def test_normality(self):
res = self.res
#> library(nortest) #Lilliefors (Kolmogorov-Smirnov) normality test
#> lt = lillie.test(residuals(fm))
#> mkhtest(lt, "lilliefors", "-")
lilliefors1 = dict(statistic=0.0723390908786589,
pvalue=0.01204113540102896,
parameters=(),
distr='-')
#> lt = lillie.test(residuals(fm)**2)
#> mkhtest(lt, "lilliefors", "-")
lilliefors2 = dict(statistic=0.301311621898024,
pvalue=1.004305736618051e-51,
parameters=(),
distr='-')
#> lt = lillie.test(residuals(fm)[1:20])
#> mkhtest(lt, "lilliefors", "-")
lilliefors3 = dict(statistic=0.1333956004203103,
pvalue=0.455683,
parameters=(),
distr='-')
lf1 = smsdia.lilliefors(res.resid)
lf2 = smsdia.lilliefors(res.resid**2)
lf3 = smsdia.lilliefors(res.resid[:20])
compare_t_est(lf1, lilliefors1, decimal=(14, 14))
compare_t_est(lf2, lilliefors2, decimal=(14, 14)) # pvalue very small
assert_allclose(lf2[1], lilliefors2['pvalue'], rtol=1e-10)
compare_t_est(lf3, lilliefors3, decimal=(14, 1))
# R uses different approximation for pvalue in last case
#> ad = ad.test(residuals(fm))
#> mkhtest(ad, "ad3", "-")
adr1 = dict(statistic=1.602209621518313,
pvalue=0.0003937979149362316,
parameters=(),
distr='-')
#> ad = ad.test(residuals(fm)**2)
#> mkhtest(ad, "ad3", "-")
adr2 = dict(statistic=np.inf, pvalue=np.nan, parameters=(), distr='-')
#> ad = ad.test(residuals(fm)[1:20])
#> mkhtest(ad, "ad3", "-")
adr3 = dict(statistic=0.3017073732210775,
pvalue=0.5443499281265933,
parameters=(),
distr='-')
ad1 = smsdia.normal_ad(res.resid)
compare_t_est(ad1, adr1, decimal=(11, 13))
ad2 = smsdia.normal_ad(res.resid**2)
assert_(np.isinf(ad2[0]))
ad3 = smsdia.normal_ad(res.resid[:20])
compare_t_est(ad3, adr3, decimal=(11, 12))
def compute(cls, widget):
"""
Anderson-Darling test for one sample
:param widget:
:return: p-value for Anderson-Darling test
"""
if isinstance(
ande.normal_ad(np.array([a[0] for a in widget.column]))[1],
float):
return ande.normal_ad(np.array([a[0] for a in widget.column]))[1]
else:
return ande.normal_ad(np.array([a[0]
for a in widget.column]))[1][0]
def test_normality(self):
res = self.res
#> library(nortest) #Lilliefors (Kolmogorov-Smirnov) normality test
#> lt = lillie.test(residuals(fm))
#> mkhtest(lt, "lillifors", "-")
lillifors1 = dict(statistic=0.0723390908786589,
pvalue=0.01204113540102896, parameters=(), distr='-')
#> lt = lillie.test(residuals(fm)**2)
#> mkhtest(lt, "lillifors", "-")
lillifors2 = dict(statistic=0.301311621898024,
pvalue=1.004305736618051e-51,
parameters=(), distr='-')
#> lt = lillie.test(residuals(fm)[1:20])
#> mkhtest(lt, "lillifors", "-")
lillifors3 = dict(statistic=0.1333956004203103,
pvalue=0.4618672180799566, parameters=(), distr='-')
lf1 = smsdia.lillifors(res.resid)
lf2 = smsdia.lillifors(res.resid**2)
lf3 = smsdia.lillifors(res.resid[:20])
compare_t_est(lf1, lillifors1, decimal=(15, 14))
compare_t_est(lf2, lillifors2, decimal=(15, 15)) #pvalue very small
assert_approx_equal(lf2[1], lillifors2['pvalue'], significant=10)
compare_t_est(lf3, lillifors3, decimal=(15, 1))
#R uses different approximation for pvalue in last case
#> ad = ad.test(residuals(fm))
#> mkhtest(ad, "ad3", "-")
adr1 = dict(statistic=1.602209621518313, pvalue=0.0003937979149362316,
parameters=(), distr='-')
#> ad = ad.test(residuals(fm)**2)
#> mkhtest(ad, "ad3", "-")
adr2 = dict(statistic=np.inf, pvalue=np.nan, parameters=(), distr='-')
#> ad = ad.test(residuals(fm)[1:20])
#> mkhtest(ad, "ad3", "-")
adr3 = dict(statistic=0.3017073732210775, pvalue=0.5443499281265933,
parameters=(), distr='-')
ad1 = smsdia.normal_ad(res.resid)
compare_t_est(ad1, adr1, decimal=(12, 15))
ad2 = smsdia.normal_ad(res.resid**2)
assert_(np.isinf(ad2[0]))
ad3 = smsdia.normal_ad(res.resid[:20])
compare_t_est(ad3, adr3, decimal=(13, 13))
def normal_errors_assumption(df, p_value_thresh=0.05):
# Calculating residuals for the Anderson-Darling test
df_results = df
print('Using the Anderson-Darling test for normal distribution')
# Performing the test on the residuals
p_value = normal_ad(df_results['residuals'])[1]
print('p-value from the test - below 0.05 generally means non-normal:',
p_value)
# Reporting the normality of the residuals
if p_value < p_value_thresh:
print('Residuals are not normally distributed')
else:
print('Residuals are normally distributed')
# Plotting the residuals distribution
plt.subplots(figsize=(12, 6))
plt.title('Distribution of Residuals')
sns.distplot(df_results['residuals'])
plt.show()
print()
if p_value > p_value_thresh:
print('Assumption satisfied')
else:
print('Assumption not satisfied')
print('Confidence intervals will likely be affected')
def multivariate_normal_assumption(p_value_thresh=0.05):
'''
Normality: Assumes that the predictors have normal distributions. If they are not normal,
a non-linear transformation like a log transformation or box-cox transformation
can be performed on the non-normal variable.
'''
from statsmodels.stats.diagnostic import normal_ad
print('\n=======================================================================================')
print('Assumption 2: All variables are multivariate normal')
print('Using the Anderson-Darling test for normal distribution')
print('p-values from the test - below 0.05 generally means normality:')
print()
non_normal_variables = 0
# Performing the Anderson-Darling test on each variable to test for normality
for feature in range(features.shape[1]):
p_value = normal_ad(features[:, feature])[1]
# Adding to total count of non-normality if p-value exceeds threshold
if p_value > p_value_thresh:
non_normal_variables += 1
# Printing p-values from the test
print('{0}: {1}'.format(feature_names[feature], p_value))
print('\n{0} non-normal variables'.format(non_normal_variables))
print()
if non_normal_variables == 0:
print('Assumption satisfied')
else:
print('Assumption not satisfied')
def normal_errors_assumption(dataframe, color, p_value_thresh=0.05):
residuals = dataframe["residuals"]
print("Using the Anderson-Darling test for normal distribution")
p_value = normal_ad(residuals)[1]
print("p-value from the test - below 0.05 generally means non-normal:",
p_value)
if p_value < p_value_thresh:
print("Residuals are not normally distributed")
else:
print("Residuals are normally distributed")
# Plotting the residuals distribution
sns.distplot(dataframe["residuals"], color=color)
plt.title(f"Normal distribution of residuals")
plt.show()
print()
if p_value > p_value_thresh:
print("Assumption satisfied")
else:
print("Assumption not satisfied")
print()
print("Confidence intervals will likely be affected")
print("Try performing nonlinear transformations on variables")
def compare_results(name1, name2, r1, r2):
print("---------------------")
print(f"{name1},{name2}> Comparison statistics")
print(normal_ad(np.array(r1)))
print(normal_ad(np.array(r2)))
d1 = DescrStatsW(r1)
print(d1.get_compare(r2).summary(use_t=True, usevar='unequal'))
print(f"{name1},{name2}>", ranksums(r1, r2))
f1 = frame_of(r1, name1)
f2 = frame_of(r2, name2)
frame = pd.concat([f1, f2])
plt.figure()
sns.boxplot(data=frame, x="source", y="time")
plt.savefig(f"output/fig{name1}x{name2}.png")
def normality(self):
"""
First we plot the residuals, then we test the normality using the Anderson-Darling test.
p-value should be > 0.05
"""
plt.subplots(figsize=(12, 6))
plt.title('Distribution of Residuals')
sns.distplot(self.results['Residuals'])
plt.show()
p_value = normal_ad(self.results['Residuals'])[1] # Second value is the p-value
if p_value < 0.05:
return "Assumption not met", p_value
return "Assumption met", p_value
def normal_errors_assumption(model, features, label, p_value_thresh=0.05):
"""
Normality: Assumes that the error terms are normally distributed. If they are not,
nonlinear transformations of variables may solve this.
This assumption being violated primarily causes issues with the confidence intervals
"""
from statsmodels.stats.diagnostic import normal_ad
print('Assumption 2: The error terms are normally distributed', '\n')
# Calculating residuals for the Anderson-Darling test
"""
# ACA PODRIA USAR OTROS TEST TAMBIEN COMO POR EJEMPLO D Agostino s K^2 Test o Shapiro Test.
# AUNQUE SEGUN ESTO "https://stackoverflow.com/questions/7781798/seeing-if-data-is-normally-distributed-in-r/7788452#7788452"
# AL NO RECHAZAR HO, NO INDICA NECESARIAMENTE NORMALIDAD EN LA DISTRIB DE LOS DATOS, POR ENDE DEBERIA
# BUSCAR UN TEST DONDE H1 SEA LA HIPOTESIS DE QUE LA DISTRIB DE LOS DATOS SON NORMALES
"""
df_results = calculate_residuals(model, features, label)
print('Using the Anderson-Darling test for normal distribution')
# Performing the test on the residuals
p_value = normal_ad(df_results['Residuals'])[1]
print('p-value from the test - below 0.05 generally means non-normal:',
p_value)
# Reporting the normality of the residuals
if p_value < p_value_thresh:
print('Residuals are not normally distributed')
else:
print('Residuals are normally distributed')
# Plotting the residuals distribution
plt.subplots(figsize=(12, 6))
plt.title('Distribution of Residuals')
sns.distplot(df_results['Residuals'])
plt.show()
print()
if p_value > p_value_thresh:
print('Assumption satisfied')
else:
print('Assumption not satisfied')
print()
print('Confidence intervals will likely be affected')
print('Try performing nonlinear transformations on variables')
def myResiduals(y,pred,name):
res = pd.Series(y.flatten()-pred)
print('Anderson-Darling Normal: ',normal_ad(res)[1],'\n\n') # if < 0.05 -> bad
fig = plt.figure()
plt.hist(res)
plt.title(name+' Residuals')
fig.savefig(my_path+'/Figures/'+name+'_ResidualHistogram'+'.png')
plt.close()
#plt.show()
fig = plt.figure()
plt.scatter(pred,res, color='green', s=50, alpha=.6)
plt.hlines(y=0, xmin=min(pred), xmax=max(pred), color='black')
plt.ylabel(name+' Residuals')
plt.xlabel(name+' Prediction')
plt.title ('Residuals vs Preditions ('+name+')')
fig.savefig(my_path+'/Figures/'+name+'_ResidualGraph'+'.png')
plt.close()
def normal_errors_assumption(p_value_thresh=0.05):
"""
Normality: Assumes that the error terms are normally distributed. If they are not,
nonlinear transformations of variables may solve this.
This assumption being violated primarily causes issues with the confidence intervals
"""
from statsmodels.stats.diagnostic import normal_ad
print(
'\n======================================================================================='
)
print('Assumption 2: The error terms are normally distributed')
print()
print('Using the Anderson-Darling test for normal distribution')
# Performing the test on the residuals
p_value = normal_ad(df_results['Residuals'])[1]
print('p-value from the test - below 0.05 generally means non-normal:',
p_value)
# Reporting the normality of the residuals
if p_value < p_value_thresh:
print('Residuals are not normally distributed')
else:
print('Residuals are normally distributed')
# Plotting the residuals distribution
plt.subplots(figsize=(12, 6))
plt.title('Distribution of Residuals')
sns.distplot(df_results['Residuals'])
plt.show()
print()
if p_value > p_value_thresh:
print('Assumption satisfied')
else:
print('Assumption not satisfied')
print()
print('Confidence intervals will likely be affected')
print('Try performing nonlinear transformations on variables')
def normal_errors_assumption(model, features, label, p_value_thresh=0.05):
"""
Normality: Assumes that the error terms are normally distributed. If they are not,
nonlinear transformations of variables may solve this.
