# -*- coding: utf-8 -*- """ .. _tut-cluster-rm-anova-spatiotemporal: ====================================================================== Repeated measures ANOVA on source data with spatio-temporal clustering ====================================================================== This example illustrates how to make use of the clustering functions for arbitrary, self-defined contrasts beyond standard t-tests. In this case we will tests if the differences in evoked responses between stimulation modality (visual VS auditory) depend on the stimulus location (left vs right) for a group of subjects (simulated here using one subject's data). For this purpose we will compute an interaction effect using a repeated measures ANOVA. The multiple comparisons problem is addressed with a cluster-level permutation test across space and time. """ # Authors: Alexandre Gramfort # Eric Larson # Denis Engemannn # # License: BSD-3-Clause # %% import numpy as np from numpy.random import randn import matplotlib.pyplot as plt import mne from mne.stats import (spatio_temporal_cluster_test, f_threshold_mway_rm, f_mway_rm, summarize_clusters_stc) from mne.minimum_norm import apply_inverse, read_inverse_operator from mne.datasets import sample print(__doc__) # %% # Set parameters # -------------- data_path = sample.data_path() meg_path = data_path / 'MEG' / 'sample' raw_fname = meg_path / 'sample_audvis_filt-0-40_raw.fif' event_fname = meg_path / 'sample_audvis_filt-0-40_raw-eve.fif' subjects_dir = data_path / 'subjects' src_fname = subjects_dir / 'fsaverage' / 'bem' / 'fsaverage-ico-5-src.fif' tmin = -0.2 tmax = 0.3 # Use a lower tmax to reduce multiple comparisons # Setup for reading the raw data raw = mne.io.read_raw_fif(raw_fname) events = mne.read_events(event_fname) # %% # Read epochs for all channels, removing a bad one # ------------------------------------------------ raw.info['bads'] += ['MEG 2443'] picks = mne.pick_types(raw.info, meg=True, eog=True, exclude='bads') # we'll load all four conditions that make up the 'two ways' of our ANOVA event_id = dict(l_aud=1, r_aud=2, l_vis=3, r_vis=4) reject = dict(grad=1000e-13, mag=4000e-15, eog=150e-6) epochs = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks, baseline=(None, 0), reject=reject, preload=True) # Equalize trial counts to eliminate bias (which would otherwise be # introduced by the abs() performed below) epochs.equalize_event_counts(event_id) # %% # Transform to source space # ------------------------- fname_inv = meg_path / 'sample_audvis-meg-oct-6-meg-inv.fif' snr = 3.0 lambda2 = 1.0 / snr ** 2 method = "dSPM" # use dSPM method (could also be MNE, sLORETA, or eLORETA) inverse_operator = read_inverse_operator(fname_inv) # we'll only use one hemisphere to speed up this example # instead of a second vertex array we'll pass an empty array sample_vertices = [inverse_operator['src'][0]['vertno'], np.array([], int)] # Let's average and compute inverse, then resample to speed things up conditions = [] for cond in ['l_aud', 'r_aud', 'l_vis', 'r_vis']: # order is important evoked = epochs[cond].average() evoked.resample(30).crop(0., None) condition = apply_inverse(evoked, inverse_operator, lambda2, method) # Let's only deal with t > 0, cropping to reduce multiple comparisons condition.crop(0, None) conditions.append(condition) tmin = conditions[0].tmin tstep = conditions[0].tstep * 1000 # convert to milliseconds # %% # Transform to common cortical space # ---------------------------------- # # Normally you would read in estimates across several subjects and morph them # to the same cortical space (e.g. fsaverage). For example purposes, we will # simulate this by just having each "subject" have the same response (just # noisy in source space) here. # # We'll only consider the left hemisphere in this tutorial. n_vertices_sample, n_times = conditions[0].lh_data.shape n_subjects = 6 print('Simulating data for %d subjects.' % n_subjects) # Let's make sure our results replicate, so set the seed. np.random.seed(0) X = randn(n_vertices_sample, n_times, n_subjects, 4) * 10 for ii, condition in enumerate(conditions): X[:, :, :, ii] += condition.lh_data[:, :, np.newaxis] # %% # It's a good idea to spatially smooth the data, and for visualization # purposes, let's morph these to fsaverage, which is a grade 5 ICO source space # with vertices 0:10242 for each hemisphere. Usually you'd have to morph # each subject's data separately, but here since all estimates are on # 'sample' we can use one morph matrix for all the heavy lifting. # Read the source space we are morphing to (just left hemisphere) src = mne.read_source_spaces(src_fname) fsave_vertices = [src[0]['vertno'], []] morph_mat = mne.compute_source_morph( src=inverse_operator['src'], subject_to='fsaverage', spacing=fsave_vertices, subjects_dir=subjects_dir, smooth=20).morph_mat morph_mat = morph_mat[:, :n_vertices_sample] # just left hemi from src n_vertices_fsave = morph_mat.shape[0] # We have to change the shape for the dot() to work properly X = X.reshape(n_vertices_sample, n_times * n_subjects * 4) print('Morphing data.') X = morph_mat.dot(X) # morph_mat is a sparse matrix X = X.reshape(n_vertices_fsave, n_times, n_subjects, 4) # %% # Now we need to prepare the group matrix for the ANOVA statistic. To make the # clustering function work correctly with the ANOVA function X needs to be a # list of