Note
Go to the end to download the full example code or to run this example in your browser via Binder
Massively univariate analysis of face vs house recognition#
A permuted Ordinary Least Squares algorithm is run at each voxel in order to determine whether or not it behaves differently under a “face viewing” condition and a “house viewing” condition. We consider the mean image per session and per condition. Otherwise, the observations cannot be exchanged at random because a time dependence exists between observations within a same session (see [1] for more detailed explanations).
The example shows the small differences that exist between Bonferroni-corrected p-values and family-wise corrected p-values obtained from a permutation test combined with a max-type procedure [2]. Bonferroni correction is a bit conservative, as revealed by the presence of a few false negative.
Note
If you are using Nilearn with a version older than 0.9.0,
then you should either upgrade your version or import maskers
from the input_data module instead of the maskers module.
That is, you should manually replace in the following example all occurrences of:
from nilearn.maskers import NiftiMasker
with:
from nilearn.input_data import NiftiMasker
References#
- [1] Winkler, A. M. et al. (2014).
Permutation inference for the general linear model. Neuroimage.
- [2] Anderson, M. J. & Robinson, J. (2001).
Permutation tests for linear models. Australian & New Zealand Journal of Statistics, 43(1), 75-88. (http://avesbiodiv.mncn.csic.es/estadistica/permut2.pdf)
Load Haxby dataset
from nilearn import datasets, image
haxby_dataset = datasets.fetch_haxby(subjects=[2])
# print basic information on the dataset
print(f"Mask nifti image (3D) is located at: {haxby_dataset.mask}")
print(f"Functional nifti image (4D) is located at: {haxby_dataset.func[0]}")
Mask nifti image (3D) is located at: /home/runner/work/nilearn/nilearn/nilearn_data/haxby2001/mask.nii.gz
Functional nifti image (4D) is located at: /home/runner/work/nilearn/nilearn/nilearn_data/haxby2001/subj2/bold.nii.gz
Restrict to faces and houses
import numpy as np
import pandas as pd
labels = pd.read_csv(haxby_dataset.session_target[0], sep=" ")
conditions = labels["labels"]
categories = conditions.unique()
conditions_encoded = np.zeros_like(conditions)
for c, category in enumerate(categories):
conditions_encoded[conditions == category] = c
sessions = labels["chunks"]
condition_mask = conditions.isin(["face", "house"])
conditions_encoded = conditions_encoded[condition_mask]
Mask data
from nilearn.image import index_img
from nilearn.maskers import NiftiMasker
mask_filename = haxby_dataset.mask
nifti_masker = NiftiMasker(
smoothing_fwhm=8,
mask_img=mask_filename,
memory="nilearn_cache", # cache options
memory_level=1,
)
func_filename = haxby_dataset.func[0]
func_reduced = index_img(func_filename, condition_mask)
fmri_masked = nifti_masker.fit_transform(func_reduced)
