def test_rainbow(self):
#rainbow test
#> rt = raintest(fm)
#> mkhtest_f(rt, 'raintest', 'f')
raintest = dict(statistic=0.6809600116739604, pvalue=0.971832843583418,
parameters=(101, 98), distr='f')
#> rt = raintest(fm, center=0.4)
#> mkhtest_f(rt, 'raintest_center_04', 'f')
raintest_center_04 = dict(statistic=0.682635074191527,
pvalue=0.971040230422121,
parameters=(101, 98), distr='f')
#> rt = raintest(fm, fraction=0.4)
#> mkhtest_f(rt, 'raintest_fraction_04', 'f')
raintest_fraction_04 = dict(statistic=0.565551237772662,
pvalue=0.997592305968473,
parameters=(122, 77), distr='f')
#> rt = raintest(fm, order.by=ggdp)
#Warning message:
#In if (order.by == "mahalanobis") { :
# the condition has length > 1 and only the first element will be used
#> mkhtest_f(rt, 'raintest_order_gdp', 'f')
raintest_order_gdp = dict(statistic=1.749346160513353,
pvalue=0.002896131042494884,
parameters=(101, 98), distr='f')
rb = smsdia.linear_rainbow(self.res)
compare_t_est(rb, raintest, decimal=(13, 14))
rb = smsdia.linear_rainbow(self.res, frac=0.4)
compare_t_est(rb, raintest_fraction_04, decimal=(13, 14))
def test_rainbow(self):
#rainbow test
#> rt = raintest(fm)
#> mkhtest_f(rt, 'raintest', 'f')
raintest = dict(statistic=0.6809600116739604, pvalue=0.971832843583418,
parameters=(101, 98), distr='f')
#> rt = raintest(fm, center=0.4)
#> mkhtest_f(rt, 'raintest_center_04', 'f')
raintest_center_04 = dict(statistic=0.682635074191527,
pvalue=0.971040230422121,
parameters=(101, 98), distr='f')
#> rt = raintest(fm, fraction=0.4)
#> mkhtest_f(rt, 'raintest_fraction_04', 'f')
raintest_fraction_04 = dict(statistic=0.565551237772662,
pvalue=0.997592305968473,
parameters=(122, 77), distr='f')
#> rt = raintest(fm, order.by=ggdp)
#Warning message:
#In if (order.by == "mahalanobis") { :
# the condition has length > 1 and only the first element will be used
#> mkhtest_f(rt, 'raintest_order_gdp', 'f')
raintest_order_gdp = dict(statistic=1.749346160513353,
pvalue=0.002896131042494884,
parameters=(101, 98), distr='f')
rb = smsdia.linear_rainbow(self.res)
compare_t_est(rb, raintest, decimal=(13, 14))
rb = smsdia.linear_rainbow(self.res, frac=0.4)
compare_t_est(rb, raintest_fraction_04, decimal=(13, 14))
def linearity_check(model):
rainbow_statistic, rainbow_p_value = linear_rainbow(model)
print("Rainbow statistic:", rainbow_statistic)
print("Rainbow p-value:", rainbow_p_value)
pass
def test_assumptions(df, model, ivar):
# model residuals
resids = model.resid
# df with only features
idv_df = df[ivar]
# Plot qq-plot for normality and scatterplot for homoscedasticity
sm.graphics.qqplot(resids, dist=stats.norm, line='45', fit=True)
fig, ax = plt.subplots()
ax.scatter(resids, model.predict())
# Rainbow fit test to check for linearity
rb_test = at.linear_rainbow(model)
#print results of rainbow fit test
print('Rainbow test statistic: {}\nRainbow test p-value: {}'.format(rb_test[0], rb_test[1]))
# Jarque-Bera (JB) test to check for normality
jb_test = sms.jarque_bera(resids)
#Print results of JB test
print('JB test statistic: {}\nJB test p-value: {}'.format(jb_test[0], jb_test[1]))
# Breusch Pagan test for homoscedasticity and scatter plot of resids and predicted values
bp_test = at.het_breuschpagan(resids, idv_df)
print('Breusch Pagan test statistic: {}\nBreusch Pagan p-value: {}'.format(bp_test[0], bp_test[1]))
# Variance Inflation Factor (VIF) to check for independence
# vif_features = pd.DataFrame()
# vif_features['vif'] = [vif(idv_df.values, i) for i in range(idv_df.shape[1])]
# vif_features['features'] = idv_df.columns
# print('VIF: {}'.format(vif_features.vif.mean()))
def rainbow_stats(model):
'''
given a regression model, this function returns the values from a rainbow test stored as a dictionary
'''
rainbow_statistic, rainbow_p_value = linear_rainbow(model)
return {
'rainbow_stat': rainbow_statistic,
'rainbow_p_value': rainbow_p_value
}
def linearity_check(model):
rainbow_statistic, rainbow_p_value = linear_rainbow(model)
print("Rainbow statistic:", rainbow_statistic)
print("Rainbow p-value:", rainbow_p_value)
print("\n")
print(
"The null hypothesis is that the model is linearly predicted by the features,\
alternative hypothesis is that it is not. Thus returning a low p-value means that the current model violates the linearity assumption."
)
def create_model(df, y, X):
"""df = dataframe with data
y = target variable
X = list of features
Runs data through ols model and prints results.
Also checks the assumptions of linear regression.
Uses Rainbow test to check linearity.
For independence, if there is more than one feature, will calculate the variance inflation factor for each feature.
Runs the Breusch-Pagan test for homoscadasticity, and plots predicted life expectancy vs the residuals.