multi-dimensional arrays (one per condition) of shape: samples # (subjects) × time × space. # # First we permute dimensions, then split the array into a list of conditions # and discard the empty dimension resulting from the split using numpy squeeze. X = np.transpose(X, [2, 1, 0, 3]) # X = [np.squeeze(x) for x in np.split(X, 4, axis=-1)] # %% # Prepare function for arbitrary contrast # --------------------------------------- # As our ANOVA function is a multi-purpose tool we need to apply a few # modifications to integrate it with the clustering function. This # includes reshaping data, setting default arguments and processing # the return values. For this reason we'll write a tiny dummy function. # # We will tell the ANOVA how to interpret the data matrix in terms of # factors. This is done via the factor levels argument which is a list # of the number factor levels for each factor. factor_levels = [2, 2] # %% # Finally we will pick the interaction effect by passing 'A:B'. # (this notation is borrowed from the R formula language). # As an aside, note that in this particular example, we cannot use the A*B # notation which return both the main and the interaction effect. The reason # is that the clustering function expects ``stat_fun`` to return a 1-D array. # To get clusters for both, you must create a loop. effects = 'A:B' # Tell the ANOVA not to compute p-values which we don't need for clustering return_pvals = False # a few more convenient bindings n_times = X[0].shape[1] n_conditions = 4 # %% # A ``stat_fun`` must deal with a variable number of input arguments. # # Inside the clustering function each condition will be passed as flattened # array, necessitated by the clustering procedure. The ANOVA however expects an # input array of dimensions: subjects × conditions × observations (optional). # # The following function catches the list input and swaps the first and the # second dimension, and finally calls ANOVA. # # .. note:: For further details on this ANOVA function consider the # corresponding # :ref:`time-frequency tutorial `. def stat_fun(*args): # get f-values only. return f_mway_rm(np.swapaxes(args, 1, 0), factor_levels=factor_levels, effects=effects, return_pvals=return_pvals)[0] # %% # Compute clustering statistic # ---------------------------- # # To use an algorithm optimized for spatio-temporal clustering, we # just pass the spatial adjacency matrix (instead of spatio-temporal). # as we only have one hemisphere we need only need half the adjacency print('Computing adjacency.') adjacency = mne.spatial_src_adjacency(src[:1]) # Now let's actually do the clustering. Please relax, on a small # notebook and one single thread only this will take a couple of minutes ... pthresh = 0.005 f_thresh = f_threshold_mway_rm(n_subjects, factor_levels, effects, pthresh) # To speed things up a bit we will ... n_permutations = 50 # ... run way fewer permutations (reduces sensitivity) print('Clustering.') F_obs, clusters, cluster_p_values, H0 = clu = \ spatio_temporal_cluster_test(X, adjacency=adjacency, n_jobs=None, threshold=f_thresh, stat_fun=stat_fun, n_permutations=n_permutations, buffer_size=None) # Now select the clusters that are sig. at p < 0.05 (note that this value # is multiple-comparisons corrected). good_cluster_inds = np.where(cluster_p_values < 0.05)[0] # %% # Visualize the clusters # ---------------------- print('Visualizing clusters.') # Now let's build a convenient representation of each cluster, where each # cluster becomes a "time point" in the SourceEstimate stc_all_cluster_vis = summarize_clusters_stc(clu, tstep=tstep, vertices=fsave_vertices, subject='fsaverage') # Let's actually plot the first "time point" in the SourceEstimate, which # shows all the clusters, weighted by duration subjects_dir = data_path / 'subjects' # The brighter the color, the stronger the interaction between # stimulus modality and stimulus location brain = stc_all_cluster_vis.plot(subjects_dir=subjects_dir, views='lat', time_label='temporal extent (ms)', clim=dict(kind='value', lims=[0, 1, 40])) brain.save_image('cluster-lh.png') brain.show_view('medial') # %% # Finally, let's investigate interaction effect by reconstructing the time # courses: inds_t, inds_v = [(clusters[cluster_ind]) for ii, cluster_ind in enumerate(good_cluster_inds)][0] # first cluster times = np.arange(X[0].shape[1]) * tstep * 1e3 plt.figure() colors = ['y', 'b', 'g', 'purple'] event_ids = ['l_aud', 'r_aud', 'l_vis', 'r_vis'] for ii, (condition, color, eve_id) in enumerate(zip(X, colors, event_ids)): # extract time course at cluster vertices condition = condition[:, :, inds_v] # normally we would normalize values across subjects but # here we use data from the same subject so we're good to just # create average time series across subjects and vertices. mean_tc = condition.mean(axis=2).mean(axis=0) std_tc = condition.std(axis=2).std(axis=0) plt.plot(times, mean_tc.T, color=color, label=eve_id) plt.fill_between(times, mean_tc + std_tc, mean_tc - std_tc, color='gray', alpha=0.5, label='') ymin, ymax = mean_tc.min() - 5, mean_tc.max() + 5 plt.xlabel('Time (ms)') plt.ylabel('Activation (F-values)') plt.xlim(times[[0, -1]]) plt.ylim(ymin, ymax) plt.fill_betweenx((ymin, ymax), times[inds_t[0]], times[inds_t[-1]], color='orange', alpha=0.3) plt.legend() plt.title('Interaction between stimulus-modality and location.') plt.show()