def breusch_pagan_test(resid, exog):
'''
Perform Breush-Paga test and print out results.
Parameters:
resid - ols residuals, Series or array
exog - dataframe or matrix like structure
'''
print('(Calculation: sigma_i = sigma * f(alpha_0 + alpha z_i))')
name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f_pvalue']
test = sms.het_breushpagan(resid, exog)
table = [[n, v] for n, v in zip(name, test)]
headers = ["Statistic", "Value"]
print(tabulate(table, headers, tablefmt="simple"))
return test
print(plot_leverage_resid2(results)) # Other plotting options can be found on the [Graphics page.](http://www.statsmodels.org/stable/graphics.html) # ## Multicollinearity # # Condition number: np.linalg.cond(results.model.exog) # ## Heteroskedasticity tests # # Breush-Pagan test: name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value'] test = sms.het_breushpagan(results.resid, results.model.exog) lzip(name, test) # Goldfeld-Quandt test name = ['F statistic', 'p-value'] test = sms.het_goldfeldquandt(results.resid, results.model.exog) lzip(name, test) # ## Linearity # # Harvey-Collier multiplier test for Null hypothesis that the linear specification is correct: name = ['t value', 'p value'] test = sms.linear_harvey_collier(results) lzip(name, test)
# Other plotting options can be found on the [Graphics page.](http://statsmodels.sourceforge.net/stable/graphics.html)
# ## Multicollinearity
#
# Condition number:
np.linalg.cond(results.model.exog)
# ## Heteroskedasticity tests
#
# Breush-Pagan test:
name = ['Lagrange multiplier statistic', 'p-value',
'f-value', 'f p-value']
test = sms.het_breushpagan(results.resid, results.model.exog)
lzip(name, test)
# Goldfeld-Quandt test
name = ['F statistic', 'p-value']
test = sms.het_goldfeldquandt(results.resid, results.model.exog)
lzip(name, test)
# ## Linearity
#
# Harvey-Collier multiplier test for Null hypothesis that the linear specification is correct:
name = ['t value', 'p value']
# This block creates the objects for each statistic we'd like printed to Excel.<br>
# <br>
# It will report $R^2$, $R^2 adj,$ residuals, the f p-value, aic, the fitted model parameters, normality of the residuals, the Bruesh-Pagan Test for heteroscedasicity and the Harvey-Collier test for linearity.
# <codecell>
r_squared = model.rsquared
r_square_adj = model.rsquared_adj
residuals = model.resid
p = model.f_pvalue
aic = model.aic
pvalues = pd.DataFrame(model.pvalues)
params = pd.DataFrame(model.params)
normality = sms.jarque_bera(model.resid)
breush_pagan_hska = sms.het_breushpagan(model.resid, model.model.exog)
harvey_collier = sms.linear_harvey_collier(model)
# <headingcell level=4>
# Print the regression results to Excel
# <codecell>
Range("Results", "O6").value = "R^2"
Range("Results", "P6").value = r_squared
Range("Results", "O7").value = "R^2 Adjusted"
Range("Results", "P7").value = r_square_adj
Range("Results", "O8").value = "p-value"
def do_stats(df):
# Only view those that received vacation and are employed
df.is_employed.replace(0.0, np.nan, inplace=True)
df.paid_vacation.replace(0.0, np.nan, inplace=True)
df.dropna(inplace=True)
# No longer need this dummy
df.drop('is_employed', axis=1, inplace=True)
