, :1] - mu) < self.bin_width) * 1.
idx = [u for (u, v) in np.argwhere(bin_mask)]
scores = ctr[idx, 1]
adj_conf = ctr[idx, 0] - mu # confound relative to bin center
# if more than 2 non NaN values do the model
if (~np.isnan(scores)).sum() > 2:
mod = sm.WLS(scores,
sm.tools.add_constant(adj_conf,
has_constant='add'),
missing='drop',
weight=bin_mask.flatten()[idx],
hasconst=True).fit()
self.zm[i] = mod.params[0] # mean
# std and confidence intervals
prstd, iv_l, iv_u = wls_prediction_std(mod, [0, 0])
self.zstd[i] = prstd
self.zci[i, :] = mod.conf_int()[0, :] # [iv_l, iv_u]
else:
self.zm[i] = np.nan
self.zci[i] = np.nan
self.zstd[i] = np.nan
dists = [np.abs(conf - self.bins) for conf in self.data[self.conf]]
idx = [np.argmin(d) for d in dists]
m = np.array([self.zm[i] for i in idx])
std = np.array([self.zstd[i] for i in idx])
nmodel = (self.data[self.score] - m) / std
self.data['LOESS_pred'] = nmodel
self.data['LOESS_residuals'] = self.data[
self.score] - self.data['LOESS_pred']
score = self._get_score()
res = self.data['LOESS_residuals'].to_numpy(dtype=np.float64)
self.SMSE_LOESS = (np.mean(res[ctr_mask]**2)**0.5) / np.std(
score[ctr_mask])
self._loess_rank()
def summary_obs(res, alpha=0.05):
from scipy import stats
from statsmodels.sandbox.regression.predstd import wls_prediction_std
infl = Influence(res)
#standard error for predicted mean
#Note: using hat_matrix only works for fitted values
predict_mean_se = np.sqrt(infl.hat_matrix_diag*res.mse_resid)
tppf = stats.t.isf(alpha/2., res.df_resid)
predict_mean_ci = np.column_stack([
res.fittedvalues - tppf * predict_mean_se,
res.fittedvalues + tppf * predict_mean_se])
#standard error for predicted observation
predict_se, predict_ci_low, predict_ci_upp = wls_prediction_std(res)
predict_ci = np.column_stack((predict_ci_low, predict_ci_upp))
#standard deviation of residual
resid_se = np.sqrt(res.mse_resid * (1 - infl.hat_matrix_diag))
table_sm = np.column_stack([
np.arange(res.nobs) + 1,
res.model.endog,
res.fittedvalues,
predict_mean_se,
predict_mean_ci[:,0],
predict_mean_ci[:,1],
predict_ci[:,0],
predict_ci[:,1],
res.resid,
resid_se,
infl.resid_studentized_internal,
infl.cooks_distance()[0]
])
#colnames, data = zip(*table_raw) #unzip
data = table_sm
ss2 = ['Obs', 'Dep Var\nPopulation', 'Predicted\nValue', 'Std Error\nMean Predict', 'Mean ci\n95% low', 'Mean ci\n95% upp', 'Predict ci\n95% low', 'Predict ci\n95% upp', 'Residual', 'Std Error\nResidual', 'Student\nResidual', "Cook's\nD"]
colnames = ss2
#self.table_data = data
#data = np.column_stack(data)
data = np.round(data,4)
#self.table = data
from statsmodels.iolib.table import SimpleTable, default_html_fmt
from statsmodels.iolib.tableformatting import fmt_base
from copy import deepcopy
fmt = deepcopy(fmt_base)
fmt_html = deepcopy(default_html_fmt)
fmt['data_fmts'] = ["%4d"] + ["%6.3f"] * (data.shape[1] - 1)
#fmt_html['data_fmts'] = fmt['data_fmts']
st = SimpleTable(data, headers=colnames, txt_fmt=fmt,
html_fmt=fmt_html)
return st, data, ss2
def predict_y_with_model(model,
intercept_included: bool,
independent_variables: List[List[float]],
iv_names: List[str],
significance_level=0.1):
"""
Format of independent_variables:
x1 [[1, 2, 3, 4, 5],
x2 [5, 4, 3, 2, 1],
x3 [6, 6, 6, 6, 6]]
"""
ivs = independent_variables
assert significance_level < 0.2
print('Predicting y with model (significance_level == {}):'.format(
significance_level))
model_parameters = {}
if intercept_included:
model_parameters['intercept'] = 1
for i in range(len(ivs)):
model_parameters[iv_names[i]] = ivs[i]
print(model_parameters)
predicted_values = model.predict(pd.DataFrame(model_parameters))
results = []
for i in range(len(independent_variables[0])):
tmp = []
for j in range(len(iv_names)):
tmp.append(independent_variables[j][i])
tmp.append(predicted_values[i])
results.extend([tmp])
results_pd = pd.DataFrame(results)
headers = []
for i in range(len(iv_names)):
headers.append(iv_names[i])
headers.append('Predicted Value')
results_pd.columns = headers
if intercept_included:
exogenous_parameters = []
for i in range(len(ivs[0])):
temp_iv = [1]
for j in range(len(ivs)):
temp_iv.append(ivs[j][i])
exogenous_parameters.append(temp_iv)
# print(f'exogenous_parameters: {exogenous_parameters}')
results_pd['Prediction Std'], results_pd['Lowers'], results_pd[
'Uppers'] = wls_prediction_std(model,
exog=exogenous_parameters,
weights=1,
alpha=significance_level)
else:
print(
'Interval prediction not available if intercept is not included.')
print(results_pd)
def fit(self, x, y):
x = array(x).reshape(-1, 1)
model = OLS(y, PolynomialFeatures(2).fit_transform(x)).fit()
self.m = model.predict(
PolynomialFeatures(2).fit_transform(AGES.reshape(-1, 1)))
self.s = wls_prediction_std(
model,
PolynomialFeatures(2).fit_transform(AGES.reshape(-1, 1)))[0]
return self
def plot(ts, trend=True, interval=False, outliers=False, ax=None, **kwargs):
'''
Plot a timeseries with optionl trend, 2 standard deviation interval and outliers
Parameters
----------
ts : A DataFrame or Series with a timeseries index with all numeric columns
trend : overlay trend linear?
