def normality_test(y):
# Realiza un test de normalidad de Kolmogorov-Smirnnof sobre la variable endógena y muestra una gráfica de
# distribución
# Parámetros:
# y (Series): Objeto Series de pandas con la variable endógena.
# Devuelve:
# Nada.
normality_test = kstest_normal(y, dist='norm')
stats = ['KS Stat', 'KS-Test p-value']
print("---Test de Kolmogorov-Smirnnof---")
print(dict(zip(stats, normality_test)))
if (normality_test[1] > 0.05):
print(
"Aceptamos la hipótesis nula, ergo la variable se distribuye según una normal."
)
else:
print(
"Fallamos al aceptar la hipótesis nula, ergo la variable no se distribuye según una normal."
)
sns.distplot(y)
plt.show()
def check_normality():
'''Check if the distribution is normal.'''
# Generate and show a distribution
numData = 100
# To get reproducable values, I provide a seed value
np.random.seed(987654321)
data = stats.norm.rvs(myMean, mySD, size=numData)
plt.hist(data)
plt.show()
# --- >>> START stats <<< ---
# Graphical test: if the data lie on a line, they are pretty much
# normally distributed
_ = stats.probplot(data, plot=plt)
plt.show()
pVals = pd.Series()
# The scipy normaltest is based on D-Agostino and Pearsons test that
# combines skew and kurtosis to produce an omnibus test of normality.
_, pVals['omnibus'] = stats.normaltest(data)
# Shapiro-Wilk test
_, pVals['Shapiro-Wilk'] = stats.shapiro(data)
# Or you can check for normality with Lilliefors-test
ksStats, pVals['Lilliefors'] = kstest_normal(data)
# Alternatively with original Kolmogorov-Smirnov test
_, pVals['KS'] = stats.kstest((data-np.mean(data))/np.std(data,ddof=1), 'norm')
print(pVals)
if pVals['omnibus'] > 0.05:
print('Data are normally distributed')
def kstestnormal (spike_features):
"""
Ranks features using a Lilliefors test for
normality
Parameters
----------
spike_features : ndarray
The spike features
Returns
-------
index_features_sorted : ndarray
The indices of selected features in order of decreasing KS test
statistic
"""
num_total_features = np.shape(spike_features)[1]
from statsmodels.stats.diagnostic import kstest_normal
ksD = np.zeros(num_total_features)
ksp = np.zeros(num_total_features)
for f in range(num_total_features):
ksD[f], ksp[f] = kstest_normal(spike_features[:,f], pvalmethod='approx')
index_features_sorted = heapq.nlargest(num_total_features, range(len(ksD)), ksD.take)
return index_features_sorted
def main():
procs = int(input("Напишите количество процессов, которые вы хотите использовать для обработки данных: "))
ests = int(input("Напишите количество выборок, которое вы хотите сгенерировать для проведения кластеризации: "))
iris, _ = fisher_iris()
start_time = time.time()
iris = np.hstack((np.arange(150).reshape((150, 1)), iris))
iris_samples = iris_sep(iris, procs)
multiprocessing.set_start_method('fork')
queue = multiprocessing.Queue()
processes = []
for proc in range(procs):
processes.append(multiprocessing.Process(target=make_all, args=(iris_samples[proc], queue, ests, procs)))
for process in processes:
process.start()
total_samples = []
for _ in range(procs):
total_samples.append(queue.get())
for process in processes:
process.join()
# Завершена работа процессов, последующее объединение подвыборок в выборку
print('Завершение работы процессов')
total_data = get_total_sample_data(procs, ests, total_samples)
silhouette_list = get_silhouette_list(total_data)
print('Список оценённых коэффициентов силуэта')
sil_time_start = time.time()
print(silhouette_list)
print('Время кластеризации и расчёта коэффициентов силуэта для {0} процессов составило: {1}'.format(ests, sil_time_start - time.time()))
print('Оценка нормальности распределения коэффициентов силуэта')
print('Тест Харке-Бера')
print(jarque_bera(silhouette_list))
PrettyTable
print('Тест Колмогорова-Смирнова')
print(kstest_normal(silhouette_list, dist='norm', pvalmethod='approx'))
# Объединение выборок из каждого потока, расчёт
print("%s seconds" % (time.time() - start_time))
def check_2samples(pd_serie1, pd_serie2, title=None):
# pd_serie1 = sag['potencia_ls_l1']
# pd_serie2 = sag['potencia_ls_l2']
## check normalidad
pd_serie1.hist(bins=50)
plt.title(title)
plt.show()
pd_serie2.hist(bins=50)
plt.title(title)
plt.show()
#qqplot
from statsmodels.graphics.gofplots import qqplot
qqplot(pd_serie1, line='r')
plt.title('qqplot pd_serie1')
plt.show()
qqplot(pd_serie2, line='r')
plt.title('qqplot pd_serie2')
plt.show()
# tests results
from scipy.stats import shapiro
from statsmodels.stats.diagnostic import kstest_normal
print('results normal tests')
print('pd_serie1')
print('shapiro p-value', shapiro(pd_serie1)[1])
print('KS p-value', kstest_normal(pd_serie1, dist='norm')[1])
print()
print('pd_serie2')
print('shapiro p-value', shapiro(pd_serie2)[1])
print('KS p-value', kstest_normal(pd_serie2, dist='norm')[1])
print()
## chequeo independencia
## correlations
from scipy.stats import pearsonr
from scipy.stats import spearmanr
print('')
print('Pearson Correlation:', pearsonr(pd_serie1, pd_serie2)[0])
print('Spearman Correlation:', spearmanr(pd_serie1, pd_serie2)[0])
plt.plot(pd_serie1, pd_serie2, '.')