# Summary stats
if not f_exists(SUMMARY_TXT):
summary = df.describe().T
summary = np.round(summary, decimals=3)
with open(SUMMARY_TXT, 'w') as f:
f.write(summary.to_string())
# Test for autocorrelation: scatter matrix, correlation, run OLS
if not f_exists(SCAT_MATRIX_PNG):
scatter_matrix(df, alpha=0.2, figsize=(64, 64), diagonal='hist')
pylab.savefig(SCAT_MATRIX_PNG, bbox_inches='tight')
if not f_exists(CORR_TXT):
corr = df.corr()
corr = corr.reindex_axis(sorted(corr.columns, key=COL_ORDER.index),
axis=0)
corr = corr.reindex_axis(sorted(corr.columns, key=COL_ORDER.index),
axis=1)
for i, k in enumerate(corr):
row = corr[k]
for j in range(len(row)):
if j > i:
row[j] = np.nan
with open(CORR_TXT, 'w') as f:
f.write(np.round(corr, decimals=3).to_string(na_rep=''))
if not f_exists(OLS1_TXT):
ols_results = smf.ols(
formula='vacation ~ paid_vacation + np.square(paid_vacation) + '
'age + fam_size + is_female + income83 + salary + '
'np.square(salary)',
data=df).fit()
with open(OLS1_TXT, 'w') as f:
f.write(str(ols_results.summary()))
f.write('\n\nCondition Number: {}'.format(
np.linalg.cond(ols_results.model.exog)))
# Need to drop salary, too much autocorrelation
df.drop('salary', axis=1, inplace=True)
# test for Heteroskedasticity
if not f_exists(HET_BP_TXT):
ols_results = smf.ols(
formula='vacation ~ paid_vacation + np.square(paid_vacation) + '
'age + fam_size + is_female + income83',
data=df).fit()
names = ['LM', 'LM P val.', 'F Stat.', 'F Stat. P val.']
test = sms.het_breushpagan(ols_results.resid, ols_results.model.exog)
f_p = test[3]
with open(HET_BP_TXT, 'w') as f:
str_ = '\n'.join('{}: {}'.format(n, v)
for n, v in zip(names, test))
f.write(str_ + '\n\n')
if f_p < .01:
f.write('No Heteroskedasticity found.\n')
else:
f.write('Warning: Heteroskedasticity found!\n')
# no Heteroskedasticity found
# final OLS results
if not f_exists(OLS2_TXT):
ols_results = smf.ols(
formula='vacation ~ paid_vacation + np.square(paid_vacation) + '
'age + fam_size + is_female + income83',
data=df).fit().get_robustcov_results(cov_type='HAC', maxlags=1)
with open(OLS2_TXT, 'w') as f:
f.write(str(ols_results.summary()))
f.write('\n\nCondition Number: {}'.format(
np.linalg.cond(ols_results.model.exog)))
return df
data_mod = data_mod.dropna(
axis=0, subset=['knowmeth', 'electric', 'radio', 'tv', 'bicycle'])
answer4 = data_mod.shape[0] * data_mod.shape[1]
'''
answer 5, 6
'''
m1 = smf.ols('ceb ~ heduc + urban + electric + radio + tv + bicycle +'\
'nevermarr + idlnchld_noans + heduc_noans + usemeth_noans +'\
'age + educ + religion + idlnchld + knowmeth + usemeth +'\
'agefm', data=data_mod)
fitted = m1.fit()
'''
answer 7
'''
bp = sms.het_breushpagan(fitted.resid, fitted.model.exog)[1]
m2 = smf.ols('ceb ~ heduc + urban + electric + radio + tv + bicycle +'\
'nevermarr + idlnchld_noans + heduc_noans + usemeth_noans +'\
'age + educ + religion + idlnchld + knowmeth + usemeth +'\
'agefm', data=data_mod)
fitted2 = m2.fit(cov_type='HC1')
'''
answer 8
'''
m3 = smf.ols('ceb ~ heduc + urban + electric + bicycle +'\
'nevermarr + idlnchld_noans + heduc_noans + usemeth_noans +'\
'age + educ + idlnchld + knowmeth + usemeth +'\
'agefm', data=data_mod)
fitted3 = m3.fit()