"""
model_df = df[[y, *X]]
Formula = y + ' ~ ' + X[0]
for i in range(len(X) - 1):
Formula += ' + '
Formula += X[i + 1]
model = ols(formula=Formula, data=model_df)
model_results = model.fit()
print(model_results.summary())
#Check Linearity
rainbow_statistic, rainbow_p_value = linear_rainbow(model_results)
print(
'\n\nCheck Assumptions of Linear Regression\n\nLinearity\nRainbow Statistic:',
rainbow_statistic)
print('Rainbow p-value:', rainbow_p_value)
#Independence
vif_df = pd.DataFrame()
rows = model_df[X].values
if len(X) != 1:
vif_df['VIF'] = [
variance_inflation_factor(rows, i) for i in range(len(X))
]
vif_df['feature'] = X
print('\n\nIndependence\n', vif_df)
# Homoscadasticity
y = model_df[y]
y_hat = model_results.predict()
fig2, ax2 = plt.subplots()
ax2.set(xlabel='Predicted Sale Price',
ylabel='Residuals (Predicted - Actual Sale Price)')
ax2.scatter(x=y_hat, y=y_hat - y, color='blue', alpha=0.2)
lm, lm_p_value, fvalue, f_p_value = het_breuschpagan(
y - y_hat, model_df[X])
print('\n\nHomoscadasticity\nLagrange Multiplier p-value:', lm_p_value)
print('F-statistic p-value:', f_p_value)
return
def rainbow_test(result):
"""
Accepts:
result = model.fit()
Performs Rainbow Test and prints results
"""
rainbow_statistic, rainbow_p_value = linear_rainbow(result)
print("Statistic =", rainbow_statistic, "P_Value =", rainbow_p_value)
print(
"The null hypothesis H0 is that the model is linearly predicted by the features,\n alternative hypothesis Ha is that it is not."
)
print(f'stat={rainbow_statistic:.3f}, p={rainbow_p_value:.3f}')
if rainbow_p_value > 0.05:
print(
f"We have {rainbow_p_value:.3f} > 0.05. We don't have evidence to reject the H0,\n thus the current model satisfies the linearity assumption."
)
else:
print(
f"We have enough evidence to reject H0, since {rainbow_p_value:.3f} < 0.05 and coclude that the model doesn't satisfy liearity assumption."
)
def ols_diag(df,X,model, nlag=1, remove_outliers=False):
### Small Info
print("Dataset:","\t",len(df))
print("X:","\t",len(X))
## Residdual Normalaity Test
print("1. Normality Test: ", "Jarque-Bera", "Test")
jb_h0="Residual Normally distributed"
jb_h1="Residual Not Normally distributed"
jb_p=smt.jarque_bera(model.resid)[1]
hypo_out(jb_p, jb_h0, jb_h1)
## Data Linearity Test
print("2. Linearity Test: ","Rainbow", "Test")
r_h0="Data have linear relationship"
r_h1="Data do not have linear relationship"
r_t,r_p=smd.linear_rainbow(model)
hypo_out(r_p, r_h0, r_h1)
## Hetrosedacity Test: Scaling error
print("3. Heteroscedasticity Test: ","Breusch-Pagan", "Test")
bp_h0="Data have same variance accross"
bp_h1="Data do not have have same variance accross"
bp_p=smd.het_breuschpagan(model.resid, model.model.exog)[1]
hypo_out(bp_p, bp_h0, bp_h1)
## Autocrrelation Test
print("4. Autocorrelation Test: ","Breusch Godfrey", "Test")
bg_h0="Data are not related to themself:"+str(nlag)+" lag"
bg_h1="Data are related to themself by:"+str(nlag)+" lag"
bg_p=smd.acorr_breusch_godfrey(model, nlag)[1]
hypo_out(bg_p, bg_h0, bg_h1)
## Sum residulas =0
print("5. Sum of residuals == 0")
sr_h0="Sum of residuals = 0"
sr_h1="Sum of residual != 0"
if round(sum(model.resid),1)==0:
sr_p=1
else:
sr_p=0
hypo_out(sr_p, sr_h0, sr_h1)
## List of outliers
print("6. Checking outliers:")
outliers(df,model,remove_outliers=False)
## Endogenity Check:
# print("7. Checking Endogenity:"; )
# heatmap(X)
## Multicolinearity test:
print("7. Checking multicolinearity")
try:
heatmap(X)
except:
print("Cannot perrform this 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
fsm = ols(formula= "price ~ sqft_living", data=fsm_df)
fsm_results = fsm.fit()
fsm_results.summary()
sns.set_theme(color_codes=True)
f, ax = plt.subplots(figsize=(10, 8))
sns.regplot(x="sqft_living", y="price", data=fsm_df, ax=ax).set_title('Model1 Visualization');
plt.savefig('viz1.png')
rainbow_statistic, rainbow_p_value = linear_rainbow(fsm_results)
print("Rainbow statistic:", rainbow_statistic)
print("Rainbow p-value:", rainbow_p_value)
resid = fsm_results.resid
qq1 = sm.qqplot(resid, line ='45', fit=True, dist=stats.t)
y = fsm_df["price"]
y_hat = fsm_results.predict()
fig2, ax2 = plt.subplots()
ax2.set(xlabel="Price",
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 get_rainbow(fsm):
"""
Gives the rainbow statistic for a given model
"""
rainbow_statistic, rainbow_p_value = linear_rainbow(fsm)
return {'statistic': rainbow_statistic, 'p-value': rainbow_p_value}