[FieldTrip] Question about cluster-based permutation tests on linear mixed models

[Alik Widge]

Eric, I don't think I understand why you would say "I do not see how these
models could be combined with permutation-based inference; they are just
different statistical frameworks". As you somewhat hint, the (G)LMM is a
regression, and the beta coefficient for the independent-variable of
interest at each voxel/vertex/sensor x timepoint can be interpreted as "how
much does the independent variable explain the brain activity?" In that
framework, it seems to me that one could do the following:

for n=1:1000
   1) Permute the condition labels (within subjects) of the individual
trials
   2) Re-fit the LMM at each (voxel,timepoint), creating a beta map and
corresponding t-map
   3) Threshold and construct cluster mass statistic as usual
end
4) Identify cluster in the original (unpermuted) analysis and report
cluster p-value


Now, the main thing that has come up when we've tried to do this is that
re-fitting a (voxel x time) GLM 1000 times by the standard iterative
maximum-likelihood engines is remarkably slow. In fieldtrip, I can imagine
it would require rewriting at least a statfun, maybe other pieces of the
code. (We had an idea that, since the betas  likely should vary smoothly
over time and space, one could use the output of one GLM as the seed to the
next, which would speed up convergence.) So it still does not seem like a
good idea, but based on the above, is there actually a *theoretical* reason
it wouldn't work?


Alik Widge, MD, PhD
Director, Translational NeuroEngineering Laboratory
Division of Neurotherapeutics, Massachusetts General Hospital
Assistant Professor of Psychiatry, Harvard Medical School
Clinical Fellow, Picower Institute for Learning & Memory (MIT)
awidge at partners.org
http://scholar.harvard.edu/awidge/
617-643-2580

Alik Widge
alik.widge at gmail.com
(206) 866-5435


On Thu, Oct 20, 2016 at 6:08 AM, Maris, E.G.G. (Eric) <e.maris at donders.ru.nl
> wrote:

> Note: this is the second time I post this reply, and the reason is that I
> forgot to add an appropriate Subject (for findability) to my email (shame
> on me…(-;)
>
> *From: *Elisabeth May <elisabethsusanne.may at gmail.com>
> *Subject: **[FieldTrip] Question about cluster-based permutation tests on
> linear mixed models*
> *Date: *27 September 2016 at 14:46:55 GMT+2
> *To: *<fieldtrip at science.ru.nl>
> *Reply-To: *FieldTrip discussion list <fieldtrip at science.ru.nl>
>
>
> Dear FieldTripers,
>
> I have a question about the potential use of cluster-based permutation
> tests for results obtained using linear mixed models.
>
> We are working with data from a 10 min EEG experiment on source level with
> the aim to quantify the relationship of brain activity in different
> frequency bands with continous perceptual ratings across 20 subjects in
> different experimental conditions. Thus, we have 10 min time courses of
> brain activity and ratings for each voxel for different conditions and want
> to test a) if there are significant relationships in the single conditions
> and b) if these relationships differ between two conditions. To this end, I
> have calculated linear mixed models in R using the lme4 toolbox. For both
> the single condition relationships and the condition contrasts, they result
> in a single t-value (and a corresponding p-value), which is based on
> information on both the single subject and the group level (i.e. we perform
> a multi-level analysis). However, with more than 2000 voxels, we have a lot
> of t-values and are wondering if there is a way to apply cluster-based
> tests to correct for multiple comparisons.
>
> The main problem I see is that I only have one multilevel t-value for the
> effect across all subjects, i.e. I don't have single subjects values, which
> I could then e.g. randomize between conditions as normally done in
> cluster-based permutation tests. (Or rather, I would be able to extract
> single subject values but would then loose the advantage of the multi-level
> analysis.)
>
> I found an old thread in the mailinglist archive where it was suggested to
> flip the signs of the t-statistic for cluster-level correction (
> https://mailman.science.ru.nl/pipermail/fieldtrip/2012-July/005375.html).
> I understand that, in our case, I would do this randomly for all voxels in
> each randomization and then build spatial clusters on the resulting (partly
> flipped) t-values. However, I am not sure if that is a valid approach based
> on the null hypothesis that there are no significant relations in my single
> conditions (a) or no significant relationship differences in my condition
> contrasts (b).
>
> For the condition contrasts, I would be able to permute the condition
> labels as normally done in cluster-based permutation tests,I think, but
> would then have to recalculate the linear mixed models for all voxels in
> every permutation. This would result in a very high computational load.
>
> Does anyone have any experience with this kind of analysis? Would the
> flipping of t-values be a valid approach (and if yes, is there anything to
> keep in mind in particular)? Can you think of other ways to combine linear
> mixed models with a multiple comparison correction on the cluster level?
>
>
> Hi Elisabeth,
>
> I’m not an expert on linear mixed modelling, at least not with respect to
> the different ways in which they can be used to deal with correlated
> observations (typically, time series). However, from a theoretical point of
> view, I do not see how these models could be combined with
> permutation-based inference; they are just different statistical
> frameworks. However, it IS possible to answer your questions ("we have 10
> min time courses of brain activity and ratings for each voxel for different
> conditions and wan to test a) if there are significant relationships in the
> single conditions and b) if these relationships differ between two
> conditions.”) within the framework of cluster-based permutation tests.
> Question b) is the most straightforward because it amounts to a
> cluster-based permutation test using the depsamplesT statfun applied to the
> regression coefficients in each of the two conditions. Answering question
> a) requires that you bin your ratings in a number of categories, calculate
> the trial-averaged EEG data for each of the categoreies, and test the
> difference between them using a cluster-based permutation test using the
> depsamplesregrT statfun. Both of these approaches have been described
> previously on this discussion list, and for the depsamplesregrT statfun
> (your question a), it was Vladimir Litvak who used it first (actually, I
> implemented it for him). The approach for question b) is actually a variant
> on the general approach for testing interactions using cluster-based
> permutation tests.
>
> Have a look here:
> http://www.fieldtriptoolbox.org/faq/how_can_i_test_for_
> correlations_between_neuronal_data_and_quantitative_
> stimulus_and_behavioural_variables
> and
> http://www.fieldtriptoolbox.org/faq/how_can_i_test_an_
> interaction_effect_using_cluster-based_permutation_tests
>
> These tutorials provide all the necessary concepts, although they do not
> answer your question in a recipe-like fashion.
>
> best,
> Eric Maris
>
>
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