model_new = sm.OLS.from_formula(formula=model.model.formula, data=data)
data_new = pd.DataFrame(pp.scale(data.values[:,:-1]), columns=['Beds','Healing_days','Income','Salary','Costs'])
model_new1 = sm.OLS.from_formula(formula=model.model.formula, data=data_new).fit()
print(model_new1.summary())
import patsy
y, X = patsy.dmatrices(model.model.formula, data, return_type='dataframe')
model_n = lm.LinearRegression()
#Кросс-Валидация
k_fold = KFold(n_splits=10)
scores = cross_val_score(model_n, X, y, cv=k_fold, scoring='r2')
predicted = cross_val_predict(model_n,X,y,cv=k_fold)
slope, intercept, r_value, p_value, std_err = st.linregress(y.values[:,0],predicted[:,0])
print(r_value*r_value)
#Гомоскедастичность (Бреуш-Паган, Голдфильд-Квандт)
test = sms.het_breushpagan(res11.resid, res11.model.exog)
name = ['Lagrange multiplier statistic', 'p-value',
'f-value', 'f p-value']
print(lzip(name, test))
name = ['F statistic', 'p-value']
test = sms.het_goldfeldquandt(res11.resid, res11.model.exog)
print(lzip(name, test))
#Q-Q
st.probplot(res4.resid,plot=plt)
sm.qqplot(res11.resid, line='s')
plt.show()
#Дарбин-Уотсон
dw = sms.stattools.durbin_watson(res11.resid)
print(dw)
def regress_excel(filename, sheetname):
"""
Define a function that takes in a data frame and a string to name the excel files produced and will returns results of
the regression performed
inputs:
* filename - name of excel file containing the dates, dependent variable, and independent variables as columns, in that
order, will be used for both _plots.xls and _results.xlsx resulting files saved in the current working
directory
* sheetname - name of the sheet in the excel file desired, will be used for both _plots.xls and _results.xlsx resulting
files saved in the current working directory
outputs: along with the [filename]_[sheetname]_plots.xls and _results.xlsx in the working directory, the function returns
* Results - has the following important attributes and methods
* .summary() - shows a summary of the regression results
* .params - is a pandas series of the parameters fitted by the model
"""
dates, dependent, independent = extract_data(filename, sheetname)
results = regress_data(dependent, independent)
parameters = pd.Series(results.params)
X = sm.add_constant(independent)
fignum = 0
# Generate test results for Breusch-Pagan LM test
bptest = sms.het_breushpagan(results.resid, results.model.exog)
plt.close()
sm.qqplot(results.resid, fit=True, line='45')
plt.title('Q-Q Plot')
plt.savefig('qq.jpg')
plt.close()
predicted = results.predict(X)
plt.plot(dates, predicted, 'r--', dates, dependent, 'b--')
plt.title('In Sample Backtesting')
plt.xlabel('Date')
plt.ylabel(dependent.name)
plt.legend()
plt.savefig('backtest.jpg')
plt.close()
w = Workbook()
ws = w.add_sheet('Plots')
plot_to_excel('qq.jpg', w, ws, fignum)
fignum += 1
plot_to_excel('backtest.jpg', w, ws, fignum)
fignum += 1
for i in range(len(results.model.exog_names)):
sm.graphics.plot_fit(results, results.model.exog_names[i])
fig_name = results.model.exog_names[i] + '_fitted.jpg'
plt.savefig(fig_name)
plt.close()
plot_to_excel(fig_name, w, ws, fignum)
fignum += 1
for i in range(len(independent.columns)):