This assumption being violated primarily causes issues with the confidence intervals
"""
print("Assumption 2: The error terms are normally distributed", "\n")
# Calculating residuals for the Anderson-Darling test
df_results = calculate_residuals(model, features, label)
print("Using the Anderson-Darling test for normal distribution")
# Performing the test on the residuals
p_value = normal_ad(df_results["Residuals"])[1]
print("p-value from the test - below 0.05 generally means non-normal:",
p_value)
# Reporting the normality of the residuals
if p_value < p_value_thresh:
print("Residuals are not normally distributed")
else:
print("Residuals are normally distributed")
# Plotting the residuals distribution
plt.subplots(figsize=(12, 6))
plt.title("Distribution of Residuals")
sns.distplot(df_results["Residuals"])
plt.show()
print()
if p_value > p_value_thresh:
print("Assumption satisfied")
else:
print("Assumption not satisfied")
print()
print("Confidence intervals will likely be affected")
print("Try performing nonlinear transformations on variables")
def normality_resid(self, p_value_thresh=0.05):
"""
Normality: Assumes that the error terms are normally distributed. If they are not,
nonlinear transformations of variables may solve this.
This assumption being violated primarily causes issues with the confidence intervals
"""
from statsmodels.stats.diagnostic import normal_ad
from scipy.stats import probplot
import pylab
import matplotlib.pyplot as plt
import seaborn as sns
from numpy import quantile, logical_or
sns.set()
if type(self.model) == str:
self.fit_model()
print(
'\n======================================================================================='
)
print('Assumption 5: The error terms are kinda normally distributed')
print()
print('Using the Anderson-Darling test for normal distribution')
# Performing the test on the residuals
p_value = normal_ad(self.resid)[1]
print('p-value from the test - below 0.05 generally means non-normal:',
p_value)
# Reporting the normality of the residuals
if p_value < p_value_thresh:
print('Residuals are not normally distributed')
else:
print('Residuals are normally distributed')
# Plotting the residuals distribution
plt.subplots(figsize=(12, 6))
plt.title('Distribution of Residuals')
sns.distplot(self.resid)
plt.show()
print()
if p_value > p_value_thresh:
print('Assumption satisfied')
self.results['Satisfied'].append('Normality')
else:
print('Assumption not satisfied')
self.results['Violated'].append('Normality')
print()
print('Confidence intervals will likely be affected')
print('Try performing nonlinear transformations on variables')
print('Building a probability plot')
quantiles = probplot(self.resid, dist='norm', plot=pylab)
plt.show()
qqq = (quantiles[0][1] - quantiles[0][1].mean()
) / quantiles[0][1].std() - quantiles[0][0]
q75 = quantile(qqq, 0.75)
q25 = quantile(qqq, 0.25)
outliers_share = (logical_or(qqq > q75 + (q75 - q25) * 1.7, qqq < q25 -
(q75 - q25) * 1.7).sum() /
qqq.shape[0]).round(3)
if outliers_share < 0.005:
print('Assumption can be considered as satisfied.')
self.results['Satisfied'].append('Sub-Normality')
elif outliers_share < 0.05:
self.results['Potentially'].append('Sub-Normality')
print(
f'\nIn your dataset you quite fat tails. You have {outliers_share} potential outliers ({logical_or(qqq>q75+(q75-q25)*1.7, qqq<q25-(q75-q25)*1.7).sum()} rows)'
)
else:
print(
f'\nIn fact outliers are super significant. Probably it is better to split your dataset into 2 different ones.'
)
self.results['Violated'].append('Sub-Normality')
def Fig_OLS_Checks():
#fs = 10 # font size used across figures
#color = str()
#OrC = 'open'
SampSizes = [
5, 6, 7, 8, 9, 10, 13, 16, 20, 30, 40, 50, 60, 70, 80, 90, 100
]
Iterations = 100
fig = plt.figure(figsize=(12, 8))
# MODEL PARAMETERS
Rare_MacIntercept_pVals = [] # List to hold coefficient p-values
Rare_MacIntercept_Coeffs = [] # List to hold coefficients
Rich_MacIntercept_pVals = []
Rich_MacIntercept_Coeffs = []
Dom_MacIntercept_pVals = []
Dom_MacIntercept_Coeffs = []
Even_MacIntercept_pVals = []
Even_MacIntercept_Coeffs = []
Rare_MicIntercept_pVals = []
Rare_MicIntercept_Coeffs = []
Rich_MicIntercept_pVals = []
Rich_MicIntercept_Coeffs = []
Dom_MicIntercept_pVals = []
Dom_MicIntercept_Coeffs = []
Even_MicIntercept_pVals = []
Even_MicIntercept_Coeffs = []
Rare_MacSlope_pVals = []
Rare_MacSlope_Coeffs = []
Rich_MacSlope_pVals = []
Rich_MacSlope_Coeffs = []
Dom_MacSlope_pVals = []
Dom_MacSlope_Coeffs = []
Even_MacSlope_pVals = []
Even_MacSlope_Coeffs = []
Rare_MicSlope_pVals = []
Rare_MicSlope_Coeffs = []
Rich_MicSlope_pVals = []
Rich_MicSlope_Coeffs = []
Dom_MicSlope_pVals = []
Dom_MicSlope_Coeffs = []
Even_MicSlope_pVals = []
Even_MicSlope_Coeffs = []
RareR2List = [] # List to hold model R2
RarepFList = [] # List to hold significance of model R2
RichR2List = [] # List to hold model R2
RichpFList = [] # List to hold significance of model R2
DomR2List = [] # List to hold model R2
DompFList = [] # List to hold significance of model R2
EvenR2List = [] # List to hold model R2
EvenpFList = [] # List to hold significance of model R2
# ASSUMPTIONS OF LINEAR REGRESSION
# 1. Error in predictor variables is negligible...presumably yes
# 2. Variables are measured at the continuous level...yes
# 3. The relationship is linear
#RarepLinListHC = []
RarepLinListRainB = []
RarepLinListLM = []
#RichpLinListHC = []
RichpLinListRainB = []
RichpLinListLM = []
#DompLinListHC = []
DompLinListRainB = []
DompLinListLM = []
#EvenpLinListHC = []
EvenpLinListRainB = []
EvenpLinListLM = []
# 4. There are no significant outliers...need to find tests or measures
# 5. Independence of observations (no serial correlation in residuals)
RarepCorrListBG = []
RarepCorrListF = []
RichpCorrListBG = []
RichpCorrListF = []
DompCorrListBG = []
DompCorrListF = []
EvenpCorrListBG = []
EvenpCorrListF = []
# 6. Homoscedacticity
RarepHomoHW = []
RarepHomoHB = []
RichpHomoHW = []
RichpHomoHB = []
DompHomoHW = []
DompHomoHB = []
EvenpHomoHW = []
EvenpHomoHB = []
# 7. Normally distributed residuals (errors)
RarepNormListOmni = [] # Omnibus test for normality
RarepNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
RarepNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
RarepNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
RichpNormListOmni = [] # Omnibus test for normality
RichpNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
RichpNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
RichpNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
DompNormListOmni = [] # Omnibus test for normality
DompNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
DompNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
DompNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
EvenpNormListOmni = [] # Omnibus test for normality
EvenpNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
EvenpNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
EvenpNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
NLIST = []
for SampSize in SampSizes:
sRare_MacIntercept_pVals = [] # List to hold coefficient p-values
sRare_MacIntercept_Coeffs = [] # List to hold coefficients
sRich_MacIntercept_pVals = [] # List to hold coefficient p-values
sRich_MacIntercept_Coeffs = [] # List to hold coefficients
sDom_MacIntercept_pVals = []
sDom_MacIntercept_Coeffs = []
sEven_MacIntercept_pVals = []
sEven_MacIntercept_Coeffs = []
sRare_MicIntercept_pVals = []
sRare_MicIntercept_Coeffs = []
sRich_MicIntercept_pVals = []
sRich_MicIntercept_Coeffs = []
sDom_MicIntercept_pVals = []
sDom_MicIntercept_Coeffs = []
sEven_MicIntercept_pVals = []
sEven_MicIntercept_Coeffs = []
sRare_MacSlope_pVals = []
sRare_MacSlope_Coeffs = []
sRich_MacSlope_pVals = []
sRich_MacSlope_Coeffs = []
sDom_MacSlope_pVals = []
sDom_MacSlope_Coeffs = []
sEven_MacSlope_pVals = []
sEven_MacSlope_Coeffs = []
sRare_MicSlope_pVals = []
sRare_MicSlope_Coeffs = []
sRich_MicSlope_pVals = []
sRich_MicSlope_Coeffs = []
sDom_MicSlope_pVals = []
sDom_MicSlope_Coeffs = []
sEven_MicSlope_pVals = []
sEven_MicSlope_Coeffs = []
sRareR2List = [] # List to hold model R2
sRarepFList = [] # List to hold significance of model R2
sRichR2List = [] # List to hold model R2
sRichpFList = [] # List to hold significance of model R2
sDomR2List = [] # List to hold model R2
sDompFList = [] # List to hold significance of model R2
sEvenR2List = [] # List to hold model R2
sEvenpFList = [] # List to hold significance of model R2
# ASSUMPTIONS OF LINEAR REGRESSION
# 1. Error in predictor variables is negligible...presumably yes
# 2. Variables are measured at the continuous level...yes
# 3. The relationship is linear
#sRarepLinListHC = []
sRarepLinListRainB = []
sRarepLinListLM = []
#sRichpLinListHC = []
sRichpLinListRainB = []
sRichpLinListLM = []
#sDompLinListHC = []
sDompLinListRainB = []
sDompLinListLM = []
#sEvenpLinListHC = []
sEvenpLinListRainB = []
sEvenpLinListLM = []
# 4. There are no significant outliers...need to find tests or measures
# 5. Independence of observations (no serial correlation in residuals)
sRarepCorrListBG = []
sRarepCorrListF = []
sRichpCorrListBG = []
sRichpCorrListF = []
sDompCorrListBG = []
sDompCorrListF = []
sEvenpCorrListBG = []
sEvenpCorrListF = []
# 6. Homoscedacticity
sRarepHomoHW = []
sRarepHomoHB = []
sRichpHomoHW = []
sRichpHomoHB = []
sDompHomoHW = []
sDompHomoHB = []
sEvenpHomoHW = []
sEvenpHomoHB = []
# 7. Normally distributed residuals (errors)
sRarepNormListOmni = [] # Omnibus test for normality
sRarepNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
sRarepNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sRarepNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
sRichpNormListOmni = [] # Omnibus test for normality
sRichpNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
sRichpNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sRichpNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
sDompNormListOmni = [] # Omnibus test for normality
sDompNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
sDompNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sDompNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
sEvenpNormListOmni = [] # Omnibus test for normality
sEvenpNormListJB = [
] # Calculate residual skewness, kurtosis, and do the JB test for normality
sEvenpNormListKS = [
] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sEvenpNormListAD = [
] # Anderson-Darling test for normal distribution unknown mean and variance
for iteration in range(Iterations):
Nlist, Slist, Evarlist, ESimplist, ENeelist, EHeiplist, EQlist = [
[], [], [], [], [], [], []
]
klist, Shanlist, BPlist, SimpDomlist, SinglesList, tenlist, onelist = [
[], [], [], [], [], [], []
]
NmaxList, rareSkews, KindList = [[], [], []]
NSlist = []
ct = 0
radDATA = []
datasets = []
GoodNames = [
'EMPclosed', 'HMP', 'BIGN', 'TARA', 'BOVINE', 'HUMAN', 'LAUB',
'SED', 'CHU', 'CHINA', 'CATLIN', 'FUNGI', 'HYDRO', 'BBS',
'CBC', 'MCDB', 'GENTRY', 'FIA'
] # all microbe data is MGRAST
mlist = ['micro', 'macro']
for m in mlist:
for name in os.listdir(mydir + 'data/' + m):
if name in GoodNames: pass
else: continue
path = mydir + 'data/' + m + '/' + name + '/' + name + '-SADMetricData.txt'
num_lines = sum(1 for line in open(path))
datasets.append([name, m, num_lines])
numMac = 0
numMic = 0
radDATA = []
for d in datasets:
name, kind, numlines = d
lines = []
lines = np.random.choice(range(1, numlines + 1),
SampSize,
replace=True)
path = mydir + 'data/' + kind + '/' + name + '/' + name + '-SADMetricData.txt'
for line in lines:
data = linecache.getline(path, line)
radDATA.append(data)
#print name, kind, numlines, len(radDATA)
for data in radDATA:
data = data.split()
if len(data) == 0:
print 'no data'
continue
name, kind, N, S, Var, Evar, ESimp, EQ, O, ENee, EPielou, EHeip, BP, SimpDom, Nmax, McN, skew, logskew, chao1, ace, jknife1, jknife2, margalef, menhinick, preston_a, preston_S = data
N = float(N)
S = float(S)
Nlist.append(float(np.log(N)))