# We consider the mean image per session and per condition.
# Otherwise, the observations cannot be exchanged at random because
# a time dependence exists between observations within a same session.
n_sessions = np.unique(sessions).size
conditions_per_session = 2
grouped_fmri_masked = np.empty(
(conditions_per_session * n_sessions, fmri_masked.shape[1])
)
grouped_conditions_encoded = np.empty((conditions_per_session * n_sessions, 1))
for s in range(n_sessions):
session_mask = sessions[condition_mask] == s
session_house_mask = np.logical_and(
session_mask, conditions[condition_mask] == "house"
)
session_face_mask = np.logical_and(
session_mask, conditions[condition_mask] == "face"
)
grouped_fmri_masked[2 * s] = fmri_masked[session_house_mask].mean(0)
grouped_fmri_masked[2 * s + 1] = fmri_masked[session_face_mask].mean(0)
grouped_conditions_encoded[2 * s] = conditions_encoded[session_house_mask][
0
]
grouped_conditions_encoded[2 * s + 1] = conditions_encoded[
session_face_mask
][0]
Perform massively univariate analysis with permuted OLS
We use a two-sided t-test to compute p-values, but we keep trace of the effect sign to add it back at the end and thus observe the signed effect
from nilearn.mass_univariate import permuted_ols
# Note that an intercept as a covariate is used by default
neg_log_pvals, t_scores_original_data, _ = permuted_ols(
grouped_conditions_encoded,
grouped_fmri_masked,
n_perm=10000,
two_sided_test=True,
verbose=1, # display progress bar
n_jobs=1, # can be changed to use more CPUs
)
signed_neg_log_pvals = neg_log_pvals * np.sign(t_scores_original_data)
signed_neg_log_pvals_unmasked = nifti_masker.inverse_transform(
signed_neg_log_pvals
)
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Job #1, processed 2390/10000 permutations (23.90%, 7.129727188014584 seconds remaining)
Job #1, processed 2400/10000 permutations (24.00%, 7.120563666025797 seconds remaining)
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Job #1, processed 2430/10000 permutations (24.30%, 7.0925636134520476 seconds remaining)
Job #1, processed 2440/10000 permutations (24.40%, 7.0824816695979385 seconds remaining)
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Job #1, processed 2470/10000 permutations (24.70%, 7.051961098605322 seconds remaining)
Job #1, processed 2480/10000 permutations (24.80%, 7.041574924222885 seconds remaining)
Job #1, processed 2490/10000 permutations (24.90%, 7.0324149103049765 seconds remaining)
Job #1, processed 2500/10000 permutations (25.00%, 7.02210545539856 seconds remaining)
Job #1, processed 2510/10000 permutations (25.10%, 7.011991023067459 seconds remaining)
Job #1, processed 2520/10000 permutations (25.20%, 7.0024415046449695 seconds remaining)
Job #1, processed 2530/10000 permutations (25.30%, 6.992657443751459 seconds remaining)
Job #1, processed 2540/10000 permutations (25.40%, 6.982349857570618 seconds remaining)
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Job #1, processed 2580/10000 permutations (25.80%, 6.9448232059330905 seconds remaining)
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Job #1, processed 2610/10000 permutations (26.10%, 6.914863665898641 seconds remaining)
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Job #1, processed 2660/10000 permutations (26.60%, 6.87688186114892 seconds remaining)
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Job #1, processed 2680/10000 permutations (26.80%, 6.857627178306011 seconds remaining)
Job #1, processed 2690/10000 permutations (26.90%, 6.847885207172663 seconds remaining)
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Job #1, processed 2720/10000 permutations (27.20%, 6.818488492685205 seconds remaining)
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Job #1, processed 2780/10000 permutations (27.80%, 6.758714094436425 seconds remaining)
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Job #1, processed 2870/10000 permutations (28.70%, 6.701236118422983 seconds remaining)
Job #1, processed 2880/10000 permutations (28.80%, 6.690839111804962 seconds remaining)
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Job #1, processed 2900/10000 permutations (29.00%, 6.670336780876949 seconds remaining)