plt.scatter(independent.iloc[:, i], results.resid)
plt.xlabel(independent.columns[i])
plt.ylabel('Residuals')
title_string = independent.columns[i] + ' vs. Residuals'
plt.title(title_string)
fig_name = independent.columns[i] + '_residuals.jpg'
plt.savefig(fig_name)
plt.close()
plot_to_excel(fig_name, w, ws, fignum)
fignum += 1
save_plots = filename[0:-5] + '_' + sheetname + '_plots.xls'
save_results = filename[0:-5] + '_' + sheetname + '_results.xlsx'
coef_plot(results, 'Coefficients.jpg')
plt.close()
plot_to_excel('Coefficients.jpg', w, ws, fignum)
fignum += 1
writer = pd.ExcelWriter(save_results, engine='xlsxwriter')
bptest = sms.het_breushpagan(results.resid, results.model.exog)
bptest = pd.DataFrame([bptest[0], bptest[1]], ['LM', 'P-Value'])
bptest.to_excel(writer, sheet_name="Breusch-Pagan")
parameters = pd.concat(
[results.params, results.bse, results.pvalues,
results.conf_int()],
axis=1)
parameters.columns = [
'Parameter', 'Std_Err', 'P-Value', 'Lower_Bound', 'Upper_Bound'
]
parameters.to_excel(writer, sheet_name='Parameters')
outliers = pd.concat([dates, results.outlier_test()], axis=1)
outliers = outliers.loc[outliers['bonf(p)'] < 0.05]
outliers.to_excel(writer, sheet_name='Outliers')
rsquared_adj = pd.DataFrame([results.rsquared_adj])
rsquared_adj.to_excel(writer, sheet_name='Adjusted R^2')
aic = pd.DataFrame([results.aic])
aic.to_excel(writer, sheet_name='AIC')
bic = pd.DataFrame([results.bic])
bic.to_excel(writer, sheet_name='BIC')
dw = sm.stats.stattools.durbin_watson(results.resid)
dw = pd.DataFrame([dw])
dw.to_excel(writer, sheet_name='Durbin Watson')
ftest = pd.DataFrame([results.fvalue, results.f_pvalue], ['F', 'P-Value'])
ftest.to_excel(writer, sheet_name="F Test")
mean_err = pd.DataFrame(
[results.mse_model, results.mse_resid, results.mse_total],
['MSR', 'MSE', 'MSTO'])
mean_err.to_excel(writer, sheet_name="Mean Squared Error")
cov_mat = pd.DataFrame(np.cov(np.transpose(independent)))
cov_mat.columns = independent.columns
cov_mat.index = independent.columns
cov_mat.to_excel(writer, sheet_name='Covariance Matrix')
writer.save()
w.save(save_plots)
for file in os.listdir(os.getcwd()):
if (file.endswith('.bmp') or file.endswith('.jpg')):
os.remove(file)
return results
import pandas as pd
import statsmodels.stats.api as sms
import statsmodels.formula.api as smf
df = pd.read_csv("trafficking_data.csv")
results = smf.ols('df["Adult victims"] ~ df["gdp"] + df["policy index"]',data=df).fit()
print sms.het_breushpagan(results.resid, results.model.exog)
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 Breush_Pagan(X,y):
ols_retults=ols(X,y)
name = ['LM statistic', 'p-value of LM test',
'f-statistic of the hypothesis', 'f p-value']
test = sms.het_breushpagan(ols_retults.resid, ols_retults.model.exog)
return lzip(name, test)
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 do_regression(data_frame, response_var, predicators):
Y = np.array(data_frame[response_var])
X = np.array(data_frame[predicators])
X = sm.add_constant(X)
linear_model = sm.OLS(Y,X)
lr = linear_model.fit()
## make a plot
fnou = response_var+"_vs_"+"("+("+".join(predicators))+")"+".pdf"
pp = PdfPages(fnou)
if(len(predicators) == 1):
## plot the data points
plt.clf()