Slist.append(float(np.log(S)))
NSlist.append(float(np.log(N / S)))
Evarlist.append(float(np.log(float(Evar))))
ESimplist.append(float(np.log(float(ESimp))))
KindList.append(kind)
BPlist.append(float(BP))
NmaxList.append(float(np.log(float(BP) * float(N))))
EHeiplist.append(float(EHeip))
# lines for the log-modulo transformation of skewnness
skew = float(skew)
sign = 1
if skew < 0: sign = -1
lms = np.log(np.abs(skew) + 1)
lms = lms * sign
#if lms > 3: print name, N, S
rareSkews.append(float(lms))
if kind == 'macro': numMac += 1
elif kind == 'micro': numMic += 1
ct += 1
#print 'Sample Size:',SampSize, ' Mic:', numMic,'Mac:', numMac
# Multiple regression for Rarity
d = pd.DataFrame({'N': list(Nlist)})
d['Rarity'] = list(rareSkews)
d['Kind'] = list(KindList)
RarityResults = smf.ols(
'Rarity ~ N * Kind',
d).fit() # Fit the dummy variable regression model
#print RarityResults.summary(), '\n'
# Multiple regression for Rarity
d = pd.DataFrame({'N': list(Nlist)})
d['Richness'] = list(Slist)
d['Kind'] = list(KindList)
RichnessResults = smf.ols(
'Richness ~ N * Kind',
d).fit() # Fit the dummy variable regression model
#print RichnessResults.summary(), '\n'
# Multiple regression for Dominance
d = pd.DataFrame({'N': list(Nlist)})
d['Dominance'] = list(NmaxList)
d['Kind'] = list(KindList)
DomResults = smf.ols(
'Dominance ~ N * Kind',
d).fit() # Fit the dummy variable regression model
#print DomResults.summary(), '\n'
# Multiple regression for Evenness
d = pd.DataFrame({'N': list(Nlist)})
d['Evenness'] = list(ESimplist)
d['Kind'] = list(KindList)
EvenResults = smf.ols(
'Evenness ~ N * Kind',
d).fit() # Fit the dummy variable regression model
#print RarityResults.summary(), '\n'
RareResids = RarityResults.resid # residuals of the model
RichResids = RichnessResults.resid # residuals of the model
DomResids = DomResults.resid # residuals of the model
EvenResids = EvenResults.resid # residuals of the model
# MODEL RESULTS/FIT
RareFpval = RarityResults.f_pvalue
Rarer2 = RarityResults.rsquared # coefficient of determination
#Adj_r2 = RareResults.rsquared_adj # adjusted
RichFpval = RichnessResults.f_pvalue
Richr2 = RichnessResults.rsquared # coefficient of determination
#Adj_r2 = RichnessResults.rsquared_adj # adjusted
DomFpval = DomResults.f_pvalue
Domr2 = DomResults.rsquared # coefficient of determination
#Adj_r2 = DomResults.rsquared_adj # adjusted
EvenFpval = EvenResults.f_pvalue
Evenr2 = EvenResults.rsquared # coefficient of determination
#Adj_r2 = EvenResuls.rsquared_adj # adjusted
# MODEL PARAMETERS and p-values
Rareparams = RarityResults.params
Rareparams = Rareparams.tolist()
Rarepvals = RarityResults.pvalues
Rarepvals = Rarepvals.tolist()
Richparams = RichnessResults.params
Richparams = Richparams.tolist()
Richpvals = RichnessResults.pvalues
Richpvals = Richpvals.tolist()
Domparams = DomResults.params
Domparams = Domparams.tolist()
Dompvals = DomResults.pvalues
Dompvals = Dompvals.tolist()
Evenparams = EvenResults.params
Evenparams = Evenparams.tolist()
Evenpvals = EvenResults.pvalues
Evenpvals = Evenpvals.tolist()
sRare_MacIntercept_pVals.append(Rarepvals[0])
sRare_MacIntercept_Coeffs.append(Rareparams[0])
sRich_MacIntercept_pVals.append(Rarepvals[0])
sRich_MacIntercept_Coeffs.append(Rareparams[0])
sDom_MacIntercept_pVals.append(Dompvals[0])
sDom_MacIntercept_Coeffs.append(Domparams[0])
sEven_MacIntercept_pVals.append(Evenpvals[0])
sEven_MacIntercept_Coeffs.append(Evenparams[0])
sRare_MicIntercept_pVals.append(Rarepvals[1])
if Rarepvals[1] > 0.05:
sRare_MicIntercept_Coeffs.append(Rareparams[1])
else:
sRare_MicIntercept_Coeffs.append(Rareparams[1])
sRich_MicIntercept_pVals.append(Richpvals[1])
if Richpvals[1] > 0.05:
sRich_MicIntercept_Coeffs.append(Richparams[1])
else:
sRich_MicIntercept_Coeffs.append(Richparams[1])
sDom_MicIntercept_pVals.append(Dompvals[1])
if Dompvals[1] > 0.05:
sDom_MicIntercept_Coeffs.append(Domparams[1])
else:
sDom_MicIntercept_Coeffs.append(Domparams[1])
sEven_MicIntercept_pVals.append(Evenpvals[1])
if Evenpvals[1] > 0.05:
sEven_MicIntercept_Coeffs.append(Evenparams[1])
else:
sEven_MicIntercept_Coeffs.append(Evenparams[1])
sRare_MacSlope_pVals.append(Rarepvals[2])
sRare_MacSlope_Coeffs.append(Rareparams[2])
sRich_MacSlope_pVals.append(Richpvals[2])
sRich_MacSlope_Coeffs.append(Richparams[2])
sDom_MacSlope_pVals.append(Dompvals[2])
sDom_MacSlope_Coeffs.append(Domparams[2])
sEven_MacSlope_pVals.append(Evenpvals[2])
sEven_MacSlope_Coeffs.append(Evenparams[2])
sRare_MicSlope_pVals.append(Rarepvals[3])
if Rarepvals[3] > 0.05:
sRare_MicSlope_Coeffs.append(Rareparams[3])
else:
sRare_MicSlope_Coeffs.append(Rareparams[3])
sRich_MicSlope_pVals.append(Richpvals[3])
if Richpvals[3] > 0.05:
sRich_MicSlope_Coeffs.append(Richparams[3])
else:
sRich_MicSlope_Coeffs.append(Richparams[3])
sDom_MicSlope_pVals.append(Dompvals[3])
if Dompvals[3] > 0.05:
sDom_MicSlope_Coeffs.append(Domparams[3])
else:
sDom_MicSlope_Coeffs.append(Domparams[3])
sEven_MicSlope_pVals.append(Evenpvals[3])
if Evenpvals[3] > 0.05:
sEven_MicSlope_Coeffs.append(Evenparams[3])
else:
sEven_MicSlope_Coeffs.append(Evenparams[3])
sRareR2List.append(Rarer2)
sRarepFList.append(RareFpval)
sRichR2List.append(Richr2)
sRichpFList.append(RichFpval)
sDomR2List.append(Domr2)
sDompFList.append(DomFpval)
sEvenR2List.append(Evenr2)
sEvenpFList.append(EvenFpval)
# TESTS OF LINEAR REGRESSION ASSUMPTIONS
# Error in predictor variables is negligible...Presumably Yes
# Variables are measured at the continuous level...Definitely Yes
# TESTS FOR LINEARITY, i.e., WHETHER THE DATA ARE CORRECTLY MODELED AS LINEAR
#HC = smd.linear_harvey_collier(RarityResults) # Harvey Collier test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
#sRarepLinListHC.append(HC)
#HC = smd.linear_harvey_collier(DomResults) # Harvey Collier test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
#sDompLinListHC.append(HC)
#HC = smd.linear_harvey_collier(EvenResults) # Harvey Collier test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
#sEvenpLinListHC.append(HC)
RB = smd.linear_rainbow(
RarityResults
) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sRarepLinListRainB.append(RB[1])
RB = smd.linear_rainbow(
RichnessResults
) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sRichpLinListRainB.append(RB[1])
RB = smd.linear_rainbow(
DomResults
) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sDompLinListRainB.append(RB[1])
RB = smd.linear_rainbow(
EvenResults
) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sEvenpLinListRainB.append(RB[1])
LM = smd.linear_lm(RarityResults.resid, RarityResults.model.exog
) # Lagrangian multiplier test for linearity
sRarepLinListLM.append(LM[1])
LM = smd.linear_lm(RichnessResults.resid,
RichnessResults.model.exog
) # Lagrangian multiplier test for linearity
sRichpLinListLM.append(LM[1])
LM = smd.linear_lm(DomResults.resid, DomResults.model.exog
) # Lagrangian multiplier test for linearity
sDompLinListLM.append(LM[1])
LM = smd.linear_lm(EvenResults.resid, EvenResults.model.exog
) # Lagrangian multiplier test for linearity
sEvenpLinListLM.append(LM[1])
# INDEPENDENCE OF OBSERVATIONS (no serial correlation in residuals)
BGtest = smd.acorr_breush_godfrey(
RarityResults, nlags=None, store=False
) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(RareResids, lags=None, boxpierce=True)
sRarepCorrListBG.append(BGtest[1])
sRarepCorrListF.append(BGtest[3])
BGtest = smd.acorr_breush_godfrey(
RichnessResults, nlags=None, store=False
) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(RichResids, lags=None, boxpierce=True)
sRichpCorrListBG.append(BGtest[1])
sRichpCorrListF.append(BGtest[3])
BGtest = smd.acorr_breush_godfrey(
DomResults, nlags=None, store=False
) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(DomResids, lags=None, boxpierce=True)
sDompCorrListBG.append(BGtest[1])
sDompCorrListF.append(BGtest[3])
BGtest = smd.acorr_breush_godfrey(
EvenResults, nlags=None, store=False
) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(EvenResids, lags=None, boxpierce=True)
sEvenpCorrListBG.append(BGtest[1])
sEvenpCorrListF.append(BGtest[3])
# There are no significant outliers...Need tests or measures/metrics
# HOMOSCEDASTICITY
# These tests return:
# 1. lagrange multiplier statistic,
# 2. p-value of lagrange multiplier test,
# 3. f-statistic of the hypothesis that the error variance does not depend on x,
# 4. p-value for the f-statistic
HW = sms.het_white(RareResids, RarityResults.model.exog)
sRarepHomoHW.append(HW[3])
HW = sms.het_white(RichResids, RichnessResults.model.exog)
sRichpHomoHW.append(HW[3])
HW = sms.het_white(DomResids, DomResults.model.exog)
sDompHomoHW.append(HW[3])
HW = sms.het_white(EvenResids, EvenResults.model.exog)
sEvenpHomoHW.append(HW[3])
HB = sms.het_breushpagan(RareResids, RarityResults.model.exog)
sRarepHomoHB.append(HB[3])
HB = sms.het_breushpagan(RichResids, RichnessResults.model.exog)
sRichpHomoHB.append(HB[3])
HB = sms.het_breushpagan(DomResids, DomResults.model.exog)
sDompHomoHB.append(HB[3])
HB = sms.het_breushpagan(EvenResids, EvenResults.model.exog)
sEvenpHomoHB.append(HB[3])
# 7. NORMALITY OF ERROR TERMS
O = sms.omni_normtest(RareResids)
sRarepNormListOmni.append(O[1])
O = sms.omni_normtest(RichResids)
sRichpNormListOmni.append(O[1])
O = sms.omni_normtest(DomResids)
sDompNormListOmni.append(O[1])
O = sms.omni_normtest(EvenResids)
sEvenpNormListOmni.append(O[1])
JB = sms.jarque_bera(RareResids)
sRarepNormListJB.append(
JB[1]
) # Calculate residual skewness, kurtosis, and do the JB test for normality
JB = sms.jarque_bera(RichResids)
sRichpNormListJB.append(
JB[1]
) # Calculate residual skewness, kurtosis, and do the JB test for normality
JB = sms.jarque_bera(DomResids)
sDompNormListJB.append(
JB[1]
) # Calculate residual skewness, kurtosis, and do the JB test for normality
JB = sms.jarque_bera(EvenResids)
sEvenpNormListJB.append(
JB[1]
) # Calculate residual skewness, kurtosis, and do the JB test for normality
KS = smd.kstest_normal(RareResids)
sRarepNormListKS.append(
KS[1]
) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
KS = smd.kstest_normal(RichResids)
sRichpNormListKS.append(
KS[1]
) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
KS = smd.kstest_normal(DomResids)
sDompNormListKS.append(
KS[1]
) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
KS = smd.kstest_normal(EvenResids)
sEvenpNormListKS.append(
KS[1]
) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
AD = smd.normal_ad(RareResids)
sRarepNormListAD.append(
AD[1]
) # Anderson-Darling test for normal distribution unknown mean and variance
AD = smd.normal_ad(RichResids)
sRichpNormListAD.append(
AD[1]
) # Anderson-Darling test for normal distribution unknown mean and variance
AD = smd.normal_ad(DomResids)
sDompNormListAD.append(
AD[1]
) # Anderson-Darling test for normal distribution unknown mean and variance
AD = smd.normal_ad(EvenResids)
sEvenpNormListAD.append(
AD[1]
) # Anderson-Darling test for normal distribution unknown mean and variance
print 'Sample size:', SampSize, 'iteration:', iteration
NLIST.append(SampSize)
Rare_MacIntercept_pVals.append(np.mean(
sRare_MacIntercept_pVals)) # List to hold coefficient p-values
Rare_MacIntercept_Coeffs.append(
np.mean(sRare_MacIntercept_Coeffs)) # List to hold coefficients
Rich_MacIntercept_pVals.append(np.mean(
sRich_MacIntercept_pVals)) # List to hold coefficient p-values
Rich_MacIntercept_Coeffs.append(
np.mean(sRich_MacIntercept_Coeffs)) # List to hold coefficients
Dom_MacIntercept_pVals.append(np.mean(sDom_MacIntercept_pVals))
Dom_MacIntercept_Coeffs.append(np.mean(sDom_MacIntercept_Coeffs))
Even_MacIntercept_pVals.append(np.mean(sEven_MacIntercept_pVals))
Even_MacIntercept_Coeffs.append(np.mean(sEven_MacIntercept_Coeffs))
Rare_MicIntercept_pVals.append(np.mean(sRare_MicIntercept_pVals))
Rare_MicIntercept_Coeffs.append(np.mean(sRare_MicIntercept_Coeffs))
Rich_MicIntercept_pVals.append(np.mean(sRich_MicIntercept_pVals))
Rich_MicIntercept_Coeffs.append(np.mean(sRich_MicIntercept_Coeffs))