interval : overlay a 2 standard deviation interval?
outliers : overlay outliers?
kwargs : aguments passed to isoutler
ax : axes to draw on (optional)
Returns
-------
axes object
'''
if not ax:
ax = gca()
# ols won't accept a date so create time in seconds from first date as the independant variable
if isinstance(ts, pd.Series):
df = (ts).to_frame() # Unify handeling of Series and DataFrame
else:
df = ts.copy()
cols = df.select_dtypes(include=[np.number]).columns
df['__Seconds'] = (ts.index - ts.index.min()).astype('timedelta64[s]')
for col in cols:
res = smf.ols(formula=col + ' ~ __Seconds', data=df).fit()
# Plot this first to get the better pandas timeseries drawing of dates on x axis
df[col].plot(ax=ax,
label="{} (r^2 = {:2.2})".format(col, res.rsquared)
if trend else col)
if trend:
res.fittedvalues.plot(ax=ax, style='--g', label="")
if interval:
prstd, iv_l, iv_u = wls_prediction_std(res)
ax.fill_between(iv_l.index,
iv_l,
iv_u,
color='#888888',
alpha=0.25)
if outliers:
df_outliers = df[col][isoutlier(df[col], **kwargs)]
if len(df_outliers) > 0:
df_outliers.plot(ax=ax, style='r*', label="")
return ax
def plot_fit(results, exog_idx, y_true=None, ax=None, **kwargs):
"""Plot fit against one regressor.
This creates one graph with the scatterplot of observed values compared to
fitted values.
Parameters
----------
results : result instance
result instance with resid, model.endog and model.exog as attributes
x_var : int or str
Name or index of regressor in exog matrix.
y_true : array_like
(optional) If this is not None, then the array is added to the plot
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
kwargs
The keyword arguments are passed to the plot command for the fitted
values points.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
"""
fig, ax = utils.create_mpl_ax(ax)
exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
results = maybe_unwrap_results(results)
#maybe add option for wendog, wexog
y = results.model.endog
x1 = results.model.exog[:, exog_idx]
x1_argsort = np.argsort(x1)
y = y[x1_argsort]
x1 = x1[x1_argsort]
ax.plot(x1, y, 'bo', label=results.model.endog_names)
if not y_true is None:
ax.plot(x1, y_true[x1_argsort], 'b-', label='True values')
title = 'Fitted values versus %s' % exog_name
prstd, iv_l, iv_u = wls_prediction_std(results)
ax.plot(x1, results.fittedvalues[x1_argsort], 'D', color='r',
label='fitted', **kwargs)
ax.vlines(x1, iv_l[x1_argsort], iv_u[x1_argsort], linewidth=1, color='k',
alpha=.7)
#ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1,
# color='k')
ax.set_title(title)
ax.set_xlabel(exog_name)
ax.set_ylabel(results.model.endog_names)
ax.legend(loc='best')
return fig
def calculate_wls_prediction_std(result):
"""
:return:
predstd : array_like, standard error of prediction same length as rows of exog
iv_l : array_like, lower confidence bound
iv_u : array_like, upper confidence bound
"""
# predstd, iv_l, iv_u = wls_prediction_std(result)
return wls_prediction_std(result)
def plot_fit(res, exog_idx, exog_name='', y_true=None, ax=None, fontsize='small'):
"""Plot fit against one regressor.
This creates one graph with the scatterplot of observed values compared to
fitted values.
Parameters
----------
res : result instance
result instance with resid, model.endog and model.exog as attributes
exog_idx : int
index of regressor in exog matrix
y_true : array_like
(optional) If this is not None, then the array is added to the plot
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Notes
-----
This is currently very simple, no options or varnames yet.
"""
fig, ax = utils.create_mpl_ax(ax)
if exog_name == '':
exog_name = 'variable %d' % exog_idx
#maybe add option for wendog, wexog
y = res.model.endog
x1 = res.model.exog[:, exog_idx]
x1_argsort = np.argsort(x1)
y = y[x1_argsort]
x1 = x1[x1_argsort]
ax.plot(x1, y, 'bo', label='observed')
if not y_true is None:
ax.plot(x1, y_true[x1_argsort], 'b-', label='true')
title = 'fitted versus regressor %s' % exog_name
else:
title = 'fitted versus regressor %s' % exog_name
prstd, iv_l, iv_u = wls_prediction_std(res)
ax.plot(x1, res.fittedvalues[x1_argsort], 'k-', label='fitted') #'k-o')
#ax.plot(x1, iv_u, 'r--')
#ax.plot(x1, iv_l, 'r--')
ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1, color='k')
ax.set_title(title, fontsize=fontsize)
return fig
def plot_fit(res, exog_idx, exog_name='', y_true=None, ax=None, fontsize='small'):
"""Plot fit against one regressor.
This creates one graph with the scatterplot of observed values compared to
fitted values.
Parameters
----------
res : result instance
result instance with resid, model.endog and model.exog as attributes
exog_idx : int
index of regressor in exog matrix
y_true : array_like
(optional) If this is not None, then the array is added to the plot
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Notes
-----
This is currently very simple, no options or varnames yet.
"""
fig, ax = utils.create_mpl_ax(ax)
if exog_name == '':
exog_name = 'variable %d' % exog_idx
#maybe add option for wendog, wexog
y = res.model.endog
x1 = res.model.exog[:, exog_idx]
x1_argsort = np.argsort(x1)
y = y[x1_argsort]
x1 = x1[x1_argsort]
ax.plot(x1, y, 'bo', label='observed')
if not y_true is None:
ax.plot(x1, y_true[x1_argsort], 'b-', label='true')
title = 'fitted versus regressor %s' % exog_name
else:
title = 'fitted versus regressor %s' % exog_name
prstd, iv_l, iv_u = wls_prediction_std(res)
ax.plot(x1, res.fittedvalues[x1_argsort], 'k-', label='fitted') #'k-o')
#ax.plot(x1, iv_u, 'r--')
#ax.plot(x1, iv_l, 'r--')
ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1, color='k')
ax.set_title(title, fontsize=fontsize)
return fig
def odds_hat_l_u(self: LassoICSelector):
Xols = self.transform_to_ols(self.X)
yhat = self.ols.predict(self.ols_results.params, Xols)
# from equation 5
odds_hat = np.exp(yhat)
# the error in yhat is
(yhat_std, yhat_l, yhat_u) = wls_prediction_std(self.ols_results, Xols)
oddshat_l = np.exp(yhat - 2 * yhat_std)
oddshat_u = np.exp(yhat + 2 * yhat_std)
return odds_hat, oddshat_l, oddshat_u
def plot_OLS_CI(self, model, x, y, y_true): prstd, iv_l, iv_u = wls_prediction_std(model) fig, ax = plt.subplots(figsize=(8,6)) ax.plot(x, y, 'o', label="data") ax.plot(x, y_true, 'b-', label="True") ax.plot(x, model.fittedvalues, 'r--.', label="OLS") ax.plot(x, iv_u, 'r--') ax.plot(x, iv_l, 'r--') ax.legend(loc='best');
def lm(x, y):
"fits an OLS from statsmodels. returns tuple."
x, y = map(_plot_friendly, [x, y])
if _isdate(x[0]):
x = np.array([i.toordinal() for i in x])
df = pd.DataFrame({'x': x, 'y': y})
df['const'] = 1.
fit = sm.OLS(df.y, df[['x', 'const']]).fit()
df['predicted_y'] = fit.fittedvalues
df['predstd'], df['interval_l'], df['interval_u'] = wls_prediction_std(fit)
return (df.predicted_y, df.interval_l, df.interval_u)
def lm(x, y):
"fits an OLS from statsmodels. returns tuple."
x, y = map(_plot_friendly, [x, y])
if _isdate(x[0]):
x = np.array([i.toordinal() for i in x])
df = pd.DataFrame({"x": x, "y": y})
df["const"] = 1.0
fit = sm.OLS(df.y, df[["x", "const"]]).fit()
df["predicted_y"] = fit.fittedvalues
df["predstd"], df["interval_l"], df["interval_u"] = wls_prediction_std(fit)
return (df.predicted_y, df.interval_l, df.interval_u)
def _predict(self, fit, df):
"""
Return a df with predictions and confidence interval
Notes
-----
The df will contain the following columns:
- 'predicted': the model output
- 'interval_u', 'interval_l': upper and lower confidence bounds.
The result will depend on the following attributes of self:
confint : float (default=0.95)
Confidence level for two-sided hypothesis
allow_negative_predictions : bool (default=True)
If False, correct negative predictions to zero (typically for energy consumption predictions)
Parameters
----------
fit : Statsmodels fit
df : pandas DataFrame or None (default)
If None, use self.df
Returns
-------
df_res : pandas DataFrame
Copy of df with additional columns 'predicted', 'interval_u' and 'interval_l'
"""
# Add model results to data as column 'predictions'
df_res = df.copy()
if 'Intercept' in fit.model.exog_names:
df_res['Intercept'] = 1.0
df_res['predicted'] = fit.predict(df_res)
if not self.allow_negative_predictions:
df_res.loc[df_res['predicted'] < 0, 'predicted'] = 0
def rename(x):
if x == 'Intercept':
return x
else:
return self.quote(x)
prstd, interval_l, interval_u = wls_prediction_std(
fit,
df_res.rename(columns=rename)[fit.model.exog_names],
alpha=1 - self.confint)
df_res['interval_l'] = interval_l
df_res['interval_u'] = interval_u
if 'Intercept' in df_res:
df_res.drop(labels=['Intercept'], axis=1, inplace=True)
return df_res
def _predict(self, fit, df):
"""
Return a df with predictions and confidence interval
Notes
-----
The df will contain the following columns:
- 'predicted': the model output
- 'interval_u', 'interval_l': upper and lower confidence bounds.
The result will depend on the following attributes of self:
confint : float (default=0.95)
Confidence level for two-sided hypothesis
allow_negative_predictions : bool (default=True)
If False, correct negative predictions to zero (typically for energy consumption predictions)
Parameters
----------
fit : Statsmodels fit
df : pandas DataFrame or None (default)
If None, use self.df
Returns
-------
df_res : pandas DataFrame
Copy of df with additional columns 'predicted', 'interval_u' and 'interval_l'
"""
# Add model results to data as column 'predictions'
df_res = df.copy()
if 'Intercept' in fit.model.exog_names:
df_res['Intercept'] = 1.0
df_res['predicted'] = fit.predict(df_res)
if not self.allow_negative_predictions:
df_res.loc[df_res['predicted'] < 0, 'predicted'] = 0
def rename(x):
if x == 'Intercept':
return x
else:
return self.quote(x)
prstd, interval_l, interval_u = wls_prediction_std(fit,
df_res.rename(columns=rename)[fit.model.exog_names],
alpha=1 - self.confint)
df_res['interval_l'] = interval_l
df_res['interval_u'] = interval_u
if 'Intercept' in df_res:
df_res.drop(labels=['Intercept'], axis=1, inplace=True)
return df_res
def plot_locality(self,gene_list,bootstraps=10,num_windows=100,sd_thresh=2):
'''
Make a fancy locality plot.
