def runTest(self):
# these values are from pchisq as found in R version 2.5.1
# it would be nice if there were some properties of chisqprob
# that could be verified but I could not find any.
self.assertAlmostEquals(chisqprob(1,1),0.6826895,6)
for k in xrange(100):
self.assertEquals(chisqprob(0,k), 0)
for i,val in enumerate([0.0000000,0.6826895,0.6321206,0.6083748,
0.5939942,0.5841198,0.5768099,0.5711201,
0.5665299,0.5627258,0.5595067]):
self.assertAlmostEquals(chisqprob(i,i),val,6)
def test_independ(self,x,y,s):
"""Test if x _|_ y | s. returns (p,s,d) where p is the probability of
the available data, given the null hypothesis of independence,
s is the test statistic, and d is the number of degrees of freedom in
the available data for this test.
"""
vars = tuple(s)
# extract the marginal factors and broadcast out to full instances (for zero censoring)
joint_counts = self._data.makeFactor(vars + (x,y))
marginal_counts_x = self._data.makeFactor(vars + (x,))
marginal_counts_y = self._data.makeFactor(vars + (y,))
marginal_counts_s = self._data.makeFactor(vars)
# calculate the number of degrees of freedom. this is equal to
# (r - 1)(c - 1)\prod_{s \in S} s
# if there exists a condition s, such that a row or column sum is zero,
# then we do not count that row or column.
i_x = sorted(marginal_counts_x.variables()).index(x)
i_y = sorted(marginal_counts_y.variables()).index(y)
d = 0
n_x = self._data.numvals(x)-1
n_y = self._data.numvals(y)-1
for s_inst in marginal_counts_s.insts():
if marginal_counts_s[s_inst] == 0:
continue
# count censored x values
c_x = 0
x_inst = list(s_inst[:i_x] + (None,) + s_inst[i_x:])
for v in self._data.values(x):
x_inst[i_x] = v
if marginal_counts_x[x_inst] == 0:
c_x += 1
# count censored y values
c_y = 0
y_inst = list(s_inst[:i_y] + (None,) + s_inst[i_y:])
for v in self._data.values(y):
y_inst[i_y] = v
if marginal_counts_y[y_inst] == 0:
c_y += 1
# the PC heuristic decrements the cell counts of each row/column by
# each censored value (provided this does not result in a negative
# DoF)
if c_x < n_x and c_y < n_y:
d += (n_x - c_x)*(n_y - c_y)
if d <= 0:
# Chi^2 is undefined!
# we favour sparse representations
# H_0 is favouring sparseness
# this is what Tetrad does.
return 1.0, 0.0, d
# convert marginal factor elements to floats from ints
marginal_counts_x.map(float)
marginal_counts_y.map(float)
marginal_counts_s.map(float)
joint_counts.map(float)
# expand out all factors to include all relevant variables
marginal_counts_x = marginal_counts_x.broadcast(joint_counts.variables())
marginal_counts_y = marginal_counts_y.broadcast(joint_counts.variables())
marginal_counts_s = marginal_counts_s.broadcast(joint_counts.variables())
# calculate some statistic that is distributed as Chi^2 though this may
# only be asymptotically distributed.
statistic = self.statistic(joint_counts, marginal_counts_x, marginal_counts_y, marginal_counts_s)
# related to Chi^2 distribution
# likelihood of independence is P(Chi > X2 | H0)
# chisqprob is the c.d.f., so we have 1 - P(Chi <= X | H0)
p = 1 - chisqprob(statistic, d)
return p, statistic, d
