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)

# Author: Virgile Fritsch, <virgile.fritsch@inria.fr>, Feb. 2014

Load Haxby dataset

from nilearn import datasets, image
haxby_dataset = datasets.fetch_haxby(subjects=[2])

# print basic information on the dataset
print('Mask nifti image (3D) is located at: %s' % haxby_dataset.mask)
print('Functional nifti image (4D) is located at: %s' % 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

Mask data

mask_filename = haxby_dataset.mask
from nilearn.image import index_img
from nilearn.maskers import NiftiMasker
nifti_masker = NiftiMasker(
    smoothing_fwhm=8,
    mask_img=mask_filename,
    memory='nilearn_cache', memory_level=1)  # cache options
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
grouped_fmri_masked = np.empty((2 * n_sessions,  # two conditions per session
                                fmri_masked.shape[1]))
grouped_conditions_encoded = np.empty((2 * 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
neg_log_pvals, t_scores_original_data, _ = permuted_ols(
    grouped_conditions_encoded, grouped_fmri_masked,
    # + intercept as a covariate by default
    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)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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Job #1, processed 2430/10000 permutations (24.30%, 7.276304824852649 seconds remaining)
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Job #1, processed 2480/10000 permutations (24.80%, 7.224649598521571 seconds remaining)
Job #1, processed 2490/10000 permutations (24.90%, 7.2173033631949055 seconds remaining)
Job #1, processed 2500/10000 permutations (25.00%, 7.20697546005249 seconds remaining)
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Job #1, processed 2520/10000 permutations (25.20%, 7.186534219317966 seconds remaining)
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Job #1, processed 2580/10000 permutations (25.80%, 7.13275079764137 seconds remaining)
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Job #1, processed 2710/10000 permutations (27.10%, 7.006731656204731 seconds remaining)
Job #1, processed 2720/10000 permutations (27.20%, 6.997506765758289 seconds remaining)
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Job #1, processed 2910/10000 permutations (29.10%, 6.8049683087470205 seconds remaining)
Job #1, processed 2920/10000 permutations (29.20%, 6.7962589296576095 seconds remaining)
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Job #1, processed 2990/10000 permutations (29.90%, 6.730085630480661 seconds remaining)
Job #1, processed 3000/10000 permutations (30.00%, 6.721039454142253 seconds remaining)
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Job #1, processed 3030/10000 permutations (30.30%, 6.692839030778841 seconds remaining)
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Job #1, processed 3080/10000 permutations (30.80%, 6.647183724812098 seconds remaining)
Job #1, processed 3090/10000 permutations (30.90%, 6.638958078372053 seconds remaining)
Job #1, processed 3100/10000 permutations (31.00%, 6.629265500653174 seconds remaining)
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Job #1, processed 3120/10000 permutations (31.20%, 6.611193913679857 seconds remaining)
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Job #1, processed 3140/10000 permutations (31.40%, 6.591923970325737 seconds remaining)
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Job #1, processed 3170/10000 permutations (31.70%, 6.567467331510237 seconds remaining)
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Job #1, processed 3200/10000 permutations (32.00%, 6.542672842741013 seconds remaining)
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Job #1, processed 3320/10000 permutations (33.20%, 6.427586710596658 seconds remaining)
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Job #1, processed 3360/10000 permutations (33.60%, 6.388148472422645 seconds remaining)
Job #1, processed 3370/10000 permutations (33.70%, 6.3786271297613295 seconds remaining)
Job #1, processed 3380/10000 permutations (33.80%, 6.368576299509354 seconds remaining)
Job #1, processed 3390/10000 permutations (33.90%, 6.358880751252525 seconds remaining)
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Job #1, processed 3410/10000 permutations (34.10%, 6.338511631985214 seconds remaining)
Job #1, processed 3420/10000 permutations (34.20%, 6.32892884706196 seconds remaining)
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Job #1, processed 3440/10000 permutations (34.40%, 6.309440435365189 seconds remaining)
Job #1, processed 3450/10000 permutations (34.50%, 6.300032857535542 seconds remaining)
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Job #1, processed 3480/10000 permutations (34.80%, 6.2749089153333655 seconds remaining)