'''
# Generate a blank fig
fig,ax = plt.subplots(figsize=(8,6))
fig.hold(True)
# Y axis is local degree (what we are TRYING to predict)
degree = self.locality(gene_list).sort('global')
ax.set_ylim(0,max(degree['local']))
ax.set_xlim(0,max(degree['global']))
if bootstraps > 0:
bs = pd.concat(
[self.locality(
self.refgen.bootstrap_candidate_genes(gene_list)
) for x in range(10)]
).sort('global')
ax.set_ylim(0,max(bs['local']))
ax.set_xlim(0,max(bs['global']))
plt.plot(bs['global'],bs['local'],'ro',alpha=0.05,label='Bootstraps')
# Plot the bootstraps and the empirical
plt.plot(degree['global'],degree['local'],'bo',label='Empirical')
emp_ols = sm.OLS(degree['local'],degree['global']).fit()
ax.plot(degree['global'],emp_ols.fittedvalues,'k:',label='Empirical OLS')
if bootstraps > 0:
# Get the OLS
bs_ols = sm.OLS(bs['local'],bs['global']).fit()
bs['resid'] = bs_ols.resid
bs['fitted'] = bs_ols.fittedvalues
ax.plot(bs['global'],bs_ols.fittedvalues,'g--',label='bootstrap OLS')
# Do lowess on the residuals
# We only care about windows within the empirical part
window_tick = len(bs)/num_windows
bs['window'] = [int(x/window_tick) for x in range(len(bs))]
# get std for each window
win_std = bs.groupby('window').apply(lambda df: df['resid'].std()).to_dict()
bs['std_envelope'] = [win_std[x] for x in bs.window.values]
# Plot confidence intervals
prstd, iv_l, iv_u = wls_prediction_std(bs_ols)
ax.plot(bs['global'], iv_u, 'g--',label='conf int.')
ax.plot(bs['global'], iv_l, 'g--')
# plot the
ax.plot(
bs['global'],bs['fitted']+(sd_thresh*bs['std_envelope']),'r--'
,label='{} s.d. envelope'.format(sd_thresh)
)
ax.plot(bs['global'],bs['fitted']-(sd_thresh*bs['std_envelope']),'r--')
ax.set_xlabel('Number Global Interactions')
ax.set_ylabel('Number Local Interactions')
legend = ax.legend(loc='best')
return plt
def predict(self, ID, ALPHA=0.5):
list1 = get_data(ID)
vector = self.vectorizer.transform([list1[0]])
vector = self.lsa.transform(vector)
array = np.array([list1[1:4]])**2.0 / self.sum
array = array**0.5
vector= np.hstack([vector, array])
vector = del_vector(vector, self.dellist)
estimated = self.results.predict(vector)
prstdn, infa, supa = wls_prediction_std(self.results, vector, alpha = ALPHA)
if infa[0] < 0:
infa[0] = 0
return estimated[0]**2.0, infa[0]**2.0, supa[0]**2.0
def run_ordinary_least_squares(ols_dates, ols_data, statsmodels_settings):
"""
This method receives the dates and prices of a Quandl data-set as well as settings for the StatsModels package,
it then calculates the regression lines and / or the confidence lines are returns the objects
"""
intercept = np.column_stack((ols_dates, ols_dates ** statsmodels_settings.exponent))
constant = sm.add_constant(intercept)
statsmodel_regression = sm.OLS(ols_data, constant).fit()
print(statsmodel_regression.summary())
if statsmodels_settings.confidence:
prstd, lower, upper = wls_prediction_std(statsmodel_regression)
return statsmodel_regression, lower, upper
else:
return statsmodel_regression
def main():
df = pickle.loads(open('OLS_data','r').read())
df = df.sort(columns='Median household income')
y = df['Tip Perc']
X = df[['Median household income','Income2','const']]
result = sm.OLS(y, X).fit()
yhat = result.predict(X)
prstd, iv_l, iv_u = wls_prediction_std(result)
plt.scatter(X['Median household income'],y,color = 'b', alpha = 0.9)
plt.plot(X['Median household income'],yhat, color = 'r', alpha = 0.7)
plt.plot(X['Median household income'], iv_u, '--', color ='r',alpha = 0.7, linewidth = 0.7)
plt.plot(X['Median household income'], iv_l, '--', color ='r', alpha = 0.7, linewidth = 0.7)
plt.text(125000, 24.5,'$R^2$=$%.3f$' % result.rsquared, ha='center', va='center')
plt.xlabel('Median Household Income ($)')
plt.ylabel('Average Tip Percentage')
plt.title('Regress Tip Percentage on Median Household Income')
plt.show()
def main():
df = pickle.loads(open("OLS_data", "r").read())
df = df.sort(columns="White")
y = df["Tip Perc"]
X = df[["White", "const"]]
result = sm.OLS(y, X).fit()
yhat = result.predict(X)
prstd, iv_l, iv_u = wls_prediction_std(result)
plt.scatter(X["White"], y, color="b", alpha=0.9)
plt.plot(X["White"], yhat, color="r", alpha=0.7)
plt.plot(X["White"], iv_u, "--", color="r", alpha=0.7, linewidth=0.7)
plt.plot(X["White"], iv_l, "--", color="r", alpha=0.7, linewidth=0.7)
plt.text(1.05, 25, "$R^2$=$%.3f$" % result.rsquared, ha="center", va="center")
plt.xlabel("White Rate")
plt.ylabel("Average Tip Percentage")
plt.title("Regress Tip Percentage on White Rate")
plt.show()
def lm(x, y, alpha=ALPHA):
"fits an OLS from statsmodels. returns tuple."
x, y = map(plot_friendly, [x,y])
if _isdate(x[0]):
x = np.array([i.toordinal() for i in x])
X = sm.add_constant(x)
fit = sm.OLS(y, X).fit()
prstd, iv_l, iv_u = wls_prediction_std(fit)
_, summary_values, summary_names = summary_table(fit, alpha=alpha)
df = pd.DataFrame(summary_values, columns=map(snakify, summary_names))
fittedvalues = df['predicted_value']
predict_mean_se = df['std_error_mean_predict']
predict_mean_ci_low = df['mean_ci_95%_low']
predict_mean_ci_upp = df['mean_ci_95%_upp']
predict_ci_low = df['predict_ci_95%_low']
predict_ci_upp = df['predict_ci_95%_upp']
return (fittedvalues, predict_mean_ci_low, predict_mean_ci_upp)
def returnOutliers(results, x, y, alpha=0.05):
o_x = []
o_y = []
#print results.cov_params().shape[0]
exog = results.model.exog
#print exog.shape
#print x.shape[0]
pred_y, iv_l, iv_u = wls_prediction_std(results, exog=x, weights=None, alpha=alpha)
i = 0
for val in y:
if (val > iv_u[i] or val < iv_l[i]):
o_x.append(x[i][1])
o_y.append(val)
i += 1
return o_x, o_y
def test_ci(self):
res_wls = self.res_wls
prstd, iv_l, iv_u = wls_prediction_std(res_wls)
pred_res = get_prediction(res_wls)
ci = pred_res.conf_int(obs=True)
assert_allclose(pred_res.se_obs, prstd, rtol=1e-13)
assert_allclose(ci, np.column_stack((iv_l, iv_u)), rtol=1e-13)
sf = pred_res.summary_frame()
col_names = ['mean', 'mean_se', 'mean_ci_lower', 'mean_ci_upper',
'obs_ci_lower', 'obs_ci_upper']
assert_equal(sf.columns.tolist(), col_names)
pred_res2 = res_wls.get_prediction()
ci2 = pred_res2.conf_int(obs=True)
assert_allclose(pred_res2.se_obs, prstd, rtol=1e-13)
assert_allclose(ci2, np.column_stack((iv_l, iv_u)), rtol=1e-13)
sf2 = pred_res2.summary_frame()
assert_equal(sf2.columns.tolist(), col_names)
# check that list works, issue 4437
x = res_wls.model.exog.mean(0)
pred_res3 = res_wls.get_prediction(x)
ci3 = pred_res3.conf_int(obs=True)
pred_res3b = res_wls.get_prediction(x.tolist())
ci3b = pred_res3b.conf_int(obs=True)
assert_allclose(pred_res3b.se_obs, pred_res3.se_obs, rtol=1e-13)
assert_allclose(ci3b, ci3, rtol=1e-13)
res_df = pred_res3b.summary_frame()
assert_equal(res_df.index.values, [0])
x = res_wls.model.exog[-2:]
pred_res3 = res_wls.get_prediction(x)
ci3 = pred_res3.conf_int(obs=True)
pred_res3b = res_wls.get_prediction(x.tolist())
ci3b = pred_res3b.conf_int(obs=True)
assert_allclose(pred_res3b.se_obs, pred_res3.se_obs, rtol=1e-13)
assert_allclose(ci3b, ci3, rtol=1e-13)
res_df = pred_res3b.summary_frame()
assert_equal(res_df.index.values, [0, 1])
def test_pred_interval(show_plot=False):
from ml_ext import examples
(coefs,df)=examples.gen_simplemodel_data(n=50,k=3)
df.sort('X1',inplace=True)
lr=LinModel()
X=df[df.columns[df.columns!='y']]
y=df.y
lr.fit(X=X,y=y)
lr.summary()
df_ci=lr.get_confidence_interval_for_mean(X)
df_pi=lr.get_prediction_interval(X)
#Now use statsmodels to compare
from statsmodels.sandbox.regression.predstd import wls_prediction_std
import statsmodels.api as sm
re = sm.OLS(y, X).fit()
prstd, iv_l, iv_u = wls_prediction_std(re)
if show_plot:
(fig,ax)=plt.subplots(nrows=2,ncols=1,figsize=[14,12])
cols=sns.color_palette('husl',n_colors=4)
ax[0].scatter(X.X1,y,label='y',color=cols[3],alpha=0.4)
ax[0].plot(X.X1,df_pi['upper_pred'],label='pred',color=cols[1],alpha=0.5)
ax[0].plot(X.X1,df_pi['lower_pred'],color=cols[1],alpha=0.5)
ax[0].plot(X.X1,df_ci['upper_mean'],color=cols[2],alpha=0.5)
ax[0].plot(X.X1,df_ci['lower_mean'],label='mean_ci',color=cols[2],alpha=0.5)
ax[0].scatter(X.X1,df_pi['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[0].legend(loc='best')
ax[1].scatter(X.X1,y,label='y',color=cols[3],alpha=0.4)
ax[1].scatter(X.X1,df_ci['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[1].plot(X.X1,iv_u,label='wls',color=cols[1],alpha=0.5)
ax[1].plot(X.X1,iv_l,color=cols[1],alpha=0.5)
ax[1].legend(loc='best')
#get difference between uppers from each and check they are within 1%
overall_diff=100*numpy.sum(iv_u-df_pi['upper_pred'])/numpy.sum(iv_u)
logging.debug("Overall % difference in prediction ranges for upper bound: {}".format(overall_diff))
assert overall_diff<0.1
def lm(x, y, alpha=ALPHA):
"fits an OLS from statsmodels. returns tuple."
x_is_date = _isdate(x.iloc[0])
if x_is_date:
x = np.array([i.toordinal() for i in x])
X = sm.add_constant(x)
fit = sm.OLS(y, X).fit()
prstd, iv_l, iv_u = wls_prediction_std(fit)
_, summary_values, summary_names = summary_table(fit, alpha=alpha)
df = pd.DataFrame(summary_values, columns=map(_snakify, summary_names))
# TODO: indexing w/ data frame is messing everything up
fittedvalues = df['predicted_value'].values
predict_mean_ci_low = df['mean_ci_95%_low'].values
predict_mean_ci_upp = df['mean_ci_95%_upp'].values
predict_ci_low = df['predict_ci_95%_low'].values
predict_ci_upp = df['predict_ci_95%_upp'].values
if x_is_date:
x = [Timestamp.fromordinal(int(i)) for i in x]
return (x, fittedvalues, predict_mean_ci_low, predict_mean_ci_upp)
def test_nonlinear():
np.random.seed(111)
n_sample = 50
max_val = 30
sig = 0.5
x = np.linspace(0, max_val, n_sample)
X = np.c_[x, np.sin(x), (x - 5)**2, np.ones(n_sample)]
beta = np.array([0.5, 0.5, -0.02, 5.0])
e = np.random.normal(size=n_sample)
#X = sm.add_constant(X, prepend=False)
y_true = np.dot(X, beta)
y = y_true + sig * e
for i in xrange(5):
print '%3d: %s %s' % (i, X[i, :], y[i])
print
print
model = sm.OLS(y, X)
results = model.fit()
print results.summary()
print
print
print results.params
print results.rsquared
print results.bse
print results.predict()
plt.figure()
plt.plot(x, y, 'o', x, y_true, 'b-')
prstd, iv_l, iv_u = wls_prediction_std(results)
plt.plot(x, results.fittedvalues, 'r--.')
