def group_analysis_signs(design, contrast, mask, signs=None):
"""
This function refits the EM model with a vector of signs.
Used in the permutation tests.
Returns the maximum of the T-statistic within mask
Parameters
----------
design: one of 'block', 'event'
contrast: str
mask: array-like
signs: ndarray, optional
Defaults to np.ones. Should have shape (*,nsubj)
where nsubj is the number of effects combined in the group analysis.
Returns
-------
minT: np.ndarray, minima of T statistic within mask, one for each
vector of signs
maxT: np.ndarray, maxima of T statistic within mask, one for each
vector of signs
"""
maska = np.asarray(mask).astype(np.bool)
# Which subjects have this (contrast, design) pair?
subjects = futil.subject_dirs(design, contrast)
sd = np.array([np.array(load_image(pjoin(s, "sd.nii")))[:,maska]
for s in subjects])
Y = np.array([np.array(load_image(pjoin(s, "effect.nii")))[:,maska]
for s in subjects])
if signs is None:
signs = np.ones((1, Y.shape[0]))
maxT = np.empty(signs.shape[0])
minT = np.empty(signs.shape[0])
for i, sign in enumerate(signs):
signY = sign[:,np.newaxis] * Y
varest = onesample.estimate_varatio(signY, sd)
random_var = varest['random']
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
T = results['t']
minT[i], maxT[i] = np.nanmin(T), np.nanmax(T)
return minT, maxT
def permutation_test(design, contrast, mask=GROUP_MASK, nsample=1000):
"""
Perform a permutation (sign) test for a given design type and
contrast. It is a Monte Carlo test because we only sample nsample
possible sign arrays.
Parameters
----------
design: one of ['block', 'event']
contrast: str
nsample: int
Returns
-------
min_vals: np.ndarray
max_vals: np.ndarray
"""
maska = np.asarray(mask).astype(np.bool)
subjects = futil.subject_dirs(design, contrast)
Y = np.array([np.array(load_image(pjoin(s, "effect.nii")))[:,maska]
for s in subjects])
nsubj = Y.shape[0]
signs = 2*np.greater(np.random.sample(size=(nsample, nsubj)), 0.5) - 1
min_vals, max_vals = group_analysis_signs(design, contrast, maska, signs)
return min_vals, max_vals
def group_analysis(design, contrast):
"""
Compute group analysis effect, sd and t
for a given contrast and design type
"""
array = np.array # shorthand
# Directory where output will be written
odir = futil.ensure_dir(futil.DATADIR, 'group', design, contrast)
# Which subjects have this (contrast, design) pair?
subjects = futil.subject_dirs(design, contrast)
sd = array([array(load_image(pjoin(s, "sd.nii"))) for s in subjects])
Y = array([array(load_image(pjoin(s, "effect.nii"))) for s in subjects])
# This function estimates the ratio of the
# fixed effects variance (sum(1/sd**2, 0))
# to the estimated random effects variance
# (sum(1/(sd+rvar)**2, 0)) where
# rvar is the random effects variance.
# The EM algorithm used is described in
#
# Worsley, K.J., Liao, C., Aston, J., Petre, V., Duncan, G.H.,
# Morales, F., Evans, A.C. (2002). \'A general statistical
# analysis for fMRI data\'. NeuroImage, 15:1-15
varest = onesample.estimate_varatio(Y, sd)
random_var = varest['random']
# XXX - if we have a smoother, use
# random_var = varest['fixed'] * smooth(varest['ratio'])
# Having estimated the random effects variance (and
# possibly smoothed it), the corresponding
# estimate of the effect and its variance is
# computed and saved.
# This is the coordmap we will use
coordmap = futil.load_image_fiac("fiac_00","wanatomical.nii").coordmap
adjusted_var = sd**2 + random_var
adjusted_sd = np.sqrt(adjusted_var)
results = onesample.estimate_mean(Y, adjusted_sd)
for n in ['effect', 'sd', 't']:
im = api.Image(results[n], coordmap.copy())
save_image(im, pjoin(odir, "%s.nii" % n))
