Note

Click here to download the full example code

# Analysing continuous features with binning and regression in sensor space¶

Predict single trial activity from a continuous variable.
A single-trial regression is performed in each sensor and timepoint
individually, resulting in an `mne.Evoked`

object which contains the
regression coefficient (beta value) for each combination of sensor and
timepoint. This example shows the regression coefficient; the t and p values
are also calculated automatically.

Here, we repeat a few of the analyses from 1. This can be easily performed by accessing the metadata object, which contains word-level information about various psycholinguistically relevant features of the words for which we have EEG activity.

For the general methodology, see e.g. 2.

## References¶

- 1
Dufau, S., Grainger, J., Midgley, KJ., Holcomb, PJ. A thousand words are worth a picture: Snapshots of printed-word processing in an event-related potential megastudy. Psychological Science, 2015

- 2
Hauk et al. The time course of visual word recognition as revealed by linear regression analysis of ERP data. Neuroimage, 2006

```
# Authors: Tal Linzen <linzen@nyu.edu>
# Denis A. Engemann <denis.engemann@gmail.com>
# Jona Sassenhagen <jona.sassenhagen@gmail.com>
#
# License: BSD (3-clause)
import pandas as pd
import mne
from mne.stats import linear_regression, fdr_correction
from mne.viz import plot_compare_evokeds
from mne.datasets import kiloword
# Load the data
path = kiloword.data_path() + '/kword_metadata-epo.fif'
epochs = mne.read_epochs(path)
print(epochs.metadata.head())
```

Out:

```
Reading /home/circleci/mne_data/MNE-kiloword-data/kword_metadata-epo.fif ...
Isotrak not found
Found the data of interest:
t = -100.00 ... 920.00 ms
0 CTF compensation matrices available
960 matching events found
No baseline correction applied
Adding metadata with 8 columns
0 projection items activated
WORD ... VisualComplexity
0 film ... 55.783710
1 cent ... 63.141553
2 shot ... 64.600033
3 cold ... 63.657457
4 main ... 68.945661
[5 rows x 8 columns]
```

Psycholinguistically relevant word characteristics are continuous. I.e., concreteness or imaginability is a graded property. In the metadata, we have concreteness ratings on a 5-point scale. We can show the dependence of the EEG on concreteness by dividing the data into bins and plotting the mean activity per bin, color coded.

```
name = "Concreteness"
df = epochs.metadata
df[name] = pd.cut(df[name], 11, labels=False) / 10
colors = {str(val): val for val in df[name].unique()}
epochs.metadata = df.assign(Intercept=1) # Add an intercept for later
evokeds = {val: epochs[name + " == " + val].average() for val in colors}
plot_compare_evokeds(evokeds, colors=colors, split_legend=True,
cmap=(name + " Percentile", "viridis"))
```

Out:

```
Replacing existing metadata with 9 columns
No picks, plotting the GFP ...
Float colors detected, mapping to percentiles ...
```

We observe that there appears to be a monotonic dependence of EEG on concreteness. We can also conduct a continuous analysis: single-trial level regression with concreteness as a continuous (although here, binned) feature. We can plot the resulting regression coefficient just like an Event-related Potential.

```
names = ["Intercept", name]
res = linear_regression(epochs, epochs.metadata[names], names=names)
for cond in names:
res[cond].beta.plot_joint(title=cond, ts_args=dict(time_unit='s'),
topomap_args=dict(time_unit='s'))
```

Out:

```
Fitting linear model to epochs, (7424 targets, 2 regressors)
Done
```

Because the *linear_regression* function also estimates p values, we can –
after applying FDR correction for multiple comparisons – also visualise the
statistical significance of the regression of word concreteness.
The `mne.viz.plot_evoked_image()`

function takes a *mask* parameter.
If we supply it with a boolean mask of the positions where we can reject
the null hypothesis, points that are not significant will be shown
transparently, and if desired, in a different colour palette and surrounded
by dark contour lines.

```
reject_H0, fdr_pvals = fdr_correction(res["Concreteness"].p_val.data)
evoked = res["Concreteness"].beta
evoked.plot_image(mask=reject_H0, time_unit='s')
```

**Total running time of the script:** ( 0 minutes 3.320 seconds)

**Estimated memory usage:** 117 MB