plt.plot(x, iv_u, 'r--')
plt.plot(x, iv_l, 'r--')
plt.title('blue: true, red: OLS')
plt.show()
def predict(self, ID, ALPHA=0.5):
list1 = get_data(ID)
vector = self.vectorizer.transform([list1[0]])
vector = self.lsa.transform(vector)
array = np.array([list1[1:4]])**2.0 / self.sum
array = array**0.5
vector= np.hstack([vector, array])
length = vector.shape[1]
'''
for i in range(length):
tmp = vector[0][i] * vector[0][i]
tmp = np.array([[tmp]])
vector = np.hstack([vector, tmp])
'''
for i in range(length):
for j in range(i, length):
tmp = vector[0][i] * vector[0][j]
tmp = np.array([[tmp]])
vector = np.hstack([vector, tmp])
vector = del_vector(vector, self.dellist)
estimated = self.results.predict(vector)
prstdn, infa, supa = wls_prediction_std(self.results, vector, alpha = ALPHA)
if infa[0] < 0:
infa[0] = 0
return estimated[0]**2.0, infa[0]**2.0, supa[0]**2.0
def test_ci(self):
res_wls = self.res_wls
prstd, iv_l, iv_u = wls_prediction_std(res_wls)
pred_res = get_prediction(res_wls)
ci = pred_res.conf_int(obs=True)
assert_allclose(pred_res.se_obs, prstd, rtol=1e-13)
assert_allclose(ci, np.column_stack((iv_l, iv_u)), rtol=1e-13)
sf = pred_res.summary_frame()
col_names = ['mean', 'mean_se', 'mean_ci_lower', 'mean_ci_upper',
'obs_ci_lower', 'obs_ci_upper']
assert_equal(sf.columns.tolist(), col_names)
pred_res2 = res_wls.get_prediction()
ci2 = pred_res2.conf_int(obs=True)
assert_allclose(pred_res2.se_obs, prstd, rtol=1e-13)
assert_allclose(ci2, np.column_stack((iv_l, iv_u)), rtol=1e-13)
sf2 = pred_res2.summary_frame()
assert_equal(sf2.columns.tolist(), col_names)
def linear(data):
# Regression
x = []
y = []
for i in range(len(data)):
x.append(i)
for p in data[headers[1]]:
y.append(p)
x = np.array(x)
y = np.array(y)
x = x.reshape(-1, 1)
y = y.reshape(-1, 1)
x_line = np.column_stack((x, x**2))
x_cons = sm.add_constant(x_line)
model = sm.OLS(y, x_cons)
results = model.fit()
print (results.summary())
print ('Coefficients: ', results.params) # Save to pfd
print ('Standard errors: ', results.bse)
print ('R2: ', results.rsquared)
# Plot
prstd, iv_l, iv_u = wls_prediction_std(results)
fig, ax = plt.subplots()
title = "Linear Regression" ,headers[1]
plt.title(title)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.get_xaxis().tick_bottom()
ax.get_yaxis().tick_left()
plt.tick_params(axis="both", which="both", bottom="on", top="off",
labelbottom="on", left="off", right="off", labelleft="on")
ax.plot(x, y, label="data")
ax.plot(x, results.fittedvalues, 'r--.', label="OLS")
ax.plot(x, iv_u, 'c--')
ax.plot(x, iv_l, 'c--')
ax.legend(loc='best')
plt.savefig('linear.png', bbox_inches="tight")
# Fit and summary:
res = sm.OLS(y, X).fit()
print(res.summary())
# Extract other quantities of interest:
print('Parameters: ', res.params)
print('Standard errors: ', res.bse)
print('Predicted values: ', res.predict())
# Draw a plot to compare the true relationship to OLS predictions. Confidence intervals around the predictions are built using the ``wls_prediction_std`` command.
prstd, iv_l, iv_u = wls_prediction_std(res)
fig, ax = plt.subplots()
ax.plot(x, y, 'o', label="data")
ax.plot(x, y_true, 'b-', label="True")
ax.plot(x, res.fittedvalues, 'r--.', label="OLS")
ax.plot(x, iv_u, 'r--')
ax.plot(x, iv_l, 'r--')
ax.legend(loc='best');
# ## OLS with dummy variables
#
# We generate some artificial data. There are 3 groups which will be modelled using dummy variables. Group 0 is the omitted/benchmark category.
se = np.round(se,4) colnames = ['x1', 'const'] rownames = ['WLS', 'OLS', 'OLS_HC0', 'OLS_HC1', 'OLS_HC3', 'OLS_HC3'] tabl = SimpleTable(se, colnames, rownames, txt_fmt=default_txt_fmt) print(tabl) # Calculate OLS prediction interval: covb = res_ols.cov_params() prediction_var = res_ols.mse_resid + (X * np.dot(covb,X.T).T).sum(1) prediction_std = np.sqrt(prediction_var) tppf = stats.t.ppf(0.975, res_ols.df_resid) prstd_ols, iv_l_ols, iv_u_ols = wls_prediction_std(res_ols) # Draw a plot to compare predicted values in WLS and OLS: prstd, iv_l, iv_u = wls_prediction_std(res_wls) fig, ax = plt.subplots() ax.plot(x, y, 'o', label="Data") ax.plot(x, y_true, 'b-', label="True") # OLS ax.plot(x, res_ols.fittedvalues, 'r--') ax.plot(x, iv_u_ols, 'r--', label="OLS") ax.plot(x, iv_l_ols, 'r--') # WLS ax.plot(x, res_wls.fittedvalues, 'g--.')
