'''calculating anova and verifying with NIST test data
compares my implementations, stats.f_oneway and anova using statsmodels.OLS
'''
from __future__ import print_function
from statsmodels.compat.python import lmap
import os
import numpy as np
from scipy import stats
filenameli = ['SiRstv.dat', 'SmLs01.dat', 'SmLs02.dat', 'SmLs03.dat', 'AtmWtAg.dat',
'SmLs04.dat', 'SmLs05.dat', 'SmLs06.dat', 'SmLs07.dat', 'SmLs08.dat',
'SmLs09.dat']
##filename = 'SmLs03.dat' #'SiRstv.dat' #'SmLs09.dat'#, 'AtmWtAg.dat' #'SmLs07.dat'
##path = __file__
##print(locals().keys()
###print(path
def getnist(filename):
fname = os.path.abspath(os.path.join('./data', filename))
content = file(fname,'r').read().split('\n')
data = [line.split() for line in content[60:]]
certified = [line.split() for line in content[40:48] if line]
dataf = np.loadtxt(fname, skiprows=60)
y,x = dataf.T
y = y.astype(int)
caty = np.unique(y)
f = float(certified[0][-1])
R2 = float(certified[2][-1])
resstd = float(certified[4][-1])
dfbn = int(certified[0][-4])
dfwn = int(certified[1][-3]) # dfbn->dfwn is this correct
prob = stats.f.sf(f,dfbn,dfwn)
return y, x, np.array([f, prob, R2, resstd]), certified, caty
from .try_catdata import groupsstats_dummy, groupstatsbin
[docs]def anova_oneway(y, x, seq=0):
# new version to match NIST
# no generalization or checking of arguments, tested only for 1d
yrvs = y[:,np.newaxis] #- min(y)
#subracting mean increases numerical accuracy for NIST test data sets
xrvs = x[:,np.newaxis] - x.mean() #for 1d#- 1e12 trick for 'SmLs09.dat'
meang, varg, xdevmeangr, countg = groupsstats_dummy(yrvs[:,:1], xrvs[:,:1])#, seq=0)
#the following does not work as replacement
#gcount, gmean , meanarr, withinvar, withinvararr = groupstatsbin(y, x)#, seq=0)
sswn = np.dot(xdevmeangr.T,xdevmeangr)
ssbn = np.dot((meang-xrvs.mean())**2, countg.T)
nobs = yrvs.shape[0]
ncat = meang.shape[1]
dfbn = ncat - 1
dfwn = nobs - ncat
msb = ssbn/float(dfbn)
msw = sswn/float(dfwn)
f = msb/msw
prob = stats.f.sf(f,dfbn,dfwn)
R2 = (ssbn/(sswn+ssbn)) #R-squared
resstd = np.sqrt(msw) #residual standard deviation
#print(f, prob
def _fix2scalar(z): # return number
if np.shape(z) == (1, 1): return z[0,0]
else: return z
f, prob, R2, resstd = lmap(_fix2scalar, (f, prob, R2, resstd))
return f, prob, R2, resstd
import statsmodels.api as sm
from .try_ols_anova import data2dummy
[docs]def anova_ols(y, x):
X = sm.add_constant(data2dummy(x), prepend=False)
res = sm.OLS(y, X).fit()
return res.fvalue, res.f_pvalue, res.rsquared, np.sqrt(res.mse_resid)
if __name__ == '__main__':
print('\n using new ANOVA anova_oneway')
print('f, prob, R2, resstd')
for fn in filenameli:
print(fn)
y, x, cert, certified, caty = getnist(fn)
res = anova_oneway(y, x)
print(np.array(res) - cert)
print('\n using stats ANOVA f_oneway')
for fn in filenameli:
print(fn)
y, x, cert, certified, caty = getnist(fn)
xlist = [x[y==ii] for ii in caty]
res = stats.f_oneway(*xlist)
print(np.array(res) - cert[:2])
print('\n using statsmodels.OLS')
print('f, prob, R2, resstd')
for fn in filenameli[:]:
print(fn)
y, x, cert, certified, caty = getnist(fn)
res = anova_ols(x, y)
print(np.array(res) - cert)
