we performed spatial exploratory factor analysis (EFA) on data from an ERP experiment in an effort to decompose the signal (61 electrodes x 1 mean of a few adjacent time points) and investigate the potential contribution of unobserved variables (the factor scores have been found to strongly correlate with a behavioural variable).

Now I've got three spatial factors at a single time point (61 electrodes x 3 factors) and my question is whether these may be used for source estimation instead of voltage values and which method offered by Brainstorm, with the use of average anatomy, would be the most appropriate. Are there any special considerations regarding electrode referencing?

If you have experience with this method, I'll appreciate any further guidance.

No, we don't have any experience with this method, so I'm not sure how to best guide you.

For sure, you wouldn't be able to use all three factors at once. But one at a time, maybe, it depends what kind of measure you obtain.
If the outputs are similar to other spatial decomposition methods (PCA/SSP or ICA), and you would like to use it as some sort of cleaning spatial filter, why not. The signals would need to "keep on looking like EEG". The spatial filter applied to the EEG would need to be applied to the forward model as well (under the form of a [Nchannel x Nchannel] mixing matrix).

With this properly set, the source estimation functions should apply this mixing matrix to the forward model before source estimation.

If your values are more a "score" and are not linear transformation of the EEG data, I don't think there is any hope for localizing them. In that case, you might be interested in computing this score on the time series extracted from a few regions of interest in source space.

Does any of this make sense to you?
If it does and you want to implement something, you might need more guidance on some the fields of the Projectors structure. Let me know.

If I understand, what you want is to view the source pattern corresponding to the sensor pattern of each of these factors. That's closely related to PLS analysis for example (and many other similar multivariate methods). @Francois, this would indeed be the same as doing it for an SSP or ICA component. I don't think this can be done directly in Brainstorm with projectors. I think in Brainstorm, projectors can only be applied to timeseries data. Right?

However, it would be easy to do! If the projector (factor) matrix was saved as a data matrix (with non-physical "relative amplitude" units), then you could apply the inverse model to it directly. You'd get 3 "time points" that correspond to your 3 factors.

I would add a note of caution however: these multivariate methods can quickly become difficult to interpret, and I have seen some instances where authors focus on "parts" of factors that relate to their hypotheses (say a specific region) and draw unsupported conclusions that probably should have been investigated with more straightforward focused approaches.

In any case, let us know if you get this working or if you need further help!