Job #1, processed 2910/10000 permutations (29.10%, 6.660764294391646 seconds remaining)
Job #1, processed 2920/10000 permutations (29.20%, 6.650473232138647 seconds remaining)
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Job #1, processed 2940/10000 permutations (29.40%, 6.631200558474274 seconds remaining)
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Job #1, processed 2960/10000 permutations (29.60%, 6.610577969937712 seconds remaining)
Job #1, processed 2970/10000 permutations (29.70%, 6.600260386964688 seconds remaining)
Job #1, processed 2980/10000 permutations (29.80%, 6.590317289301213 seconds remaining)
Job #1, processed 2990/10000 permutations (29.90%, 6.580491267717802 seconds remaining)
Job #1, processed 3000/10000 permutations (30.00%, 6.569971243540446 seconds remaining)
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Job #1, processed 3030/10000 permutations (30.30%, 6.5397980984288075 seconds remaining)
Job #1, processed 3040/10000 permutations (30.40%, 6.529714314561141 seconds remaining)
Job #1, processed 3050/10000 permutations (30.50%, 6.519299214003516 seconds remaining)
Job #1, processed 3060/10000 permutations (30.60%, 6.509425906574025 seconds remaining)
Job #1, processed 3070/10000 permutations (30.70%, 6.498872650562746 seconds remaining)
Job #1, processed 3080/10000 permutations (30.80%, 6.488901949548102 seconds remaining)
Job #1, processed 3090/10000 permutations (30.90%, 6.479054089117204 seconds remaining)
Job #1, processed 3100/10000 permutations (31.00%, 6.470658302307128 seconds remaining)
Job #1, processed 3110/10000 permutations (31.10%, 6.460496581252365 seconds remaining)
Job #1, processed 3120/10000 permutations (31.20%, 6.450714906056723 seconds remaining)
Job #1, processed 3130/10000 permutations (31.30%, 6.440266642707606 seconds remaining)
Job #1, processed 3140/10000 permutations (31.40%, 6.4312180181977086 seconds remaining)
Job #1, processed 3150/10000 permutations (31.50%, 6.421861519889226 seconds remaining)
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Job #1, processed 3200/10000 permutations (32.00%, 6.3722134828567505 seconds remaining)
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Job #1, processed 3220/10000 permutations (32.20%, 6.351471249361214 seconds remaining)
Job #1, processed 3230/10000 permutations (32.30%, 6.341317720088428 seconds remaining)
Job #1, processed 3240/10000 permutations (32.40%, 6.330725646313326 seconds remaining)
Job #1, processed 3250/10000 permutations (32.50%, 6.320696353912354 seconds remaining)
Job #1, processed 3260/10000 permutations (32.60%, 6.310012084574788 seconds remaining)
Job #1, processed 3270/10000 permutations (32.70%, 6.300572409906882 seconds remaining)
Job #1, processed 3280/10000 permutations (32.80%, 6.290197535258968 seconds remaining)
Job #1, processed 3290/10000 permutations (32.90%, 6.280236876844272 seconds remaining)
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Job #1, processed 3310/10000 permutations (33.10%, 6.26053223725172 seconds remaining)
Job #1, processed 3320/10000 permutations (33.20%, 6.250641480985894 seconds remaining)
Job #1, processed 3330/10000 permutations (33.30%, 6.240631350525866 seconds remaining)
Job #1, processed 3340/10000 permutations (33.40%, 6.231672031436851 seconds remaining)
Job #1, processed 3350/10000 permutations (33.50%, 6.2219571142054315 seconds remaining)
Job #1, processed 3360/10000 permutations (33.60%, 6.212316547121321 seconds remaining)
Job #1, processed 3370/10000 permutations (33.70%, 6.204253607050954 seconds remaining)
Job #1, processed 3380/10000 permutations (33.80%, 6.195295635765121 seconds remaining)
Job #1, processed 3390/10000 permutations (33.90%, 6.185456405347075 seconds remaining)
Job #1, processed 3400/10000 permutations (34.00%, 6.176280035692103 seconds remaining)
Job #1, processed 3410/10000 permutations (34.10%, 6.166756487312205 seconds remaining)
Job #1, processed 3420/10000 permutations (34.20%, 6.1567706504063295 seconds remaining)
Job #1, processed 3430/10000 permutations (34.30%, 6.146807733152073 seconds remaining)
Job #1, processed 3440/10000 permutations (34.40%, 6.136918833089429 seconds remaining)