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Job #1, processed 3500/10000 permutations (35.00%, 6.2548288617815295 seconds remaining)
Job #1, processed 3510/10000 permutations (35.10%, 6.245053075317644 seconds remaining)
Job #1, processed 3520/10000 permutations (35.20%, 6.234702343290501 seconds remaining)
Job #1, processed 3530/10000 permutations (35.30%, 6.225495020998775 seconds remaining)
Job #1, processed 3540/10000 permutations (35.40%, 6.21500103083034 seconds remaining)
Job #1, processed 3550/10000 permutations (35.50%, 6.2048646564215 seconds remaining)
Job #1, processed 3560/10000 permutations (35.60%, 6.194867768984162 seconds remaining)
Job #1, processed 3570/10000 permutations (35.70%, 6.184458910918035 seconds remaining)
Job #1, processed 3580/10000 permutations (35.80%, 6.174652068974586 seconds remaining)
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Job #1, processed 3600/10000 permutations (36.00%, 6.154719882541232 seconds remaining)
Job #1, processed 3610/10000 permutations (36.10%, 6.1443048500948665 seconds remaining)
Job #1, processed 3620/10000 permutations (36.20%, 6.134749718133915 seconds remaining)
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Job #1, processed 3670/10000 permutations (36.70%, 6.084470609228357 seconds remaining)
Job #1, processed 3680/10000 permutations (36.80%, 6.074707751688751 seconds remaining)
Job #1, processed 3690/10000 permutations (36.90%, 6.065440729704653 seconds remaining)
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Job #1, processed 3710/10000 permutations (37.10%, 6.046757583026937 seconds remaining)
Job #1, processed 3720/10000 permutations (37.20%, 6.037855076533491 seconds remaining)
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Job #1, processed 3750/10000 permutations (37.50%, 6.010398864746094 seconds remaining)
Job #1, processed 3760/10000 permutations (37.60%, 6.002075641713244 seconds remaining)
Job #1, processed 3770/10000 permutations (37.70%, 5.99325523705318 seconds remaining)
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Job #1, processed 3880/10000 permutations (38.80%, 5.89436430783616 seconds remaining)
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Job #1, processed 3920/10000 permutations (39.20%, 5.862807546343121 seconds remaining)
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Job #1, processed 3980/10000 permutations (39.80%, 5.805611412728852 seconds remaining)
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Job #1, processed 4000/10000 permutations (40.00%, 5.786771893501282 seconds remaining)
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Job #1, processed 4080/10000 permutations (40.80%, 5.70889581418505 seconds remaining)
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Job #1, processed 4100/10000 permutations (41.00%, 5.689133568507869 seconds remaining)
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Job #1, processed 4120/10000 permutations (41.20%, 5.668844246169895 seconds remaining)
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Job #1, processed 4370/10000 permutations (43.70%, 5.429469648160432 seconds remaining)
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Job #1, processed 4390/10000 permutations (43.90%, 5.4109445519762325 seconds remaining)
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Job #1, processed 5270/10000 permutations (52.70%, 4.567309164231823 seconds remaining)
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Job #1, processed 5290/10000 permutations (52.90%, 4.547658114442303 seconds remaining)
Job #1, processed 5300/10000 permutations (53.00%, 4.537640112750935 seconds remaining)
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Job #1, processed 5340/10000 permutations (53.40%, 4.499147664295154 seconds remaining)
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Job #1, processed 5370/10000 permutations (53.70%, 4.4798971581059455 seconds remaining)
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Job #1, processed 5390/10000 permutations (53.90%, 4.460166362751835 seconds remaining)
Job #1, processed 5400/10000 permutations (54.00%, 4.450688830128422 seconds remaining)
Job #1, processed 5410/10000 permutations (54.10%, 4.440669417601637 seconds remaining)
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Job #1, processed 5470/10000 permutations (54.70%, 4.381941281899238 seconds remaining)
Job #1, processed 5480/10000 permutations (54.80%, 4.371932797188307 seconds remaining)
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Job #1, processed 5500/10000 permutations (55.00%, 4.35231952233748 seconds remaining)
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Job #1, processed 5520/10000 permutations (55.20%, 4.333185997562132 seconds remaining)