Dom_MicIntercept_pVals.append(np.mean(sDom_MicIntercept_pVals))
Dom_MicIntercept_Coeffs.append(np.mean(sDom_MicIntercept_Coeffs))
Even_MicIntercept_pVals.append(np.mean(sEven_MicIntercept_pVals))
Even_MicIntercept_Coeffs.append(np.mean(sEven_MicIntercept_Coeffs))
Rare_MacSlope_pVals.append(
np.mean(sRare_MacSlope_pVals)) # List to hold coefficient p-values
Rare_MacSlope_Coeffs.append(
np.mean(sRare_MacSlope_Coeffs)) # List to hold coefficients
Rich_MacSlope_pVals.append(
np.mean(sRich_MacSlope_pVals)) # List to hold coefficient p-values
Rich_MacSlope_Coeffs.append(
np.mean(sRich_MacSlope_Coeffs)) # List to hold coefficients
Dom_MacSlope_pVals.append(np.mean(sDom_MacSlope_pVals))
Dom_MacSlope_Coeffs.append(np.mean(sDom_MacSlope_Coeffs))
Even_MacSlope_pVals.append(np.mean(sEven_MacSlope_pVals))
Even_MacSlope_Coeffs.append(np.mean(sEven_MacSlope_Coeffs))
Rare_MicSlope_pVals.append(np.mean(sRare_MicSlope_pVals))
Rare_MicSlope_Coeffs.append(np.mean(sRare_MicSlope_Coeffs))
Rich_MicSlope_pVals.append(np.mean(sRich_MicSlope_pVals))
Rich_MicSlope_Coeffs.append(np.mean(sRich_MicSlope_Coeffs))
Dom_MicSlope_pVals.append(np.mean(sDom_MicSlope_pVals))
Dom_MicSlope_Coeffs.append(np.mean(sDom_MicSlope_Coeffs))
Even_MicSlope_pVals.append(np.mean(sEven_MicSlope_pVals))
Even_MicSlope_Coeffs.append(np.mean(sEven_MicSlope_Coeffs))
RareR2List.append(np.mean(sRareR2List))
RarepFList.append(np.mean(sRarepFList))
RichR2List.append(np.mean(sRichR2List))
RichpFList.append(np.mean(sRichpFList))
DomR2List.append(np.mean(sDomR2List))
DompFList.append(np.mean(sDompFList))
EvenR2List.append(np.mean(sEvenR2List))
EvenpFList.append(np.mean(sEvenpFList))
# ASSUMPTIONS OF LINEAR REGRESSION
# 1. Error in predictor variables is negligible...presumably yes
# 2. Variables are measured at the continuous level...yes
# 3. The relationship is linear
#RarepLinListHC.append(np.mean(sRarepLinListHC))
RarepLinListRainB.append(np.mean(sRarepLinListRainB))
RarepLinListLM.append(np.mean(sRarepLinListLM))
#RichpLinListHC.append(np.mean(sRichpLinListHC))
RichpLinListRainB.append(np.mean(sRichpLinListRainB))
RichpLinListLM.append(np.mean(sRichpLinListLM))
#DompLinListHC.append(np.mean(sDompLinListHC))
DompLinListRainB.append(np.mean(sDompLinListRainB))
DompLinListLM.append(np.mean(sDompLinListLM))
#EvenpLinListHC.append(np.mean(sEvenpLinListHC))
EvenpLinListRainB.append(np.mean(sEvenpLinListRainB))
EvenpLinListLM.append(np.mean(sEvenpLinListLM))
# 4. There are no significant outliers...need to find tests or measures
# 5. Independence of observations (no serial correlation in residuals)
RarepCorrListBG.append(np.mean(sRarepCorrListBG))
RarepCorrListF.append(np.mean(sRarepCorrListF))
RichpCorrListBG.append(np.mean(sRichpCorrListBG))
RichpCorrListF.append(np.mean(sRichpCorrListF))
DompCorrListBG.append(np.mean(sDompCorrListBG))
DompCorrListF.append(np.mean(sDompCorrListF))
EvenpCorrListBG.append(np.mean(sEvenpCorrListBG))
EvenpCorrListF.append(np.mean(sEvenpCorrListF))
# 6. Homoscedacticity
RarepHomoHW.append(np.mean(sRarepHomoHW))
RarepHomoHB.append(np.mean(sRarepHomoHB))
RichpHomoHB.append(np.mean(sRichpHomoHB))
RichpHomoHW.append(np.mean(sRichpHomoHW))
DompHomoHW.append(np.mean(sDompHomoHW))
DompHomoHB.append(np.mean(sDompHomoHB))
EvenpHomoHW.append(np.mean(sEvenpHomoHW))
EvenpHomoHB.append(np.mean(sEvenpHomoHB))
# 7. Normally distributed residuals (errors)
RarepNormListOmni.append(np.mean(sRarepNormListOmni))
RarepNormListJB.append(np.mean(sRarepNormListJB))
RarepNormListKS.append(np.mean(sRarepNormListKS))
RarepNormListAD.append(np.mean(sRarepNormListAD))
RichpNormListOmni.append(np.mean(sRichpNormListOmni))
RichpNormListJB.append(np.mean(sRichpNormListJB))
RichpNormListKS.append(np.mean(sRichpNormListKS))
RichpNormListAD.append(np.mean(sRichpNormListAD))
DompNormListOmni.append(np.mean(sDompNormListOmni))
DompNormListJB.append(np.mean(sDompNormListJB))
DompNormListKS.append(np.mean(sDompNormListKS))
DompNormListAD.append(np.mean(sDompNormListAD))
EvenpNormListOmni.append(np.mean(sEvenpNormListOmni))
EvenpNormListJB.append(np.mean(sEvenpNormListJB))
EvenpNormListKS.append(np.mean(sEvenpNormListKS))
EvenpNormListAD.append(np.mean(sEvenpNormListAD))
fig.add_subplot(4, 3, 1)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
plt.ylim(0, 1)
plt.xscale('log')
# Rarity R2 vs. Sample Size
plt.plot(NLIST, RareR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
plt.text(1.01, 0.6, 'Rarity', rotation='vertical', fontsize=16)
leg = plt.legend(loc=4, prop={'size': 14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 2)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
plt.xscale('log')
plt.ylim(0.0, 0.16)
# Rarity Coeffs vs. Sample Size
plt.plot(NLIST, Rare_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Rare_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, RareIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
leg = plt.legend(loc=10, prop={'size': 8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 3)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
plt.ylim(0.0, 0.6)
plt.xscale('log')
# Rarity p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(RarepLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST,RarepLinListRainB, c='m')
plt.plot(NLIST, RarepLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST,RarepCorrListBG, c='c')
plt.plot(NLIST, RarepCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST, RarepHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST,RarepHomoHB, c='r', ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST, RarepNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST,RarepNormListJB, c='Lime', ls='-')
#plt.plot(NLIST,RarepNormListKS, c='Lime', ls='--', lw=3)
#plt.plot(NLIST,RarepNormListAD, c='Lime', ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
leg = plt.legend(loc=1, prop={'size': 8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 4)
plt.xscale('log')
plt.ylim(0, 1)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
# Dominance R2 vs. Sample Size
plt.plot(NLIST, DomR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
plt.text(1.01, 0.82, 'Dominance', rotation='vertical', fontsize=16)
leg = plt.legend(loc=4, prop={'size': 14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 5)
plt.ylim(-0.2, 1.2)
plt.xscale('log')
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
# Dominance Coeffs vs. Sample Size
plt.plot(NLIST, Dom_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Dom_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, DomIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
leg = plt.legend(loc=10, prop={'size': 8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 6)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
plt.xscale('log')
#plt.yscale('log')
plt.ylim(0, 0.6)
# Dominance p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(DompLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST, DompLinListRainB, c='m')
plt.plot(NLIST, DompLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST, DompCorrListBG, c='c')
plt.plot(NLIST, DompCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST, DompHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST, DompHomoHB, c='r',ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST, DompNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST, DompNormListJB, c='Lime', ls='-')
#plt.plot(NLIST, DompNormListKS, c='Lime', ls='--', lw=3)
#plt.plot(NLIST, DompNormListAD, c='Lime', ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
leg = plt.legend(loc=1, prop={'size': 8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 7)
plt.text(1.01, 0.7, 'Evenness', rotation='vertical', fontsize=16)
plt.xscale('log')
plt.ylim(0, 1)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
# Evenness R2 vs. Sample Size
plt.plot(NLIST, EvenR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
leg = plt.legend(loc=4, prop={'size': 14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 8)
plt.ylim(-0.25, 0.0)
plt.xscale('log')
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
# Evenness Coeffs vs. Sample Size
plt.plot(NLIST, Even_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Even_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, EvenIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
leg = plt.legend(loc=10, prop={'size': 8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 9)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
plt.xscale('log')
plt.ylim(0.0, 0.3)
# Evenness p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(EvenpLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST, EvenpLinListRainB, c='m')
plt.plot(NLIST, EvenpLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST, EvenpCorrListBG, c='c')
plt.plot(NLIST, EvenpCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST, EvenpHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST, EvenpHomoHB, c='r', ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST, EvenpNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST, EvenpNormListJB, c='Lime', alpha=0.9, ls='-')
#plt.plot(NLIST, EvenpNormListKS, c='Lime', alpha=0.9, ls='--', lw=3)
#plt.plot(NLIST, EvenpNormListAD, c='Lime', alpha=0.9, ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
leg = plt.legend(loc=1, prop={'size': 8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 10)
plt.xscale('log')
plt.ylim(0, 1)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
# Dominance R2 vs. Sample Size
plt.plot(NLIST, RichR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
plt.xlabel('Sample size', fontsize=14)
plt.text(1.01, 0.82, 'Richness', rotation='vertical', fontsize=16)
leg = plt.legend(loc=4, prop={'size': 14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 11)
plt.ylim(-0.2, 1.2)
plt.xscale('log')
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
# Richness Coeffs vs. Sample Size
plt.plot(NLIST, Rich_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Rich_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, RichIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
plt.xlabel('Sample size', fontsize=14)
leg = plt.legend(loc=10, prop={'size': 8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 12)
plt.xlim(min(SampSizes) - 1, max(SampSizes) + 10)
plt.xscale('log')
# Richness p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(RichpLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST,RichpLinListRainB, c='m')
plt.plot(NLIST, RichpLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST,RichpCorrListBG, c='c')
plt.plot(NLIST, EvenpCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST, RichpHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST,RichpHomoHB, c='r', ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST, RichpNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST,RichpNormListJB, c='Lime', ls='-')
#plt.plot(NLIST,RichpNormListKS, c='Lime', ls='--', lw=3)
#plt.plot(NLIST,RichpNormListAD, c='Lime', ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
plt.xlabel('Sample size', fontsize=14)
leg = plt.legend(loc=1, prop={'size': 8})
leg.draw_frame(False)
#plt.tick_params(axis='both', which='major', labelsize=fs-3)
plt.subplots_adjust(wspace=0.4, hspace=0.4)
plt.savefig(mydir + 'figs/appendix/SampleSize/SampleSizeEffects.png',
dpi=600,
bbox_inches="tight")
#plt.close()
#plt.show()
return
def test(self) -> AndersonDarlingTestResult:
df_results = self.__calculate_residuals()
statistics, p_value = normal_ad(df_results['Residuals'])
return AndersonDarlingTestResult(p_value, statistics)
def find_group_DW(tree, dist_matrix, mes=0, seed_max=0, l_significance=0.1):
'''
For more details, see the Kim et al. 2008.
tree :
Tree structure returned from Pycluster module.
dist_matrix :
Distance matrix (= 1. - correlation matrix)
mes = 0 :
Total number of measurement of each light curve.
seed_max = 0 :
To get more tighter seed. 1 ~ 10 are good values. '10' gets more tighter clusters than '1'.
return :
List of clusters.