Job #1, processed 3450/10000 permutations (34.50%, 6.128036357354427 seconds remaining)
Job #1, processed 3460/10000 permutations (34.60%, 6.1181262793568525 seconds remaining)
Job #1, processed 3470/10000 permutations (34.70%, 6.108646871033593 seconds remaining)
Job #1, processed 3480/10000 permutations (34.80%, 6.099170344999468 seconds remaining)
Job #1, processed 3490/10000 permutations (34.90%, 6.08963040362798 seconds remaining)
Job #1, processed 3500/10000 permutations (35.00%, 6.080003534044539 seconds remaining)
Job #1, processed 3510/10000 permutations (35.10%, 6.0709830002907 seconds remaining)
Job #1, processed 3520/10000 permutations (35.20%, 6.061262564225629 seconds remaining)
Job #1, processed 3530/10000 permutations (35.30%, 6.051698274720493 seconds remaining)
Job #1, processed 3540/10000 permutations (35.40%, 6.042718395674969 seconds remaining)
Job #1, processed 3550/10000 permutations (35.50%, 6.033018773710224 seconds remaining)
Job #1, processed 3560/10000 permutations (35.60%, 6.023375211137064 seconds remaining)
Job #1, processed 3570/10000 permutations (35.70%, 6.013818767558292 seconds remaining)
Job #1, processed 3580/10000 permutations (35.80%, 6.0046480354650065 seconds remaining)
Job #1, processed 3590/10000 permutations (35.90%, 5.995788613401747 seconds remaining)
Job #1, processed 3600/10000 permutations (36.00%, 5.98664813571506 seconds remaining)
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Job #1, processed 3620/10000 permutations (36.20%, 5.968186853998932 seconds remaining)
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Job #1, processed 3650/10000 permutations (36.50%, 5.9422398495347535 seconds remaining)
Job #1, processed 3660/10000 permutations (36.60%, 5.933259595287302 seconds remaining)
Job #1, processed 3670/10000 permutations (36.70%, 5.923809356845367 seconds remaining)
Job #1, processed 3680/10000 permutations (36.80%, 5.914268187854602 seconds remaining)
Job #1, processed 3690/10000 permutations (36.90%, 5.904889221759992 seconds remaining)
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Job #1, processed 3720/10000 permutations (37.20%, 5.878468008451564 seconds remaining)
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Job #1, processed 3760/10000 permutations (37.60%, 5.840897692010758 seconds remaining)
Job #1, processed 3770/10000 permutations (37.70%, 5.831064718787802 seconds remaining)
Job #1, processed 3780/10000 permutations (37.80%, 5.821548829002987 seconds remaining)
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Job #1, processed 3800/10000 permutations (38.00%, 5.8034203805421525 seconds remaining)
Job #1, processed 3810/10000 permutations (38.10%, 5.796159791821257 seconds remaining)
Job #1, processed 3820/10000 permutations (38.20%, 5.786864159618997 seconds remaining)
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Job #1, processed 3860/10000 permutations (38.60%, 5.749273539824807 seconds remaining)
Job #1, processed 3870/10000 permutations (38.70%, 5.740278132510123 seconds remaining)
Job #1, processed 3880/10000 permutations (38.80%, 5.746481571000876 seconds remaining)
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Job #1, processed 3900/10000 permutations (39.00%, 5.729923162704859 seconds remaining)
Job #1, processed 3910/10000 permutations (39.10%, 5.7202701160060165 seconds remaining)
Job #1, processed 3920/10000 permutations (39.20%, 5.7108492559316195 seconds remaining)
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Job #1, processed 3960/10000 permutations (39.60%, 5.6730204977170375 seconds remaining)
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Job #1, processed 3980/10000 permutations (39.80%, 5.65438556790951 seconds remaining)
Job #1, processed 3990/10000 permutations (39.90%, 5.645100744744591 seconds remaining)
Job #1, processed 4000/10000 permutations (40.00%, 5.636816740036011 seconds remaining)
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Job #1, processed 4060/10000 permutations (40.60%, 5.580838821204424 seconds remaining)
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Job #1, processed 4080/10000 permutations (40.80%, 5.561397430943509 seconds remaining)