def summary_table(res, alpha=0.05):
'''generate summary table of outlier and influence similar to SAS
Parameters
----------
alpha : float
significance level for confidence interval
Returns
-------
st : SimpleTable instance
table with results that can be printed
data : ndarray
calculated measures and statistics for the table
ss2 : list of strings
column_names for table (Note: rows of table are observations)
'''
from scipy import stats
from statsmodels.sandbox.regression.predstd import wls_prediction_std
infl = OLSInfluence(res)
#standard error for predicted mean
#Note: using hat_matrix only works for fitted values
predict_mean_se = np.sqrt(infl.hat_matrix_diag*res.mse_resid)
tppf = stats.t.isf(alpha/2., res.df_resid)
predict_mean_ci = np.column_stack([
res.fittedvalues - tppf * predict_mean_se,
res.fittedvalues + tppf * predict_mean_se])
#standard error for predicted observation
predict_se, predict_ci_low, predict_ci_upp = wls_prediction_std(res)
predict_ci = np.column_stack((predict_ci_low, predict_ci_upp))
#standard deviation of residual
resid_se = np.sqrt(res.mse_resid * (1 - infl.hat_matrix_diag))
table_sm = np.column_stack([
np.arange(res.nobs) + 1,
res.model.endog,
res.fittedvalues,
predict_mean_se,
predict_mean_ci[:,0],
predict_mean_ci[:,1],
predict_ci[:,0],
predict_ci[:,1],
res.resid,
resid_se,
infl.resid_studentized_internal,
infl.cooks_distance[0]
])
#colnames, data = zip(*table_raw) #unzip
data = table_sm
ss2 = ['Obs', 'Dep Var\nPopulation', 'Predicted\nValue', 'Std Error\nMean Predict', 'Mean ci\n95% low', 'Mean ci\n95% upp', 'Predict ci\n95% low', 'Predict ci\n95% upp', 'Residual', 'Std Error\nResidual', 'Student\nResidual', "Cook's\nD"]
colnames = ss2
#self.table_data = data
#data = np.column_stack(data)
from statsmodels.iolib.table import SimpleTable, default_html_fmt
from statsmodels.iolib.tableformatting import fmt_base
from copy import deepcopy
fmt = deepcopy(fmt_base)
fmt_html = deepcopy(default_html_fmt)
fmt['data_fmts'] = ["%4d"] + ["%6.3f"] * (data.shape[1] - 1)
#fmt_html['data_fmts'] = fmt['data_fmts']
st = SimpleTable(data, headers=colnames, txt_fmt=fmt,
html_fmt=fmt_html)
return st, data, ss2
__author__ = 'Yas' import numpy as np import statsmodels.api as sm import matplotlib.pyplot as plt from statsmodels.sandbox.regression.predstd import wls_prediction_std np.random.seed(1024) X= [1,2,3,4,5,6,7] #X = range(1,8) Y = [1,7,3,20,5,6,2] #X = sm.add_constant(X) wls_model = sm.WLS(Y,X, weights=[0.1,0.1,0.1,0.0,0.1,0.1,0.1]) res_wls = wls_model.fit() print res_wls.params print res_wls.tvalues #print(results.t_test([1, 0])) plt.plot(X, res_wls.fittedvalues, 'g--'); prstd, iv_l, iv_u = wls_prediction_std(res_wls) #print(results.f_test([0, 1])) plt.ylim(-50,50) plt.xlim(0,30) plt.plot(X,Y, 'o') plt.plot(X, iv_u, 'b--'); plt.plot(X, iv_l, 'r--'); #plt.plot(X,res_wls.f, '.') plt.show()
#Read data
filename = 'griliches.dta'
df = rd_stata(filename)
x = []
#===========Least square regression
#=====================
#lw VS multivariates
#=====================
x= df[['rns','mrt','smsa','med','iq','kww','age','s','expr']]
y = df.lw
X = sm.add_constant(x)
model = sm.OLS(y, X)
results = model.fit()
print(results.summary())
#plot the results
plt.figure();
plt.plot(x, y, 'o');
prstd, iv_l, iv_u = wls_prediction_std(results)
plt.plot(x, results.fittedvalues, 'g--.')