'''
#r.library('nortest') ############################################################################################
clusters = []
#print tree, len(tree)
density_list = []
for i in range(len(dist_matrix) - 1):
for j in range(i + 1, len(dist_matrix)):
density_list.append(dist_matrix[i][j])
density_list_clip = sigma_clipping(density_list, sigma=3.)
overall_density = (max(density_list_clip) - min(density_list_clip)) / len(dist_matrix)
#print overall_density, mean(density_list_clip), std(density_list_clip)
#get highly correlated pair of elements.
initial_seed = []
for i in range(len(tree)):
#both left and right element has to be star. not a link to other cluster.
if tree[i].left >= 0 and tree[i].right >= 0:
#to get more tight elements.
if dist_matrix[tree[i].left][tree[i].right] <= median(density_list_clip) / seed_max:
if mes == 0:
initial_seed.append(i)
elif dist_matrix[tree[i].left][tree[i].right] <= (1. - 3. / math.sqrt(mes)):
initial_seed.append(i)
#print initial_seed
#start from highly correlated initial pair.
for i in initial_seed:
#print tree[i]
current_node = i
while current_node < len(tree) - 1:
cluster_1 = []
cluster_2 = []
#find base cluster --> cluster_1
simplify_group(find_group_with_node_index(tree, current_node), cluster_1)
#find cluster which will be merged --> cluster_2
dummy = find_one_side_group(tree, (current_node + 1) * -1)
current_node = dummy[0]
simplify_group(dummy[1], cluster_2)
#check the density changes with overall density
#initial density
d_1 = []
for ele_i in range(len(cluster_1) - 1):
for ele_j in range(ele_i + 1, len(cluster_1)):
if ele_i != ele_j:
d_1.append(dist_matrix[cluster_1[ele_i]][cluster_1[ele_j]])
#density after merged
d_merge = []
cluster_3 = hstack([cluster_1, cluster_2])
for ele_i in range(len(cluster_3) - 1):
for ele_j in range(ele_i + 1, len(cluster_3)):
if ele_i != ele_j:
d_merge.append(dist_matrix[cluster_3[ele_i]][cluster_3[ele_j]])
d_1 = array(d_1)
d_merge = array(d_merge)
if len(d_merge) < 8:
continue
else:
#the resulting clusters are almost identical. not use anymore.
#d_merge = array(d_merge)
#d_merge = .5 * log((1. + d_merge) / (1. - d_merge))
#ad = r.ad_test(d_merge) ############################################################################################
ad = normal_ad(d_merge)
ad_p = ad[1]
p_value = ad_p
#check the level of significance
#if it's out of normality, the previous cluster is the final cluster.
if p_value < l_significance:
#becausd AD test needs at least 8 elements.
if len(cluster_1) >= 5:
#print cluster_1
clusters.append(cluster_1)
break
#it's still gaussian, but if there comes outliers into clusters, stop it.
#the resulting clusters are almost identical. not use anymore.
#elif len(d_1[where(d_1 > mean(density_list_clip))]) > 0:
# if len(cluster_1) >= 5:
# clusters.append(cluster_1)
# break
return clusters
def test_normal_errors_distribution(model_path, data_path):
from statsmodels.stats.diagnostic import normal_ad
df_results = calculate_residuals(model_path, data_path)
p_value = normal_ad(df_results.Residuals)[1]
assert p_value < 0.05
print("----------------------------------------------")
col_count = self.data.dropna().value_counts()
col_count_percent = self.data.dropna() \
.value_counts(normalize=True) \
.apply(lambda x: str(round(x * 100, 2)) + '%')
print(pd.concat([col_count, col_count_percent], axis=1))
except ValueError as err:
print('An error occurred while performing range analysis: ', err)
def _distribution_analysis(self):
""" output : boolean
Outputs whether the data follows a normal distribution or not and also plots the histogram and Normal Probability plot"""
print("\nDistribution Analysis")
print("----------------------------------------------")
try:
ad_test_statistic, pvalue = normal_ad(self.data[~np.isnan(self.data)])
print('Anderson-Darling Test Coefficient: ', ad_test_statistic)
if pvalue > 0.05:
print('Normal Distribution: ', True)
elif pvalue < 0.05:
print('Normal Distribution: ', False)
else:
print('We need to collect more data to check if the data follows a normal distribution')
plt.figure(1)
# histogram of the data
plt.subplot(2, 1, 1)
plt.hist(self.data[~np.isnan(self.data)], bins=30)
plt.title('Histogram')
plt.xlabel('Values')
plt.ylabel('Frequency')
# Normal Probability Plot
data1 = np.loadtxt('Data1.txt')
data2 = np.loadtxt('Data2.txt')
#Calculate bandwidth with Cross Validation Least Seuqares
dens1 = KDEMultivariate(data=[data1], var_type='c', bw='cv_ls')
dens2 = KDEMultivariate(data=[data2], var_type='c', bw='cv_ls')
#Calculate bandwidth with Silverman's rule of thumb
bw1 = np.std(data1)*(4./(3.*len(data1)))**(1./5.)
bw2 = np.std(data2)*(4./(3.*len(data2)))**(1./5.)
#Analyzing Data 1: KDE, Parent distribution, std and mean
x_grid1 = np.linspace(0,70,1000)
pdf1 = dens1.pdf(x_grid1)
mean1, std1 = np.mean(data1),np.std(data1)
x1, y1 = gauss(std1,mean1)
p1 = normal_ad(data1)[1]
mean_kde1, std_kde1 = np.mean(pdf1),np.std(pdf1)
#Analyzing Data 2: KDE, Parent distribution, std and mean
x_grid2 = np.linspace(0,70,1000)
pdf2 = dens2.pdf(x_grid2)
mean2, std2 = np.mean(data2),np.std(data2)
x2,y2 = lognormal(0.2,1.0)
p2 = ks_2samp(y2,data2)[1]
mean_kde2, std_kde2 = np.mean(pdf2),np.std(pdf2)
#Plot the histograms, the parent distributions and the KDEs
plt.ion()
plt.clf()
fig = plt.figure(00,figsize=(15,5))
ax1 = fig.add_subplot(121)
def gauss(sig=1, x0=0):
x = np.linspace(x0 - 10 * sig, x0 + 10 * sig, 1000)
y = 1.0 / (np.sqrt(2 * np.pi) * sig) * np.exp(-(x - x0)**2 / (2 * sig**2))
return x, y
# Histogram of CO2 Emissions
plt.figure(2)
hist = plt.hist(data_2015_simple.CO2_emissions, bins=50, density=True)
x_gauss, y_gauss = gauss(sig=std, x0=mean)
plt.figure(3)
plt.plot(x_gauss, y_gauss, 'r--')
#plt.savefig('Attempted_Gaussian_Fit')
ad, p = normal_ad(data_2015_simple.CO2_emissions) # A-D test
print(p) # Basically 0
# KDE Estimation
kde = gaussian_kde(data_2015_simple.CO2_emissions)
xvals = np.linspace(0, 50, 10000)
plt.figure(4)
plt.plot(xvals, kde.pdf(xvals), 'r--')
plt.xlim(0, 50)
plt.hist(data_2015_simple.CO2_emissions, bins=np.arange(50), density=True)
plt.ylabel('Frequency', fontsize=12)
plt.xlabel('CO2 Emissions Per Capita', fontsize=12)
plt.title('KDE Plot')
#plt.savefig('CO2_Emissions_KDE.png')
ds.nonparametric_summary(df['y']) # alphap=0.33 betap=0.33 by default
ds.nonparametric_summary(df['y'], alphap=0, betap=0) # Minitab
df.min()
df.max()
df.mean()
df.std()
df.var()
df.skew()
df.kurt()
df.count()
adresult = anderson(df['y'], dist='norm')
adresult.statistic
smd.normal_ad(df['y'])
sm.norm.interval(0.95,
loc=np.mean(df['y']),
scale=sm.sem(df['y']))
sm.t.interval(0.95,
len(df['y']-1),
loc=np.mean(df['y']),
scale=sm.sem(df['y']))
fig = sm.graphics.tsa.plot_acf(sunspot_data.values.squeeze(), lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(sunspot_data, lags=40, ax=ax2)
arma_mod20 = sm.tsa.ARMA(sunspot_data, (2,0)).fit()
arma_mod30 = sm.tsa.ARMA(sunspot_data, (3,0)).fit()
stattools.durbin_watson(arma_mod30.resid.values)
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax = arma_mod30.resid.plot(ax=ax)
resid = arma_mod30.resid
diag.normal_ad(resid)
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
fig = qqplot(resid, line='q', ax=ax, fit=True)
fig = plt.figure(figsize=(12,8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(resid.values.squeeze(), lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2)
r,q,p = sm.tsa.acf(resid.values.squeeze(), qstat=True)
data = np.c_[range(1,41), r[1:], q, p]
table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"])
print(table.set_index('lag'))
visualizer = ResidualsPlot(regressor, hist=False)
visualizer.fit(X_train, y_train)
visualizer.score(X_test, y_test)
visualizer.show()
# Observed vs Predicted
sns.residplot(y_test, y_pred)
np.mean(y_test-y_pred)
# Statistic method to check normality (Using the Anderson-Darling test for normal distribution)
from statsmodels.stats.diagnostic import normal_ad
p_value_thresh = .05
# Performing the test on the residuals
p_value = normal_ad(y_test-y_pred)[1]
print('p-value from the test - below 0.05 generally means non-normal:', p_value)
# Reporting the normality of the residuals
if p_value < p_value_thresh:
print('Residuals are not normally distributed')
else:
print('Residuals are normally distributed')
# Plotting the residuals distribution with Histogram to see the how the residuals are spread
plt.subplots(figsize=(12, 6))
plt.title('Distribution of Residuals')
sns.distplot(y_test-y_pred)
plt.show()
def validate(self, all=False):
'''
validate
Method that validates the main assumptions of linear regressions
Thanks to https://jeffmacaluso.github.io/post/LinearRegressionAssumptions/
'''
p_value_thresh = 0.05 # (5% double sided)
self.err = self.y_pred - self.y
display(HTML("<h1>Linear Regression Validation Report</h1>"))
display(HTML("<h3>Metrics</h3>"))
display(HTML(
f"<b>R2:</b> {r2_score(self.y, self.y_pred)} <br> \
<b>RMSE:</b> {mean_squared_error(self.y, self.y_pred, squared=False)}"
))
display(HTML("<h3>Linear Assumption</h3>"))
# Predicted vs Real
fig = plt.figure(figsize=(4, 3))
df_ = pd.DataFrame(self.y.rename("y"), index=self.y.index).join(pd.DataFrame(self.y_pred.rename("y_pred"), index=self.y_pred.index))
sns.scatterplot(x='y', y='y_pred', data=df_)
# Plotting the diagonal line
min_ = max(self.y.min(),self.y_pred.min())
max_ = max(self.y.max(),self.y_pred.max())
plt.plot((min_, max_), (min_, max_), color='darkorange', linestyle='--')
plt.title('Real vs. Predicted')
plt.show()
display(HTML("<h3>Normal Assumption of errors - Anderson-Darling</h3>"))
# Using the Anderson-Darling test for normal distribution
p_value = normal_ad(self.err)[1]
if p_value <= p_value_thresh: display(HTML(f'<span style="color:red;font-weight:bold">Normal assumption not satisfied (p_value: {p_value})</span> --> confidence intervals will likely be affected. Try to perform nonliear transformations on variables. Info on QQPlot: <a href="https://seankross.com/2016/02/29/A-Q-Q-Plot-Dissection-Kit.html">here</a>.'))
# Normal error distribution
fig, axes = plt.subplots(1, 2, figsize=(8,3))
plt.tight_layout(pad=0.3)
sns.distplot(
self.y,
fit = norm,
ax = axes[0],
)
axes[0].set_title(f"Error normality (skw: {round(self.err.skew(),2)})")
#qqplot
sm.qqplot(self.err, line ='q', ax=axes[1])
axes[1].set_title(f"qqplot")
plt.show()
display(HTML("<h3>Assumption of non-autocorrelation</h3>"))
# Assumes that there is no autocorrelation in the residuals. If there is
# autocorrelation, then there is a pattern that is not explained due to
# the current value being dependent on the previous value.
# This may be resolved by adding a lag variable of either the dependent
# variable or some of the predictors.
# Durbin-Watson Test
# Values of 1.5 < d < 2.5 generally show that there is no autocorrelation in the data
# 0 to 2< is positive autocorrelation
# >2 to 4 is negative autocorrelation
durbinWatson = durbin_watson(self.err)
if durbinWatson < 1.5:
display(HTML('<span style="color:red;font-weight:bold">Signs of positive autocorrelation</span>'))
elif durbinWatson > 2.5:
display(HTML('<span style="color:red;font-weight:bold">Signs of negative autocorrelation</span>'))
else:
display(HTML('No signs of autocorrelation'))
display(HTML("<h3>Assumption of Random error vs predictors - Homoscedasticity</h3>"))
# If heteroscedasticity: Variables with high ranges may be the cause
# For the dependent variable, use rates or per capita ratios instead of raw variables. That may change the project.
#
fig = plt.figure(figsize=(4, 3))
sns.scatterplot(x=self.y_pred, y=self.err)
plt.title('Error vs. Predicted')
plt.show()
if all:
# Random errors vs predictors
num_pred = len(self.X.columns)
fig_columns = 3
fig, axes = plt.subplots(math.ceil(num_pred/fig_columns), fig_columns, figsize=(4*fig_columns, math.ceil(num_pred/fig_columns)*3))
#plt.tight_layout(pad=1)
row = 0
col = 0
for i in range(num_pred):
axes[row, col].axhline(y=0, linewidth=4, color='r')
axes[row, col].set_title(f"Err vs {self.X.columns[i]}")
sns.scatterplot(
x = self.X.iloc[:,i],
y = self.err,
ax = axes[row, col]
)
if ((i+1)%fig_columns == 0): col = 0
else: col+=1
if col == 0: row += 1
plt.show()
# summarize feature importance
df_imp_ = pd.DataFrame(self.lrmodel.coef_, index=self.X.columns, columns=["importance"])
df_imp_["importance_abs"] = df_imp_["importance"].abs()
df_imp_.sort_values(by="importance_abs", ascending=False, inplace=True)
df_imp_.drop("importance_abs", axis=1, inplace=True)
s_imp_ = df_imp_["importance"]
# plot feature importance
fig = plt.figure(figsize=(15,4))
plt.xticks(rotation=90)
sns.barplot(x=s_imp_.index, y=s_imp_.values)
plt.show()
plt.show()
#T test
mvp = np.array([-0.038736455,-0.136159028,-0.186696644,-0.069105119,-0.225828899,-0.377797055,-0.151966429,0.138888407,0.177621218,-0.149457563,-0.164333338,-0.069042195,])
mE= np.array([-0.2,-0.274,-0.12,-0.22,-0.33,-0.57,-0.34,0.13,0.05,-0.26,-0.03,-0.12,])
"""geting means and sample variances"""
svp = np.std(mvp,ddof=1)
sE = np.std(mE,ddof=1)
meanvp = np.mean(mvp)
meanE = np.mean(mE)
"""Test for normality"""
print('Anderson Darling Test for normality')
print(diagnostic.normal_ad(mvp))
print(diagnostic.normal_ad(mE))
print(stats.ttest_1samp(mvp, 0))
print(stats.ttest_1samp(mE, 0))
#print(stats.anderson(pvMO_Hres,dist='norm'))
"""Test for Different Means two-tailed t-test"""
print('Two-tailed T-test for different means')
two_sample_diff_var = stats.ttest_ind(mvp, mE, equal_var=False)
print(two_sample_diff_var)
Pairs = ['O/OH','O/OH$_{2}$','O/O$_{2}$','O/OOH','N/NH','N/NH$_{2}$','NH/NH$_{2}$','C/CH','C/CH$_{2}$','C/CH$_{3}$','C/CO','O/CH$_{3}$']
me = [0.43,0.096,0.53,0.74,0.65,0.29,0.47,0.83,0.47,0.24,0.57,0.66]
mv = [0.63,0.37,0.65,0.96,0.98,0.86,0.81,0.7,0.42,0.5,0.6,0.78]
mvp = [0.59,0.23,0.46,0.89,0.75,0.48,0.66,0.84,0.60,0.35,0.44,0.71]
def Fig_OLS_Checks():
#fs = 10 # font size used across figures
#color = str()
#OrC = 'open'
SampSizes = [5, 6, 7, 8, 9, 10, 13, 16, 20, 30, 40, 50, 60, 70, 80, 90, 100]
Iterations = 100
fig = plt.figure(figsize=(12, 8))
# MODEL PARAMETERS
Rare_MacIntercept_pVals = [] # List to hold coefficient p-values
Rare_MacIntercept_Coeffs = [] # List to hold coefficients
Rich_MacIntercept_pVals = []
Rich_MacIntercept_Coeffs = []
Dom_MacIntercept_pVals = []
Dom_MacIntercept_Coeffs = []
Even_MacIntercept_pVals = []
Even_MacIntercept_Coeffs = []
Rare_MicIntercept_pVals = []
Rare_MicIntercept_Coeffs = []
Rich_MicIntercept_pVals = []
Rich_MicIntercept_Coeffs = []
Dom_MicIntercept_pVals = []
Dom_MicIntercept_Coeffs = []
Even_MicIntercept_pVals = []
Even_MicIntercept_Coeffs = []
Rare_MacSlope_pVals = []
Rare_MacSlope_Coeffs = []
Rich_MacSlope_pVals = []
Rich_MacSlope_Coeffs = []
Dom_MacSlope_pVals = []
Dom_MacSlope_Coeffs = []
Even_MacSlope_pVals = []
Even_MacSlope_Coeffs = []
Rare_MicSlope_pVals = []
Rare_MicSlope_Coeffs = []
Rich_MicSlope_pVals = []
Rich_MicSlope_Coeffs = []
Dom_MicSlope_pVals = []
Dom_MicSlope_Coeffs = []
Even_MicSlope_pVals = []
Even_MicSlope_Coeffs = []
RareR2List = [] # List to hold model R2
RarepFList = [] # List to hold significance of model R2
RichR2List = [] # List to hold model R2
RichpFList = [] # List to hold significance of model R2
DomR2List = [] # List to hold model R2
DompFList = [] # List to hold significance of model R2
EvenR2List = [] # List to hold model R2
EvenpFList = [] # List to hold significance of model R2
# ASSUMPTIONS OF LINEAR REGRESSION
# 1. Error in predictor variables is negligible...presumably yes
# 2. Variables are measured at the continuous level...yes
# 3. The relationship is linear
#RarepLinListHC = []
RarepLinListRainB = []
RarepLinListLM = []
#RichpLinListHC = []
RichpLinListRainB = []
RichpLinListLM = []
#DompLinListHC = []
DompLinListRainB = []
DompLinListLM = []
#EvenpLinListHC = []
EvenpLinListRainB = []
EvenpLinListLM = []
# 4. There are no significant outliers...need to find tests or measures
# 5. Independence of observations (no serial correlation in residuals)
RarepCorrListBG = []
RarepCorrListF = []
RichpCorrListBG = []
RichpCorrListF = []
DompCorrListBG = []
DompCorrListF = []
EvenpCorrListBG = []
EvenpCorrListF = []
# 6. Homoscedacticity
RarepHomoHW = []
RarepHomoHB = []
RichpHomoHW = []
RichpHomoHB = []
DompHomoHW = []
DompHomoHB = []
EvenpHomoHW = []
EvenpHomoHB = []
# 7. Normally distributed residuals (errors)
RarepNormListOmni = [] # Omnibus test for normality
RarepNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
RarepNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
RarepNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
RichpNormListOmni = [] # Omnibus test for normality
RichpNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
RichpNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
RichpNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
DompNormListOmni = [] # Omnibus test for normality
DompNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
DompNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
DompNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
EvenpNormListOmni = [] # Omnibus test for normality
EvenpNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
EvenpNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
EvenpNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
NLIST = []
for SampSize in SampSizes:
sRare_MacIntercept_pVals = [] # List to hold coefficient p-values
sRare_MacIntercept_Coeffs = [] # List to hold coefficients
sRich_MacIntercept_pVals = [] # List to hold coefficient p-values
sRich_MacIntercept_Coeffs = [] # List to hold coefficients
sDom_MacIntercept_pVals = []
sDom_MacIntercept_Coeffs = []
sEven_MacIntercept_pVals = []
sEven_MacIntercept_Coeffs = []
sRare_MicIntercept_pVals = []
sRare_MicIntercept_Coeffs = []
sRich_MicIntercept_pVals = []
sRich_MicIntercept_Coeffs = []
sDom_MicIntercept_pVals = []
sDom_MicIntercept_Coeffs = []
sEven_MicIntercept_pVals = []
sEven_MicIntercept_Coeffs = []
sRare_MacSlope_pVals = []
sRare_MacSlope_Coeffs = []
sRich_MacSlope_pVals = []
sRich_MacSlope_Coeffs = []
sDom_MacSlope_pVals = []
sDom_MacSlope_Coeffs = []
sEven_MacSlope_pVals = []
sEven_MacSlope_Coeffs = []
sRare_MicSlope_pVals = []
sRare_MicSlope_Coeffs = []
sRich_MicSlope_pVals = []
sRich_MicSlope_Coeffs = []
sDom_MicSlope_pVals = []
sDom_MicSlope_Coeffs = []
sEven_MicSlope_pVals = []
sEven_MicSlope_Coeffs = []
sRareR2List = [] # List to hold model R2
sRarepFList = [] # List to hold significance of model R2
sRichR2List = [] # List to hold model R2
sRichpFList = [] # List to hold significance of model R2
sDomR2List = [] # List to hold model R2
sDompFList = [] # List to hold significance of model R2
sEvenR2List = [] # List to hold model R2
sEvenpFList = [] # List to hold significance of model R2
# ASSUMPTIONS OF LINEAR REGRESSION
# 1. Error in predictor variables is negligible...presumably yes
# 2. Variables are measured at the continuous level...yes
# 3. The relationship is linear
#sRarepLinListHC = []
sRarepLinListRainB = []
sRarepLinListLM = []
#sRichpLinListHC = []
sRichpLinListRainB = []
sRichpLinListLM = []
#sDompLinListHC = []
sDompLinListRainB = []
sDompLinListLM = []
#sEvenpLinListHC = []
sEvenpLinListRainB = []
sEvenpLinListLM = []
# 4. There are no significant outliers...need to find tests or measures
# 5. Independence of observations (no serial correlation in residuals)
sRarepCorrListBG = []
sRarepCorrListF = []
sRichpCorrListBG = []
sRichpCorrListF = []
sDompCorrListBG = []
sDompCorrListF = []
sEvenpCorrListBG = []
sEvenpCorrListF = []
# 6. Homoscedacticity
sRarepHomoHW = []
sRarepHomoHB = []
sRichpHomoHW = []
sRichpHomoHB = []
sDompHomoHW = []
sDompHomoHB = []
sEvenpHomoHW = []
sEvenpHomoHB = []
# 7. Normally distributed residuals (errors)
sRarepNormListOmni = [] # Omnibus test for normality
sRarepNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
sRarepNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sRarepNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
sRichpNormListOmni = [] # Omnibus test for normality
sRichpNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
sRichpNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sRichpNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
sDompNormListOmni = [] # Omnibus test for normality
sDompNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
sDompNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sDompNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
sEvenpNormListOmni = [] # Omnibus test for normality
sEvenpNormListJB = [] # Calculate residual skewness, kurtosis, and do the JB test for normality
sEvenpNormListKS = [] # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
sEvenpNormListAD = [] # Anderson-Darling test for normal distribution unknown mean and variance
for iteration in range(Iterations):
Nlist, Slist, Evarlist, ESimplist, ENeelist, EHeiplist, EQlist = [[], [], [], [], [], [], []]
klist, Shanlist, BPlist, SimpDomlist, SinglesList, tenlist, onelist = [[], [], [], [], [], [], []]
NmaxList, rareSkews, KindList = [[], [], []]
NSlist = []
ct = 0
radDATA = []
datasets = []
GoodNames = ['EMPclosed', 'HMP', 'BIGN', 'TARA', 'BOVINE', 'HUMAN', 'LAUB', 'SED', 'CHU', 'CHINA', 'CATLIN', 'FUNGI', 'HYDRO', 'BBS', 'CBC', 'MCDB', 'GENTRY', 'FIA'] # all microbe data is MGRAST
mlist = ['micro', 'macro']
for m in mlist:
for name in os.listdir(mydir +'data/'+m):
if name in GoodNames: pass
else: continue
path = mydir+'data/'+m+'/'+name+'/'+name+'-SADMetricData.txt'
num_lines = sum(1 for line in open(path))
datasets.append([name, m, num_lines])
numMac = 0
numMic = 0
radDATA = []
for d in datasets:
name, kind, numlines = d
lines = []
lines = np.random.choice(range(1, numlines+1), SampSize, replace=True)
path = mydir+'data/'+kind+'/'+name+'/'+name+'-SADMetricData.txt'
for line in lines:
data = linecache.getline(path, line)
radDATA.append(data)
#print name, kind, numlines, len(radDATA)
for data in radDATA:
data = data.split()
if len(data) == 0:
print 'no data'
continue
name, kind, N, S, Var, Evar, ESimp, EQ, O, ENee, EPielou, EHeip, BP, SimpDom, Nmax, McN, skew, logskew, chao1, ace, jknife1, jknife2, margalef, menhinick, preston_a, preston_S = data
N = float(N)
S = float(S)
Nlist.append(float(np.log(N)))
Slist.append(float(np.log(S)))
NSlist.append(float(np.log(N/S)))
Evarlist.append(float(np.log(float(Evar))))
ESimplist.append(float(np.log(float(ESimp))))
KindList.append(kind)
BPlist.append(float(BP))
NmaxList.append(float(np.log(float(BP)*float(N))))
EHeiplist.append(float(EHeip))
# lines for the log-modulo transformation of skewnness
skew = float(skew)
sign = 1
if skew < 0: sign = -1
lms = np.log(np.abs(skew) + 1)
lms = lms * sign
#if lms > 3: print name, N, S
rareSkews.append(float(lms))
if kind == 'macro': numMac += 1
elif kind == 'micro': numMic += 1
ct+=1
#print 'Sample Size:',SampSize, ' Mic:', numMic,'Mac:', numMac