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Job #1, processed 5580/10000 permutations (55.80%, 4.274873478010991 seconds remaining)
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Job #1, processed 5600/10000 permutations (56.00%, 4.255471570151193 seconds remaining)
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Job #1, processed 5670/10000 permutations (56.70%, 4.187080056579024 seconds remaining)
Job #1, processed 5680/10000 permutations (56.80%, 4.177282716186954 seconds remaining)
Job #1, processed 5690/10000 permutations (56.90%, 4.16730599830775 seconds remaining)
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Job #1, processed 5770/10000 permutations (57.70%, 4.088927007837146 seconds remaining)
Job #1, processed 5780/10000 permutations (57.80%, 4.07914820096897 seconds remaining)
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Job #1, processed 5870/10000 permutations (58.70%, 3.992131367655791 seconds remaining)
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Job #1, processed 5920/10000 permutations (59.20%, 3.9430598374959582 seconds remaining)
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Job #1, processed 5960/10000 permutations (59.60%, 3.9038971718525723 seconds remaining)
Job #1, processed 5970/10000 permutations (59.70%, 3.8942186049680214 seconds remaining)
Job #1, processed 5980/10000 permutations (59.80%, 3.8847057301065204 seconds remaining)
Job #1, processed 5990/10000 permutations (59.90%, 3.87482466641969 seconds remaining)
Job #1, processed 6000/10000 permutations (60.00%, 3.865039825439453 seconds remaining)
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Job #1, processed 6030/10000 permutations (60.30%, 3.8355755260334687 seconds remaining)
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Job #1, processed 6060/10000 permutations (60.60%, 3.8065374558514886 seconds remaining)
Job #1, processed 6070/10000 permutations (60.70%, 3.7966688413792813 seconds remaining)
Job #1, processed 6080/10000 permutations (60.80%, 3.7868025773449956 seconds remaining)
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Job #1, processed 6100/10000 permutations (61.00%, 3.767504453659058 seconds remaining)
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Job #1, processed 6240/10000 permutations (62.40%, 3.6328215048863344 seconds remaining)
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Job #1, processed 6270/10000 permutations (62.70%, 3.603633394271753 seconds remaining)
Job #1, processed 6280/10000 permutations (62.80%, 3.594033885153996 seconds remaining)
Job #1, processed 6290/10000 permutations (62.90%, 3.584124754267391 seconds remaining)
Job #1, processed 6300/10000 permutations (63.00%, 3.5743693889133517 seconds remaining)
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Job #1, processed 6360/10000 permutations (63.60%, 3.515552118889191 seconds remaining)
Job #1, processed 6370/10000 permutations (63.70%, 3.505641564843793 seconds remaining)
Job #1, processed 6380/10000 permutations (63.80%, 3.4957966363542137 seconds remaining)
Job #1, processed 6390/10000 permutations (63.90%, 3.486050712483963 seconds remaining)
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Job #1, processed 6560/10000 permutations (65.60%, 3.3205155483106297 seconds remaining)
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Job #1, processed 6660/10000 permutations (66.60%, 3.2250001179921384 seconds remaining)
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Job #1, processed 6720/10000 permutations (67.20%, 3.1664971198354444 seconds remaining)
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Job #1, processed 6760/10000 permutations (67.60%, 3.1276306485283314 seconds remaining)
Job #1, processed 6770/10000 permutations (67.70%, 3.11786674537546 seconds remaining)
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[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    9.6s finished

scikit-learn F-scores for comparison

F-test does not allow to observe the effect sign (pure two-sided test)

/usr/share/miniconda3/envs/testenv/lib/python3.9/site-packages/sklearn/utils/validation.py:1111: 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.plotting import plot_stat_map, show

# Use the fmri mean image as a surrogate of anatomical data
from nilearn import image
from nilearn.image import get_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)'
         '\n%d detections') % n_detections

display.title(title, y=1.1)

# 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)'
         '\n%d detections') % n_detections

display.title(title, y=1.1)

show()
  • plot haxby mass univariate
  • plot haxby mass univariate

Total running time of the script: ( 0 minutes 25.796 seconds)

Estimated memory usage: 1018 MB

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