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Job #1, processed 4100/10000 permutations (41.00%, 5.5427105833844434 seconds remaining)
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Job #1, processed 4120/10000 permutations (41.20%, 5.5240295488857525 seconds remaining)
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Job #1, processed 4140/10000 permutations (41.40%, 5.505034918946345 seconds remaining)
Job #1, processed 4150/10000 permutations (41.50%, 5.495215054017952 seconds remaining)
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Job #1, processed 4200/10000 permutations (42.00%, 5.447667405718849 seconds remaining)
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Job #1, processed 4220/10000 permutations (42.20%, 5.429016803678177 seconds remaining)
Job #1, processed 4230/10000 permutations (42.30%, 5.420944395922037 seconds remaining)
Job #1, processed 4240/10000 permutations (42.40%, 5.411259885104198 seconds remaining)
Job #1, processed 4250/10000 permutations (42.50%, 5.401761924519259 seconds remaining)
Job #1, processed 4260/10000 permutations (42.60%, 5.391972150041464 seconds remaining)
Job #1, processed 4270/10000 permutations (42.70%, 5.3825500123115555 seconds remaining)
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Job #1, processed 4290/10000 permutations (42.90%, 5.363085088196335 seconds remaining)
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Job #1, processed 4370/10000 permutations (43.70%, 5.287280200002395 seconds remaining)
Job #1, processed 4380/10000 permutations (43.80%, 5.277617038657132 seconds remaining)
Job #1, processed 4390/10000 permutations (43.90%, 5.267851882208997 seconds remaining)
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Job #1, processed 5240/10000 permutations (52.40%, 4.483923879288535 seconds remaining)
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Job #1, processed 5760/10000 permutations (57.60%, 3.9928146335813732 seconds remaining)
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scikit-learn F-scores for comparison
F-test does not allow to observe the effect sign (pure two-sided test)
from sklearn.feature_selection import f_regression
# f_regression implicitly adds intercept
_, pvals_bonferroni = f_regression(
grouped_fmri_masked, grouped_conditions_encoded
)
pvals_bonferroni *= fmri_masked.shape[1]
pvals_bonferroni[np.isnan(pvals_bonferroni)] = 1
pvals_bonferroni[pvals_bonferroni > 1] = 1
neg_log_pvals_bonferroni = -np.log10(pvals_bonferroni)
neg_log_pvals_bonferroni_unmasked = nifti_masker.inverse_transform(
neg_log_pvals_bonferroni
)
/usr/share/miniconda3/envs/testenv/lib/python3.9/site-packages/sklearn/utils/validation.py:1183: DataConversionWarning:
A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
Visualization
import matplotlib.pyplot as plt
from nilearn.image import get_data
from nilearn.plotting import plot_stat_map, show
# Use the fmri mean image as a surrogate of anatomical data
mean_fmri_img = image.mean_img(func_filename)
threshold = -np.log10(0.1) # 10% corrected
vmax = min(signed_neg_log_pvals.max(), neg_log_pvals_bonferroni.max())
# Plot thresholded p-values map corresponding to F-scores
display = plot_stat_map(
neg_log_pvals_bonferroni_unmasked,
mean_fmri_img,
threshold=threshold,
cmap=plt.cm.RdBu_r,
display_mode="z",
cut_coords=[-1],
vmax=vmax,
)
neg_log_pvals_bonferroni_data = get_data(neg_log_pvals_bonferroni_unmasked)
n_detections = (neg_log_pvals_bonferroni_data > threshold).sum()
title = (
"Negative $\\log_{10}$ p-values"
"\n(Parametric two-sided F-test"
"\n+ Bonferroni correction)"
f"\n{n_detections} detections"
)
display.title(title, size=10)
# Plot permutation p-values map
display = plot_stat_map(
signed_neg_log_pvals_unmasked,
mean_fmri_img,
threshold=threshold,
cmap=plt.cm.RdBu_r,
display_mode="z",
cut_coords=[-1],
vmax=vmax,
)
n_detections = (np.abs(signed_neg_log_pvals) > threshold).sum()
title = (
"Negative $\\log_{10}$ p-values"
"\n(Non-parametric two-sided test"
"\n+ max-type correction)"
f"\n{n_detections} detections"
)
display.title(title, size=10)
show()
Total running time of the script: (0 minutes 25.074 seconds)
Estimated memory usage: 949 MB
