Linear Model with Overlap Correction

Note

We recommend you briefly go over the mass-univariate linear modelling tutorial

In this notebook we will fit regression models to (simulated) EEG data. We will see that we need some type of overlap correction, as the events are close in time to each other, so that the respective brain responses overlap. If you want more detailed introduction to this topic check out our paper.

Setting up & loading the data

using Unfold
using UnfoldSim
using UnfoldMakie,CairoMakie
using DataFrames

data, evts = UnfoldSim.predef_eeg()

Overlap Correction

For an overlap correction analysis we will do one additional step: define a temporal basisfunction. The steps are as following:

specify a temporal basisfunction
specify a formula
fit a linear model for each channel (one for all timepoints!)
visualize the results.

Timeexpanded / Deconvolved ModelFit

1. specify a temporal basisfunction

By default, we would want to use a FIR basisfunction. See Basis Functions for more details.

basisfunction = firbasis(τ=(-0.4,.8),sfreq=100)

2. specify a formula

We specify the same formula as before

f  = @formula 0~1+condition+continuous

3. fit the linear model

The formula and basisfunction is not enough on their own. We also need to specify which event and which formula matches - this is important in cases where there are multiple events with different formulas

bf_vec = [Any=>(f,basisfunction)]

Note

The Any means to use all rows in evts. In case you have multiple events, you'd want to specify multiple basisfunctions e.g. bfDict = ["stimulus"=>(f1,basisfunction1), "response"=>(f2,basisfunction2)]

You likely have to specify a further argument to fit: eventcolumn="type" with type being the column in evts that codes for the event (stimulus / response in this case)

Now we are ready to fit a UnfoldLinearModel. Not that instead of times as in the mass-univariate case, we have to provide the BasisFunction type now.

m = fit(UnfoldModel,bf_vec,evts,data);

4. Visualize the model

Similarly to the previous tutorial, we can visualize the model

results = coeftable(m)
plot_erp(results)

Cool! All overlapping activity has been removed and we recovered the simulated underlying signal.