# Multiple regression for Rarity
d = pd.DataFrame({'N': list(Nlist)})
d['Rarity'] = list(rareSkews)
d['Kind'] = list(KindList)
RarityResults = smf.ols('Rarity ~ N * Kind', d).fit() # Fit the dummy variable regression model
#print RarityResults.summary(), '\n'
# Multiple regression for Rarity
d = pd.DataFrame({'N': list(Nlist)})
d['Richness'] = list(Slist)
d['Kind'] = list(KindList)
RichnessResults = smf.ols('Richness ~ N * Kind', d).fit() # Fit the dummy variable regression model
#print RichnessResults.summary(), '\n'
# Multiple regression for Dominance
d = pd.DataFrame({'N': list(Nlist)})
d['Dominance'] = list(NmaxList)
d['Kind'] = list(KindList)
DomResults = smf.ols('Dominance ~ N * Kind', d).fit() # Fit the dummy variable regression model
#print DomResults.summary(), '\n'
# Multiple regression for Evenness
d = pd.DataFrame({'N': list(Nlist)})
d['Evenness'] = list(ESimplist)
d['Kind'] = list(KindList)
EvenResults = smf.ols('Evenness ~ N * Kind', d).fit() # Fit the dummy variable regression model
#print RarityResults.summary(), '\n'
RareResids = RarityResults.resid # residuals of the model
RichResids = RichnessResults.resid # residuals of the model
DomResids = DomResults.resid # residuals of the model
EvenResids = EvenResults.resid # residuals of the model
# MODEL RESULTS/FIT
RareFpval = RarityResults.f_pvalue
Rarer2 = RarityResults.rsquared # coefficient of determination
#Adj_r2 = RareResults.rsquared_adj # adjusted
RichFpval = RichnessResults.f_pvalue
Richr2 = RichnessResults.rsquared # coefficient of determination
#Adj_r2 = RichnessResults.rsquared_adj # adjusted
DomFpval = DomResults.f_pvalue
Domr2 = DomResults.rsquared # coefficient of determination
#Adj_r2 = DomResults.rsquared_adj # adjusted
EvenFpval = EvenResults.f_pvalue
Evenr2 = EvenResults.rsquared # coefficient of determination
#Adj_r2 = EvenResuls.rsquared_adj # adjusted
# MODEL PARAMETERS and p-values
Rareparams = RarityResults.params
Rareparams = Rareparams.tolist()
Rarepvals = RarityResults.pvalues
Rarepvals = Rarepvals.tolist()
Richparams = RichnessResults.params
Richparams = Richparams.tolist()
Richpvals = RichnessResults.pvalues
Richpvals = Richpvals.tolist()
Domparams = DomResults.params
Domparams = Domparams.tolist()
Dompvals = DomResults.pvalues
Dompvals = Dompvals.tolist()
Evenparams = EvenResults.params
Evenparams = Evenparams.tolist()
Evenpvals = EvenResults.pvalues
Evenpvals = Evenpvals.tolist()
sRare_MacIntercept_pVals.append(Rarepvals[0])
sRare_MacIntercept_Coeffs.append(Rareparams[0])
sRich_MacIntercept_pVals.append(Rarepvals[0])
sRich_MacIntercept_Coeffs.append(Rareparams[0])
sDom_MacIntercept_pVals.append(Dompvals[0])
sDom_MacIntercept_Coeffs.append(Domparams[0])
sEven_MacIntercept_pVals.append(Evenpvals[0])
sEven_MacIntercept_Coeffs.append(Evenparams[0])
sRare_MicIntercept_pVals.append(Rarepvals[1])
if Rarepvals[1] > 0.05:
sRare_MicIntercept_Coeffs.append(Rareparams[1])
else:
sRare_MicIntercept_Coeffs.append(Rareparams[1])
sRich_MicIntercept_pVals.append(Richpvals[1])
if Richpvals[1] > 0.05:
sRich_MicIntercept_Coeffs.append(Richparams[1])
else:
sRich_MicIntercept_Coeffs.append(Richparams[1])
sDom_MicIntercept_pVals.append(Dompvals[1])
if Dompvals[1] > 0.05:
sDom_MicIntercept_Coeffs.append(Domparams[1])
else:
sDom_MicIntercept_Coeffs.append(Domparams[1])
sEven_MicIntercept_pVals.append(Evenpvals[1])
if Evenpvals[1] > 0.05:
sEven_MicIntercept_Coeffs.append(Evenparams[1])
else:
sEven_MicIntercept_Coeffs.append(Evenparams[1])
sRare_MacSlope_pVals.append(Rarepvals[2])
sRare_MacSlope_Coeffs.append(Rareparams[2])
sRich_MacSlope_pVals.append(Richpvals[2])
sRich_MacSlope_Coeffs.append(Richparams[2])
sDom_MacSlope_pVals.append(Dompvals[2])
sDom_MacSlope_Coeffs.append(Domparams[2])
sEven_MacSlope_pVals.append(Evenpvals[2])
sEven_MacSlope_Coeffs.append(Evenparams[2])
sRare_MicSlope_pVals.append(Rarepvals[3])
if Rarepvals[3] > 0.05:
sRare_MicSlope_Coeffs.append(Rareparams[3])
else:
sRare_MicSlope_Coeffs.append(Rareparams[3])
sRich_MicSlope_pVals.append(Richpvals[3])
if Richpvals[3] > 0.05:
sRich_MicSlope_Coeffs.append(Richparams[3])
else:
sRich_MicSlope_Coeffs.append(Richparams[3])
sDom_MicSlope_pVals.append(Dompvals[3])
if Dompvals[3] > 0.05:
sDom_MicSlope_Coeffs.append(Domparams[3])
else:
sDom_MicSlope_Coeffs.append(Domparams[3])
sEven_MicSlope_pVals.append(Evenpvals[3])
if Evenpvals[3] > 0.05:
sEven_MicSlope_Coeffs.append(Evenparams[3])
else:
sEven_MicSlope_Coeffs.append(Evenparams[3])
sRareR2List.append(Rarer2)
sRarepFList.append(RareFpval)
sRichR2List.append(Richr2)
sRichpFList.append(RichFpval)
sDomR2List.append(Domr2)
sDompFList.append(DomFpval)
sEvenR2List.append(Evenr2)
sEvenpFList.append(EvenFpval)
# TESTS OF LINEAR REGRESSION ASSUMPTIONS
# Error in predictor variables is negligible...Presumably Yes
# Variables are measured at the continuous level...Definitely Yes
# TESTS FOR LINEARITY, i.e., WHETHER THE DATA ARE CORRECTLY MODELED AS LINEAR
#HC = smd.linear_harvey_collier(RarityResults) # Harvey Collier test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
#sRarepLinListHC.append(HC)
#HC = smd.linear_harvey_collier(DomResults) # Harvey Collier test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
#sDompLinListHC.append(HC)
#HC = smd.linear_harvey_collier(EvenResults) # Harvey Collier test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
#sEvenpLinListHC.append(HC)
RB = smd.linear_rainbow(RarityResults) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sRarepLinListRainB.append(RB[1])
RB = smd.linear_rainbow(RichnessResults) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sRichpLinListRainB.append(RB[1])
RB = smd.linear_rainbow(DomResults) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sDompLinListRainB.append(RB[1])
RB = smd.linear_rainbow(EvenResults) # Rainbow test for linearity. The Null hypothesis is that the regression is correctly modeled as linear.
sEvenpLinListRainB.append(RB[1])
LM = smd.linear_lm(RarityResults.resid, RarityResults.model.exog) # Lagrangian multiplier test for linearity
sRarepLinListLM.append(LM[1])
LM = smd.linear_lm(RichnessResults.resid, RichnessResults.model.exog) # Lagrangian multiplier test for linearity
sRichpLinListLM.append(LM[1])
LM = smd.linear_lm(DomResults.resid, DomResults.model.exog) # Lagrangian multiplier test for linearity
sDompLinListLM.append(LM[1])
LM = smd.linear_lm(EvenResults.resid, EvenResults.model.exog) # Lagrangian multiplier test for linearity
sEvenpLinListLM.append(LM[1])
# INDEPENDENCE OF OBSERVATIONS (no serial correlation in residuals)
BGtest = smd.acorr_breush_godfrey(RarityResults, nlags=None, store=False) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(RareResids, lags=None, boxpierce=True)
sRarepCorrListBG.append(BGtest[1])
sRarepCorrListF.append(BGtest[3])
BGtest = smd.acorr_breush_godfrey(RichnessResults, nlags=None, store=False) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(RichResids, lags=None, boxpierce=True)
sRichpCorrListBG.append(BGtest[1])
sRichpCorrListF.append(BGtest[3])
BGtest = smd.acorr_breush_godfrey(DomResults, nlags=None, store=False) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(DomResids, lags=None, boxpierce=True)
sDompCorrListBG.append(BGtest[1])
sDompCorrListF.append(BGtest[3])
BGtest = smd.acorr_breush_godfrey(EvenResults, nlags=None, store=False) # Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
# Lagrange multiplier test statistic, p-value for Lagrange multiplier test, fstatistic for F test, pvalue for F test
#BGtest = smd.acorr_ljungbox(EvenResids, lags=None, boxpierce=True)
sEvenpCorrListBG.append(BGtest[1])
sEvenpCorrListF.append(BGtest[3])
# There are no significant outliers...Need tests or measures/metrics
# HOMOSCEDASTICITY
# These tests return:
# 1. lagrange multiplier statistic,
# 2. p-value of lagrange multiplier test,
# 3. f-statistic of the hypothesis that the error variance does not depend on x,
# 4. p-value for the f-statistic
HW = sms.het_white(RareResids, RarityResults.model.exog)
sRarepHomoHW.append(HW[3])
HW = sms.het_white(RichResids, RichnessResults.model.exog)
sRichpHomoHW.append(HW[3])
HW = sms.het_white(DomResids, DomResults.model.exog)
sDompHomoHW.append(HW[3])
HW = sms.het_white(EvenResids, EvenResults.model.exog)
sEvenpHomoHW.append(HW[3])
HB = sms.het_breushpagan(RareResids, RarityResults.model.exog)
sRarepHomoHB.append(HB[3])
HB = sms.het_breushpagan(RichResids, RichnessResults.model.exog)
sRichpHomoHB.append(HB[3])
HB = sms.het_breushpagan(DomResids, DomResults.model.exog)
sDompHomoHB.append(HB[3])
HB = sms.het_breushpagan(EvenResids, EvenResults.model.exog)
sEvenpHomoHB.append(HB[3])
# 7. NORMALITY OF ERROR TERMS
O = sms.omni_normtest(RareResids)
sRarepNormListOmni.append(O[1])
O = sms.omni_normtest(RichResids)
sRichpNormListOmni.append(O[1])
O = sms.omni_normtest(DomResids)
sDompNormListOmni.append(O[1])
O = sms.omni_normtest(EvenResids)
sEvenpNormListOmni.append(O[1])
JB = sms.jarque_bera(RareResids)
sRarepNormListJB.append(JB[1]) # Calculate residual skewness, kurtosis, and do the JB test for normality
JB = sms.jarque_bera(RichResids)
sRichpNormListJB.append(JB[1]) # Calculate residual skewness, kurtosis, and do the JB test for normality
JB = sms.jarque_bera(DomResids)
sDompNormListJB.append(JB[1]) # Calculate residual skewness, kurtosis, and do the JB test for normality
JB = sms.jarque_bera(EvenResids)
sEvenpNormListJB.append(JB[1]) # Calculate residual skewness, kurtosis, and do the JB test for normality
KS = smd.kstest_normal(RareResids)
sRarepNormListKS.append(KS[1]) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
KS = smd.kstest_normal(RichResids)
sRichpNormListKS.append(KS[1]) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
KS = smd.kstest_normal(DomResids)
sDompNormListKS.append(KS[1]) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
KS = smd.kstest_normal(EvenResids)
sEvenpNormListKS.append(KS[1]) # Lillifors test for normality, Kolmogorov Smirnov test with estimated mean and variance
AD = smd.normal_ad(RareResids)
sRarepNormListAD.append(AD[1]) # Anderson-Darling test for normal distribution unknown mean and variance
AD = smd.normal_ad(RichResids)
sRichpNormListAD.append(AD[1]) # Anderson-Darling test for normal distribution unknown mean and variance
AD = smd.normal_ad(DomResids)
sDompNormListAD.append(AD[1]) # Anderson-Darling test for normal distribution unknown mean and variance
AD = smd.normal_ad(EvenResids)
sEvenpNormListAD.append(AD[1]) # Anderson-Darling test for normal distribution unknown mean and variance
print 'Sample size:',SampSize, 'iteration:',iteration
NLIST.append(SampSize)
Rare_MacIntercept_pVals.append(np.mean(sRare_MacIntercept_pVals)) # List to hold coefficient p-values
Rare_MacIntercept_Coeffs.append(np.mean(sRare_MacIntercept_Coeffs)) # List to hold coefficients
Rich_MacIntercept_pVals.append(np.mean(sRich_MacIntercept_pVals)) # List to hold coefficient p-values
Rich_MacIntercept_Coeffs.append(np.mean(sRich_MacIntercept_Coeffs)) # List to hold coefficients
Dom_MacIntercept_pVals.append(np.mean(sDom_MacIntercept_pVals))
Dom_MacIntercept_Coeffs.append(np.mean(sDom_MacIntercept_Coeffs))
Even_MacIntercept_pVals.append(np.mean(sEven_MacIntercept_pVals))
Even_MacIntercept_Coeffs.append(np.mean(sEven_MacIntercept_Coeffs))
Rare_MicIntercept_pVals.append(np.mean(sRare_MicIntercept_pVals))
Rare_MicIntercept_Coeffs.append(np.mean(sRare_MicIntercept_Coeffs))
Rich_MicIntercept_pVals.append(np.mean(sRich_MicIntercept_pVals))
Rich_MicIntercept_Coeffs.append(np.mean(sRich_MicIntercept_Coeffs))