plt.title('distribucion ')
def test_residuals_normality(methods):
threshold_p = 0.05
print("> Kolmogorov-Smirnov test")
for method in methods:
ksstat, pvalue = kstest_normal(method.residuals,
dist='norm',
pvalmethod='table')
print(
f"{method.name}: ks={ksstat}, p={pvalue}. {'❌' if pvalue < threshold_p else '✅'}."
)
def check_normal(pd_serie, bins=None):
# pd_serie = pd.Series(mod1.resid_pearson)
# pd_serie = sag_l1['bwi_ls_l1']
name = pd_serie.name
if isinstance(name, (str)) != True:
name = ''
## check normalidad
sns.distplot(pd_serie, bins=bins)
if name != '':
plt.title(name)
plt.show()
#qqplot
from statsmodels.graphics.gofplots import qqplot
# import matplotlib.pyplot as plt
qqplot(pd_serie, line='r')
plt.title('qqplot ' + name)
plt.show()
# tests results
from scipy.stats import shapiro
from statsmodels.stats.diagnostic import kstest_normal
shapiro_scipystats = shapiro(pd_serie)
ktest_statsmodelsstatsdiagnostic = kstest_normal(pd_serie, dist='norm')
print('results normal tests', name)
print('shapiro p-value', shapiro_scipystats[1])
print('KS p-value', ktest_statsmodelsstatsdiagnostic[1])
print()
print(
'Test used scipy.stats.shapiro and statsmodels.stats.diagnostic.ktest_normal'
)
print()
return {
'shapiro': shapiro_scipystats,
'ktest': ktest_statsmodelsstatsdiagnostic
}
def check_normal(pd_serie, bins=None):
name = pd_serie.name
if isinstance(name, (str)) != True:
name = ''
shapiro_scipystats = shapiro(pd_serie)
ktest_statsmodelsstatsdiagnostic = kstest_normal(pd_serie, dist='norm')
print('results normal tests', name)
print('shapiro p-value', shapiro_scipystats[1])
print('KS p-value', ktest_statsmodelsstatsdiagnostic[1])
print()
print(
'Test used scipy.stats.shapiro and statsmodels.stats.diagnostic.ktest_normal'
)
print()
return {
'shapiro': shapiro_scipystats,
'ktest': ktest_statsmodelsstatsdiagnostic
}
def entender_2017(df_2017):
style.use('ggplot')
altura = df_2017['Altura']
print('Media de la estatura de los runningbacks de la temporada 2017: ')
print(altura.loc[(df_2017['Status']=='ACT') & (df_2017['Yardas'] > 100)].mean())
print('Mediana de la estatura de los runningbacks de la temporada 2017: ')
print(altura.loc[(df_2017['Status']=='ACT') & (df_2017['Yardas'] > 100)].median())
espacio = ' '
fig = plt.figure()
ax = fig.add_subplot(111)
n, bins, patches = ax.hist(altura, bins = 9, color = 'orange', normed = True)
x_min, x_max = min(bins), max(bins)
lnspc = np.linspace(x_min, x_max, len(altura))
mu, sigma = stats.norm.fit(altura)
pdf = stats.norm.pdf(lnspc, mu, sigma)
ax.plot(lnspc, pdf, color = 'dodgerblue')
fig.subplots_adjust(bottom = 0.10)
ax.text(x = 165, y = -0.008,
s = ' ©Mauricio Mani' + espacio*150 + 'Source: NFL: www.nfl.com/players ',
fontsize = 12, color = '#f0f0f0', backgroundcolor = 'grey')
ax.text(x = 168, y = 0.087, s = "Estatura de runningbacks activos del 2017 - NFL ",
fontsize = 23, weight = 'bold', alpha = .75)
ax.text(x = 167, y = 0.083,
s = 'Histograma de la estatura de corredores activos comparados con una distribución normal',
fontsize = 16, alpha = .85)
fig = plt.figure()
ax = fig.add_subplot(111)
stats.probplot(altura, plot=plt)
ax.set_title('Normal Q-Q plot')
plt.show()
#Prueba kolmogorov-smirnov para normailidad (bondad de ajuste), similar a Lilliefors, pero con distribución KS.
