def test_make_correlated_xy(corr, size, tol, seed):
out = datasets.make_correlated_xy(corr=corr, size=size,
tol=tol, seed=seed)
# ensure output is expected shape
assert out.shape[1:] == size
assert len(out) == len(corr) if hasattr(corr, '__len__') else 2
# check outputs are correlated within specified tolerance
realcorr = np.corrcoef(out.reshape(len(out), -1))
if len(realcorr) == 2 and not hasattr(corr, '__len__'):
realcorr = realcorr[0, 1]
assert np.all(np.abs(realcorr - corr) < tol)
# check that seed generates reproducible values
duplicate = datasets.make_correlated_xy(corr=corr, size=size,
tol=tol, seed=seed)
assert np.allclose(out, duplicate)
def test_permtest_pearsonr():
np.random.seed(12345678)
x, y = datasets.make_correlated_xy(corr=0.1, size=100)
r, p = stats.permtest_pearsonr(x, y)
assert np.allclose([r, p], [0.10032564626876286, 0.3046953046953047])
x, y = datasets.make_correlated_xy(corr=0.5, size=100)
r, p = stats.permtest_pearsonr(x, y)
assert np.allclose([r, p], [0.500040365781984, 0.000999000999000999])
z = x + np.random.normal(loc=1, size=100)
r, p = stats.permtest_pearsonr(x, np.column_stack([y, z]))
assert np.allclose(r, np.array([0.50004037, 0.25843187]))
assert np.allclose(p, np.array([0.000999, 0.01098901]))
a, b = datasets.make_correlated_xy(corr=0.9, size=100)
r, p = stats.permtest_pearsonr(np.column_stack([x, a]),
np.column_stack([y, b]))
assert np.allclose(r, np.array([0.50004037, 0.89927523]))
assert np.allclose(p, np.array([0.000999, 0.000999]))
def test_make_correlated_xy_errors(corr):
with pytest.raises(ValueError):
datasets.make_correlated_xy(corr)
=================================== This example shows how to perform "spin-tests" (a la Alexander-Bloch et al., 2018, NeuroImage) to assess whether two brain patterns are correlated above and beyond what would be expected from a spatially-autocorrelated null model. For the original MATLAB toolbox published alongside the paper by Alexander-Bloch and colleagues refer to https://github.com/spin-test/spin-test. """ ############################################################################### # First let's generate some randomly correlated data. We'll set a random seed # to make sure that things are reproducible: from netneurotools import datasets x, y = datasets.make_correlated_xy(size=68, seed=1234) ############################################################################### # We can correlate the resulting vectors to see how related they are: from scipy.stats import pearsonr r, p = pearsonr(x, y) print(r, p) ############################################################################### # The p-value suggests that our data are, indeed, highly correlated. # Unfortunately, when doing this sort of correlation with brain data the null # model used in generating the p-value does not take into account that the data # are constrained by a spatial toplogy (i.e., the brain) and thus spatially # auto-correlated. The p-values will be "inflated" because our true degrees of # freedom are less than the number of samples we have!
def matching_multinorm_grfs(corr,
tol=0.005,
*,
alpha=3.0,
normalize=True,
seed=None,
debug=False):
"""
Generates two surface GRFs (fsaverage5) that correlate at r = `corr`
Starts by generating two random variables from a multivariate normal
distribution with correlation `corr`, adds spatial autocorrelation with
specified `alpha`, and projects to the surface. Continues this procedure
until two variables are generated that have correlation `corr` on the
surface.
Parameters
----------
corr : float
Desired correlation of generated GRFs
tol : float
Tolerance for correlation between generated GRFs
alpha : float (positive), optional
Exponent of the power-law distribution. Only used if `use_gstools` is
set to False. Default: 3.0
normalize : bool, optional
Whether to normalize the returned field to unit variance. Default: True
seed : None, int, default_rng, optional
Random state to seed GRF generation. Default: None
debug : bool, optional
Whether to print debug info
Return
------
x, y : (20484,) np.ndarray
Generated surface GRFs
"""
rs = np.random.default_rng(seed)
acorr, n = np.inf, 0
while np.abs(np.abs(acorr) - corr) > tol:
if alpha > 0:
x, y = make_correlated_xy(corr,
size=902629,
seed=rs.integers(MSEED))
# smooth correlated noise vectors + project to surface
xs = create_surface_grf(noise=x, alpha=alpha, normalize=normalize)
ys = create_surface_grf(noise=y, alpha=alpha, normalize=normalize)
else:
xs, ys = make_correlated_xy(corr,
size=20484,
seed=rs.integers(MSEED))
# remove medial wall to ensure data are still sufficiently correlated.
# this is important for parcellations that will ignore the medial wall
xs, ys = _mod_medial(xs, remove=True), _mod_medial(ys, remove=True)
acorr = np.corrcoef(xs, ys)[0, 1]
if debug:
# n:>3 because dear lord i hope it doesn't take more than 999 tries
print(f'{n:>3}: {acorr:>6.3f}')
n += 1
if acorr < 0:
ys *= -1
if normalize:
xs, ys = sstats.zscore(xs), sstats.zscore(ys)
return _mod_medial(xs, remove=False), _mod_medial(ys, remove=False)
np.random.normal(scale=0.2, size=500)) print(nnstats.permtest_rel(rvs1, rvs3)) ############################################################################### # Permutation tests for correlations # ---------------------------------- # # Sometimes rather than assessing differences in means we want to assess the # strength of a relationship between two variables. While we might normally do # this with a Pearson (or Spearman) correlation, we can assess the significance # of this relationship via permutation tests. # # First, we'll generate two correlated variables: from netneurotools import datasets x, y = datasets.make_correlated_xy(corr=0.2, size=100) ############################################################################### # We can generate the Pearson correlation with the standard parametric p-value: print(stats.pearsonr(x, y)) ############################################################################### # Or use permutation testing to derive the p-value: print(nnstats.permtest_pearsonr(x, y)) ############################################################################### # All the same arguments as with :func:`~.permtest_1samp` and # :func:`~.permtest_rel` apply here, so you can provide same-sized arrays and # correlations will only be calculated for paired columns:
