Sensor space least squares regression¶

Predict single trial activity from a continuous variable. A single-trial regression is performed in each sensor and timepoint individually, resulting in an Evoked object which contains the regression coefficient (beta value) for each combination of sensor and timepoint. Example also shows the T statistics and the associated p-values.

Note that this example is for educational purposes and that the data used here do not contain any significant effect.

(See Hauk et al. (2006). The time course of visual word recognition as revealed by linear regression analysis of ERP data. Neuroimage.)

# Authors: Tal Linzen <linzen@nyu.edu>
#          Denis A. Engemann <denis.engemann@gmail.com>
#
# License: BSD (3-clause)

import numpy as np

import mne
from mne.datasets import sample
from mne.stats.regression import linear_regression

print(__doc__)

data_path = sample.data_path()

Set parameters and read data

raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
event_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'
tmin, tmax = -0.2, 0.5
event_id = dict(aud_l=1, aud_r=2)

# Setup for reading the raw data
raw = mne.io.read_raw_fif(raw_fname)
events = mne.read_events(event_fname)

picks = mne.pick_types(raw.info, meg='mag', eeg=False, stim=False,
                       eog=False, exclude='bads')

# Reject some epochs based on amplitude
reject = dict(mag=5e-12)
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, proj=True,
                    picks=picks, baseline=(None, 0), preload=True,
                    reject=reject)

Out:

Opening raw data file /home/ubuntu/mne_data/MNE-sample-data/MEG/sample/sample_audvis_filt-0-40_raw.fif...
    Read a total of 4 projection items:
        PCA-v1 (1 x 102)  idle
        PCA-v2 (1 x 102)  idle
        PCA-v3 (1 x 102)  idle
        Average EEG reference (1 x 60)  idle
    Range : 6450 ... 48149 =     42.956 ...   320.665 secs
Ready.
Current compensation grade : 0
145 matching events found
Created an SSP operator (subspace dimension = 3)
4 projection items activated
Loading data for 145 events and 106 original time points ...
    Rejecting  epoch based on MAG : [u'MEG 1711']
    Rejecting  epoch based on MAG : [u'MEG 1711']
2 bad epochs dropped

Run regression

names = ['intercept', 'trial-count']

intercept = np.ones((len(epochs),), dtype=np.float)
design_matrix = np.column_stack([intercept,  # intercept
                                 np.linspace(0, 1, len(intercept))])

# also accepts source estimates
lm = linear_regression(epochs, design_matrix, names)


def plot_topomap(x, unit):
    x.plot_topomap(ch_type='mag', scale=1, size=1.5, vmax=np.max,
                   unit=unit, times=np.linspace(0.1, 0.2, 5))

trial_count = lm['trial-count']

plot_topomap(trial_count.beta, unit='z (beta)')
plot_topomap(trial_count.t_val, unit='t')
plot_topomap(trial_count.mlog10_p_val, unit='-log10 p')
plot_topomap(trial_count.stderr, unit='z (error)')

Out:

Fitting linear model to epochs, (10812 targets, 2 regressors)
Done

Total running time of the script: ( 0 minutes 8.272 seconds)

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