ks, p_v = kstest_normal(altura)
print('El valor de la prueba Kolmogorov-Smirnov es: ' + str(ks))
print('El valor p de la prueba es: ' + str(p_v))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.hist(altura, bins = 9, cumulative=True, normed=True, histtype = 'step', linewidth=1.4)
cdf = stats.norm.cdf(lnspc, mu, sigma)
ax.plot(lnspc, cdf, color = 'dodgerblue')
plt.xlim(xmin=x_min, xmax = x_max)
fig.subplots_adjust(bottom = 0.10)
ax.text(x = 166, y = -0.10,
s = ' ©Mauricio Mani' + espacio*130 + 'Source: NFL: www.nfl.com/players ',
fontsize = 12, color = '#f0f0f0', backgroundcolor = 'grey')
ax.text(x = 167, y = 1.12, s = "Distribución acumulada de la estatura de corredores 2017 - NFL",
fontsize = 21, weight = 'bold', alpha = .75)
ax.text(x = 170, y = 1.05,
s = 'Para uso de la prueba de normalidad Kolmogorov-Smirnov y Lilliefors.',
fontsize = 16, alpha = .85)
ax.text(x = 169.5, y = 0.8,
s = 'Prueba Kolmogorov-Smirnov: ' + str(ks),
fontsize = 10)
ax.text(x = 169.5, y = 0.75,
s = 'P-value: ' + str(p_v),
fontsize = 10)
sw, sw_pv = stats.shapiro(altura)
print('El valor de la prueba Shapiro-Wilk es: ' + str(sw))
print('El valor p de la prueba es: ' + str(sw_pv))
plt.show()
fig = plt.figure()
ax = fig.add_subplot(111)
ax.boxplot(df_2017['Altura'].loc[(df_2017['Status']=='ACT') & (df_2017['Yardas'] > 800)])
print('Estadisticas básicas: ')
print('Media: ')
print(df_2017['Altura'].loc[(df_2017['Status']=='ACT') & (df_2017['Yardas'] > 800)].mean())
print('Meidana: ')
print(df_2017['Altura'].loc[(df_2017['Status']=='ACT') & (df_2017['Yardas'] > 800)].median())
print('Moda: ')
print(df_2017['Altura'].loc[(df_2017['Status']=='ACT') & (df_2017['Yardas'] > 800)].mode())
#La mediana y la moda son muy similares.
#El boxplot tamnien nos sirve para revisar la normalidad de un dataset.
plt.xticks([1], ['Mas de 800 yardas'])
fig.subplots_adjust(bottom = 0.10)
ax.text(x = 0.5, y = 169.5,
s = ' ©Mauricio Mani' + espacio*120 + 'Source: NFL: www.nfl.com/players ',
fontsize = 12, color = '#f0f0f0', backgroundcolor = 'grey')
ax.text(x = 0.5, y = 195, s = "Entender como funcionan los diagramas de caja - Boxplot",
fontsize = 22, weight = 'bold', alpha = .75)
ax.text(x = 0.5, y = 193,
s = 'Con un ejemplo sencillo de la National Football League con la estatura de los corredores con mas\nde 800 yardas en la temporada 2017.',
fontsize = 15, alpha = .85)
ax.annotate(s = 'Esta es la mediana\n"NO es la media"', xy =(1.075, 180), xytext = (1.15, 180), arrowprops=dict(facecolor='red', color='red'))
ax.annotate(s = 'Q1 o 25% de los datos', xy =(1.075, 177), xytext = (1.15, 177), arrowprops=dict(facecolor='red', color='red'))
ax.annotate(s = 'Q3 o 75% de los datos', xy =(0.925, 182.6), xytext = (0.72, 182.6), arrowprops=dict(facecolor='red', color='red'))
ax.annotate(s = 'Q3 + 1.5 * Rango Intercuatil', xy =(1.04, 185.9), xytext = (1.1, 185.9), arrowprops=dict(facecolor='red', color='red'))
ax.annotate(s = 'Q1 - 1.5 * Rango Intercuartil', xy =(0.96, 172.5), xytext = (0.7, 172.5), arrowprops=dict(facecolor='red', color='red'))
ax.annotate(s = 'Latavius Murray\nOutlier', xy =(1, 191.8), xytext = (0.85, 189), arrowprops=dict(facecolor='red', color='red'))
return(df_2017.loc[(df_2017['Status']=='ACT') & (df_2017['Yardas'] > 800)])
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 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 check_normality(df, variable, alpha=0.05):
##use only KS or Anderson Starling also?
ks, p = kstest_normal(df[variable])
if p>alpha:
return True
return False