plt.plot(x, iv_u, 'r--')
plt.plot(x, iv_l, 'r--')
plt.xlabel('multivariates')
plt.ylabel('Log Wage')
plt.title('Multivariates');
plt.savefig('1-multivariates.png')
plt.show()
def regression_and_scatter(df_x_path, x_name, y_names, df_y_path=None, roi_normalize=True, confidence_intervals=False, prediction_intervals=False, animals=None, ): df = pd.read_csv(df_x_path, index_col=0) if df_y_path: dfy = pd.read_csv(df_y_path, index_col=0) df = pd.concat([df, dfy], axis=1) if animals: df = df.loc[animals] if roi_normalize: df[x_cols] = df[x_cols].apply(lambda x: (x / x.mean())) fig, ax = plt.subplots() ax.set_xmargin(0.1) ax.set_ymargin(0.11) df[x_cols] = df[x_cols].apply(lambda x: (x / x.mean())) fig, ax = plt.subplots() ax.set_xmargin(0.1) ax.set_ymargin(0.11) for ix, y_name in enumerate(y_names): x = df[[x_name]].values y = df[[y_name]].values x_ = sm.add_constant(x) # constant intercept term model = sm.OLS(y, x_) for ix, y_name in enumerate(y_names): x = df[[x_name]].values y = df[[y_name]].values x_ = sm.add_constant(x) # constant intercept term model = sm.OLS(y, x_) fitted = model.fit() x_pred = np.linspace(x.min(), x.max(), 50) x_pred2 = sm.add_constant(x_pred) y_pred = fitted.predict(x_pred2) y_hat = fitted.predict(x_) y_err = y - y_hat mean_x = x.mean() n = len(x) dof = n - fitted.df_model - 1 t = stats.t.ppf(0.05, df=dof) s_err = np.sum(np.power(y_err, 2)) if confidence_intervals: conf = t * np.sqrt((s_err/(n-2))*(1.0/n + (np.power((x_pred-mean_x),2) / ((np.sum(np.power(x_pred,2))) - n*(np.power(mean_x,2)))))) upper_conf = y_pred + abs(conf) lower_conf = y_pred - abs(conf) ax.fill_between(x_pred, lower_conf, upper_conf, color=qualitative_colorset[ix], alpha=0.3) if prediction_intervals: sdev_pred, lower_pred, upper_pred = wls_prediction_std(fitted, exog=x_pred2, alpha=0.05) ax.fill_between(x_pred, lower_pred, upper_pred, color=qualitative_colorset[ix], alpha=0.08) data_points = ax.plot(x,y,'o',color=qualitative_colorset[ix],markeredgecolor=qualitative_colorset[ix]) ax.tick_params(axis="both",which="both",bottom="off",top="off",length=0) ax.plot(x_pred, y_pred, '-', color=qualitative_colorset[ix], linewidth=2, label=y_name) plt.legend(loc="best")
def first_ens_prod_fig():
""" This plot is based on a production model taking into account:
Tout, vWind and the production 24 hours before
"""
plt.close('all')
cols = ['Tout', 'vWind', 'prod24h_before']
ts1 = ens.gen_hourly_timesteps(dt.datetime(2015,12,17,1), dt.datetime(2016,1,15,0))
ts2 = ens.gen_hourly_timesteps(dt.datetime(2016,1,20,1), dt.datetime(2016,1,28,0))
#load the data
fit_data = ens.repack_ens_mean_as_df()
fit_data['prod24h_before'] = sq.fetch_production(dt.datetime(2015,12,16,1), dt.datetime(2016,1,14,0))
vali_data = ens.repack_ens_mean_as_df(dt.datetime(2016,1,20,1), dt.datetime(2016,1,28,0))
vali_data['prod24h_before'] = sq.fetch_production(dt.datetime(2016,1,19,1), dt.datetime(2016,1,27,0))
# do the fit
X = fit_data[cols]
y = fit_data['prod']
res = mlin_regression(y, X, add_const=True)
fig, [ax1, ax2] = plt.subplots(2,1, figsize=(40,20))
# load ensemble data
ens_data1 = ens.load_ens_timeseries_as_df(ts_start=ts1[0], ts_end=ts1[-1])
ens_data1['prod24h_before'] = fit_data['prod24h_before']
ens_data2 = ens.load_ens_timeseries_as_df(ts_start=ts2[0], ts_end=ts2[-1])
ens_data2['prod24h_before'] = vali_data['prod24h_before']
all_ens_data = pd.concat([ens_data1, ens_data2])
all_ts = ts1 + ts2
# calculate production for each ensemble member
ens_prods = np.zeros((len(all_ts), 25))
for i in range(25):
ens_cols = ['Tout' + str(i), 'vWind' + str(i), 'prod24h_before']
ens_params = pd.Series({'Tout' + str(i):res.params['Tout'],
'vWind' + str(i):res.params['vWind'],
'const':res.params['const'],
'prod24h_before':res.params['prod24h_before']})
ens_prods[:,i] = linear_map(all_ens_data, ens_params, ens_cols)
# calculate combined confint
prstd, iv_l, iv_u = wls_prediction_std(res)
mean_conf_int_spread = np.mean(res.fittedvalues - iv_l)
model_std = np.concatenate([prstd, (1./1.9599)*mean_conf_int_spread*np.ones(len(ts2))])
ens_std = ens_prods.std(axis=1)
combined_std = np.sqrt(model_std**2 + ens_std**2)
all_prod_model = np.concatenate([res.fittedvalues, linear_map(vali_data, res.params, cols)])
combined_ub95 = all_prod_model + 1.9599*combined_std
combined_lb95 = all_prod_model - 1.9599*combined_std
# plot confint
ax1.fill_between(all_ts, combined_lb95, combined_ub95, label='Combined 95% conf. int.')
ax1.fill_between(all_ts, all_prod_model - 1.9599*ens_std, all_prod_model + 1.9599*ens_std, facecolor='grey', label='Ensemble 95% conf. int.')
# plot ensempble models
ax1.plot_date(all_ts, ens_prods, '-', lw=0.5)
ax1.plot_date(ts1, y, 'k-', lw=2, label='Actual production')
ax1.plot_date(ts1, res.fittedvalues,'r-', lw=2, label='Model on ensemble mean')
ax1.plot_date(ts2, vali_data['prod'], 'k-', lw=2, label='')
ax1.plot_date(ts2, linear_map(vali_data, res.params, cols), 'r-', lw=2)
ax1.set_ylabel('[MW]')
ax1.legend(loc=2)
vali_resid = linear_map(vali_data, res.params, cols) - vali_data['prod']
ax2.plot_date(ts1, res.resid, '-', label='Residual, fitted data')
ax2.plot_date(ts2, vali_resid, '-', label='Residual, validation data')
ax2.set_ylabel('[MW]')
ax2.legend(loc=2)
print "MAE = " + str(mae(vali_resid))
print "MAPE = " + str(mape(vali_resid, vali_data['prod']))
print "RMSE = " + str(rmse(vali_resid))
print "ME = " + str(np.mean(vali_resid))
print "MAE (fit) = " + str(mae(res.resid))
print "MAPE (fit) = " + str(mape(res.resid, fit_data['prod']))
print "RMSE (fit)= " + str(rmse(res.resid))
print "ME (fit)= " + str(np.mean(res.resid))
plt.savefig('figures/ens_prod_models.pdf', dpi=600)
plt.figure()
plt.plot_date(all_ts, ens_std)
plt.ylabel('Std. of ensemble production models [MW]')
plt.savefig('figures/std_ens_prod_models.pdf', dpi=600)
sns.jointplot(x=ens_std, y=np.concatenate([res.resid, vali_resid]))
return res, all_ens_data, all_ts, fit_data['prod'], vali_data['prod']