Dom_MicIntercept_pVals.append(np.mean(sDom_MicIntercept_pVals))
Dom_MicIntercept_Coeffs.append(np.mean(sDom_MicIntercept_Coeffs))
Even_MicIntercept_pVals.append(np.mean(sEven_MicIntercept_pVals))
Even_MicIntercept_Coeffs.append(np.mean(sEven_MicIntercept_Coeffs))
Rare_MacSlope_pVals.append(np.mean(sRare_MacSlope_pVals)) # List to hold coefficient p-values
Rare_MacSlope_Coeffs.append(np.mean(sRare_MacSlope_Coeffs)) # List to hold coefficients
Rich_MacSlope_pVals.append(np.mean(sRich_MacSlope_pVals)) # List to hold coefficient p-values
Rich_MacSlope_Coeffs.append(np.mean(sRich_MacSlope_Coeffs)) # List to hold coefficients
Dom_MacSlope_pVals.append(np.mean(sDom_MacSlope_pVals))
Dom_MacSlope_Coeffs.append(np.mean(sDom_MacSlope_Coeffs))
Even_MacSlope_pVals.append(np.mean(sEven_MacSlope_pVals))
Even_MacSlope_Coeffs.append(np.mean(sEven_MacSlope_Coeffs))
Rare_MicSlope_pVals.append(np.mean(sRare_MicSlope_pVals))
Rare_MicSlope_Coeffs.append(np.mean(sRare_MicSlope_Coeffs))
Rich_MicSlope_pVals.append(np.mean(sRich_MicSlope_pVals))
Rich_MicSlope_Coeffs.append(np.mean(sRich_MicSlope_Coeffs))
Dom_MicSlope_pVals.append(np.mean(sDom_MicSlope_pVals))
Dom_MicSlope_Coeffs.append(np.mean(sDom_MicSlope_Coeffs))
Even_MicSlope_pVals.append(np.mean(sEven_MicSlope_pVals))
Even_MicSlope_Coeffs.append(np.mean(sEven_MicSlope_Coeffs))
RareR2List.append(np.mean(sRareR2List))
RarepFList.append(np.mean(sRarepFList))
RichR2List.append(np.mean(sRichR2List))
RichpFList.append(np.mean(sRichpFList))
DomR2List.append(np.mean(sDomR2List))
DompFList.append(np.mean(sDompFList))
EvenR2List.append(np.mean(sEvenR2List))
EvenpFList.append(np.mean(sEvenpFList))
# ASSUMPTIONS OF LINEAR REGRESSION
# 1. Error in predictor variables is negligible...presumably yes
# 2. Variables are measured at the continuous level...yes
# 3. The relationship is linear
#RarepLinListHC.append(np.mean(sRarepLinListHC))
RarepLinListRainB.append(np.mean(sRarepLinListRainB))
RarepLinListLM.append(np.mean(sRarepLinListLM))
#RichpLinListHC.append(np.mean(sRichpLinListHC))
RichpLinListRainB.append(np.mean(sRichpLinListRainB))
RichpLinListLM.append(np.mean(sRichpLinListLM))
#DompLinListHC.append(np.mean(sDompLinListHC))
DompLinListRainB.append(np.mean(sDompLinListRainB))
DompLinListLM.append(np.mean(sDompLinListLM))
#EvenpLinListHC.append(np.mean(sEvenpLinListHC))
EvenpLinListRainB.append(np.mean(sEvenpLinListRainB))
EvenpLinListLM.append(np.mean(sEvenpLinListLM))
# 4. There are no significant outliers...need to find tests or measures
# 5. Independence of observations (no serial correlation in residuals)
RarepCorrListBG.append(np.mean(sRarepCorrListBG))
RarepCorrListF.append(np.mean(sRarepCorrListF))
RichpCorrListBG.append(np.mean(sRichpCorrListBG))
RichpCorrListF.append(np.mean(sRichpCorrListF))
DompCorrListBG.append(np.mean(sDompCorrListBG))
DompCorrListF.append(np.mean(sDompCorrListF))
EvenpCorrListBG.append(np.mean(sEvenpCorrListBG))
EvenpCorrListF.append(np.mean(sEvenpCorrListF))
# 6. Homoscedacticity
RarepHomoHW.append(np.mean(sRarepHomoHW))
RarepHomoHB.append(np.mean(sRarepHomoHB))
RichpHomoHB.append(np.mean(sRichpHomoHB))
RichpHomoHW.append(np.mean(sRichpHomoHW))
DompHomoHW.append(np.mean(sDompHomoHW))
DompHomoHB.append(np.mean(sDompHomoHB))
EvenpHomoHW.append(np.mean(sEvenpHomoHW))
EvenpHomoHB.append(np.mean(sEvenpHomoHB))
# 7. Normally distributed residuals (errors)
RarepNormListOmni.append(np.mean(sRarepNormListOmni))
RarepNormListJB.append(np.mean(sRarepNormListJB))
RarepNormListKS.append(np.mean(sRarepNormListKS))
RarepNormListAD.append(np.mean(sRarepNormListAD))
RichpNormListOmni.append(np.mean(sRichpNormListOmni))
RichpNormListJB.append(np.mean(sRichpNormListJB))
RichpNormListKS.append(np.mean(sRichpNormListKS))
RichpNormListAD.append(np.mean(sRichpNormListAD))
DompNormListOmni.append(np.mean(sDompNormListOmni))
DompNormListJB.append(np.mean(sDompNormListJB))
DompNormListKS.append(np.mean(sDompNormListKS))
DompNormListAD.append(np.mean(sDompNormListAD))
EvenpNormListOmni.append(np.mean(sEvenpNormListOmni))
EvenpNormListJB.append(np.mean(sEvenpNormListJB))
EvenpNormListKS.append(np.mean(sEvenpNormListKS))
EvenpNormListAD.append(np.mean(sEvenpNormListAD))
fig.add_subplot(4, 3, 1)
plt.xlim(min(SampSizes)-1,max(SampSizes)+10)
plt.ylim(0,1)
plt.xscale('log')
# Rarity R2 vs. Sample Size
plt.plot(NLIST,RareR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
plt.text(1.01, 0.6, 'Rarity', rotation='vertical', fontsize=16)
leg = plt.legend(loc=4,prop={'size':14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 2)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
plt.xscale('log')
plt.ylim(0.0, 0.16)
# Rarity Coeffs vs. Sample Size
plt.plot(NLIST, Rare_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Rare_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, RareIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
leg = plt.legend(loc=10,prop={'size':8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 3)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
plt.ylim(0.0, 0.6)
plt.xscale('log')
# Rarity p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(RarepLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST,RarepLinListRainB, c='m')
plt.plot(NLIST,RarepLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST,RarepCorrListBG, c='c')
plt.plot(NLIST,RarepCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST,RarepHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST,RarepHomoHB, c='r', ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST,RarepNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST,RarepNormListJB, c='Lime', ls='-')
#plt.plot(NLIST,RarepNormListKS, c='Lime', ls='--', lw=3)
#plt.plot(NLIST,RarepNormListAD, c='Lime', ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
leg = plt.legend(loc=1,prop={'size':8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 4)
plt.xscale('log')
plt.ylim(0,1)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
# Dominance R2 vs. Sample Size
plt.plot(NLIST, DomR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
plt.text(1.01, 0.82, 'Dominance', rotation='vertical', fontsize=16)
leg = plt.legend(loc=4,prop={'size':14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 5)
plt.ylim(-0.2, 1.2)
plt.xscale('log')
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
# Dominance Coeffs vs. Sample Size
plt.plot(NLIST, Dom_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Dom_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, DomIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
leg = plt.legend(loc=10,prop={'size':8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 6)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
plt.xscale('log')
#plt.yscale('log')
plt.ylim(0, 0.6)
# Dominance p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(DompLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST, DompLinListRainB, c='m')
plt.plot(NLIST, DompLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST, DompCorrListBG, c='c')
plt.plot(NLIST, DompCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST, DompHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST, DompHomoHB, c='r',ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST, DompNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST, DompNormListJB, c='Lime', ls='-')
#plt.plot(NLIST, DompNormListKS, c='Lime', ls='--', lw=3)
#plt.plot(NLIST, DompNormListAD, c='Lime', ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
leg = plt.legend(loc=1,prop={'size':8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 7)
plt.text(1.01, 0.7, 'Evenness', rotation='vertical', fontsize=16)
plt.xscale('log')
plt.ylim(0,1)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
# Evenness R2 vs. Sample Size
plt.plot(NLIST, EvenR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
leg = plt.legend(loc=4,prop={'size':14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 8)
plt.ylim(-0.25, 0.0)
plt.xscale('log')
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
# Evenness Coeffs vs. Sample Size
plt.plot(NLIST, Even_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Even_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, EvenIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
leg = plt.legend(loc=10,prop={'size':8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 9)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
plt.xscale('log')
plt.ylim(0.0, 0.3)
# Evenness p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(EvenpLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST, EvenpLinListRainB, c='m')
plt.plot(NLIST, EvenpLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST, EvenpCorrListBG, c='c')
plt.plot(NLIST, EvenpCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST, EvenpHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST, EvenpHomoHB, c='r', ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST, EvenpNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST, EvenpNormListJB, c='Lime', alpha=0.9, ls='-')
#plt.plot(NLIST, EvenpNormListKS, c='Lime', alpha=0.9, ls='--', lw=3)
#plt.plot(NLIST, EvenpNormListAD, c='Lime', alpha=0.9, ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
leg = plt.legend(loc=1,prop={'size':8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 10)
plt.xscale('log')
plt.ylim(0,1)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
# Dominance R2 vs. Sample Size
plt.plot(NLIST, RichR2List, c='0.2', ls='--', lw=2, label=r'$R^2$')
plt.ylabel(r'$R^2$', fontsize=14)
plt.xlabel('Sample size', fontsize=14)
plt.text(1.01, 0.82, 'Richness', rotation='vertical', fontsize=16)
leg = plt.legend(loc=4,prop={'size':14})
leg.draw_frame(False)
fig.add_subplot(4, 3, 11)
plt.ylim(-0.2, 1.2)
plt.xscale('log')
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
# Richness Coeffs vs. Sample Size
plt.plot(NLIST, Rich_MicSlope_Coeffs, c='r', lw=2, label='Microbe')
plt.plot(NLIST, Rich_MacSlope_Coeffs, c='b', lw=2, label='Macrobe')
#plt.plot(NLIST, RichIntCoeffList, c='g', label='Interaction')
plt.ylabel('Coefficient')
plt.xlabel('Sample size', fontsize=14)
leg = plt.legend(loc=10,prop={'size':8})
leg.draw_frame(False)
fig.add_subplot(4, 3, 12)
plt.xlim(min(SampSizes)-1, max(SampSizes)+10)
plt.xscale('log')
# Richness p-vals vs. Sample Size
# 3. The relationship is linear
#plt.plot(RichpLinListHC, NLIST, c='m', alpha=0.8)
#plt.plot(NLIST,RichpLinListRainB, c='m')
plt.plot(NLIST,RichpLinListLM, c='m', ls='-', label='linearity')
# 5. Independence of observations (no serial correlation in residuals)
#plt.plot(NLIST,RichpCorrListBG, c='c')
plt.plot(NLIST, EvenpCorrListF, c='c', ls='-', label='autocorrelation')
# 6. Homoscedacticity
plt.plot(NLIST,RichpHomoHW, c='orange', ls='-', label='homoscedasticity')
#plt.plot(NLIST,RichpHomoHB, c='r', ls='-')
# 7. Normally distributed residuals (errors)
plt.plot(NLIST,RichpNormListOmni, c='Lime', ls='-', label='normality')
#plt.plot(NLIST,RichpNormListJB, c='Lime', ls='-')
#plt.plot(NLIST,RichpNormListKS, c='Lime', ls='--', lw=3)
#plt.plot(NLIST,RichpNormListAD, c='Lime', ls='--')
plt.plot([1, 100], [0.05, 0.05], c='0.2', ls='--')
plt.ylabel('p-value')
plt.xlabel('Sample size', fontsize=14)
leg = plt.legend(loc=1,prop={'size':8})
leg.draw_frame(False)
#plt.tick_params(axis='both', which='major', labelsize=fs-3)
plt.subplots_adjust(wspace=0.4, hspace=0.4)
plt.savefig(mydir+'figs/appendix/SampleSize/SampleSizeEffects.png', dpi=600, bbox_inches = "tight")
#plt.close()
#plt.show()
return
