"""calculating anova and verifying with NIST test data
compares my implementations, stats.f_oneway and anova using statsmodels.OLS
"""
from statsmodels.compat.python import lmap
import os
import numpy as np
from scipy import stats
from statsmodels.regression.linear_model import OLS
from statsmodels.tools.tools import add_constant
from .try_ols_anova import data2dummy
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'
def getnist(filename):
here = os.path.dirname(__file__)
fname = os.path.abspath(os.path.join(here, "data", filename))
with open(fname, encoding="utf-8") as fd:
content = fd.read().split("\n")
[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
[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'
from .try_catdata import groupsstats_dummy
meang, varg, xdevmeangr, countg = groupsstats_dummy(yrvs[:, :1], xrvs[:, :1])
# TODO: the following does not work as replacement
# from .try_catdata import groupsstats_dummy, groupstatsbin
# gcount, gmean , meanarr, withinvar, withinvararr = groupstatsbin(y, x)
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
[docs]
def anova_ols(y, x):
X = add_constant(data2dummy(x), prepend=False)
res = 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)
# TODO: figure out why these results are less accurate/precise
# than others
rtol = {"SmLs08.dat": 0.027, "SmLs07.dat": 1.7e-3, "SmLs09.dat": 1e-4}.get(
fn, 1e-7
)
np.testing.assert_allclose(np.array(res), cert, rtol=rtol)
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)