plt.scatter(X[:,1], Y[:], s=0.5, c='b')
## plot the fitting line
x1 = np.arange(min(X[:,1]), max(X[:,1]), (max(X[:,1])-min(X[:,1]))*0.01 )
y1 = x1 * lr.params[1] + lr.params[0]
plt.plot(x1,y1,'b--')
plt.xlabel(predicators[0])
plt.ylabel(response_var)
plt.title(response_var+"_vs_"+predicators[0])
pp.savefig(bbox_inches='tight', papertype='a4')
## plot the residule-x
plt.clf()
plt.scatter(X[:,1], lr.resid, s = 5.0, c='b', alpha=0.4, linewidth=0.0)
plt.xlabel(predicators[0])
plt.ylabel("Residual")
pp.savefig(bbox_inches='tight', papertype='a4')
## plot residual square-x
plt.clf()
plt.scatter(X[:,1], lr.resid**2, s = 5.0, c='b', alpha=0.4, linewidth=0.0)
plt.xlabel(predicators[0])
plt.ylabel("Residual Square")
pp.savefig(bbox_inches='tight', papertype='a4')
y_pred = lr.predict(X)
## plot the residule-y-pred
plt.clf()
plt.scatter(y_pred, lr.resid, s = 5.0, c='r', alpha=0.4, linewidth=0.0)
plt.xlabel(response_var)
plt.ylabel("Residual")
pp.savefig(bbox_inches='tight', papertype='a4')
## plot residual square-y-pred
plt.clf()
plt.scatter(y_pred, lr.resid**2, s = 5.0, c='r', alpha=0.4, linewidth=0.0)
plt.xlabel(response_var)
plt.ylabel("Residual Square")
pp.savefig(bbox_inches='tight', papertype='a4')
## plot observed-predicted
plt.clf()
plt.scatter(y_pred, Y, s = 5.0, c='g', alpha=0.4, linewidth=0.0)
y1 = np.arange(min(Y),max(Y),(max(Y)-min(Y))*0.01)
plt.plot(y1,y1,'b--')
plt.xlabel("Predicted")
plt.ylabel("Observed")
#plt.title("Aggregated Regression")
plt.axis('equal')
pp.savefig(bbox_inches='tight', papertype='a4')
## make a histogram of residual
plt.clf()
plt.hist(lr.resid, bins=40)
plt.title("Regression Residual Distribution")
res_hist = np.histogram(lr.resid,bins=40)
bin_w = res_hist[1][1] - res_hist[1][0]
res_mean = np.mean(lr.resid)
res_std = np.std(lr.resid)
x1 = np.arange(min(lr.resid), max(lr.resid), (max(lr.resid)-min(lr.resid))*0.01 )
y1 = norm.pdf((x1-res_mean)/res_std)*len(lr.resid)*bin_w/res_std
plt.plot(x1,y1,'b--')
pp.savefig(bbox_inches='tight', papertype='a4')
pp.close()
print("fitting parameters : ")
for i in range(len(lr.params)):
print(" %4d %6.4g"%(i,lr.params[i]))
print("standard error : ")
for i in range(len(lr.bse)):
print(" %4d %6.4g"%(i,lr.bse[i]))
print("p-value : ")
for i in range(len(lr.pvalues)):
print(" %4d %6.4g"%(i,lr.pvalues[i]))
#print(lr.ssr)
print("r-square : ", lr.rsquared)
print("** residual analysis **")
print("skewness of residual : %6.4g"%(skew(lr.resid)))
print("kurtosis of residual : %6.4g"%(kurtosis(lr.resid)))
print("** BreuschPagan test **")
test = sms.het_breushpagan(lr.resid, lr.model.exog)
name = ['Lagrange multiplier statistic', 'p-value',
'f-value', 'f p-value']
for i in range(len(test)):
print("%s : %5.3g"%(name[i],test[i]))
print("** Normality of residual **")
k2, p = stats.normaltest(lr.resid)
print("p-value = ", p)
## write a line of record to the output data file
fpou = open("data_output.txt","a")
buf = "%d %s %s"%(len(predicators), response_var, " ".join(predicators) )
buf = buf + " %6.4g"%(lr.rsquared)
for i in range(len(lr.params)):
buf = buf + " %6.4g"%(lr.params[i])
for i in range(len(lr.pvalues)):
buf = buf + " %6.4g"%(lr.pvalues[i])
fpou.write(buf+"\n")
fpou.close()
