[R] Appropriate specification of random effects structure for EEG/ERP data: including Channels or not?

[Phillip Alday]

You might also want to take a look at the recent paper from the Federmeier group, especially the supplementary materials. There are a few technical inaccuracies (ANOVA is a special case of hierarchical modelling, not the other way around), but they discuss some of the issues involved. And relevant for your work: they model channel as a grouping variable in the random-effects structure.

Payne, B. R., Lee, C.-L., and Federmeier, K. D. (2015). Revisiting the incremental effects of context on word processing: Evidence from single-word event-related brain potentials. Psychophysiology.

http://dx.doi.org/10.1111/psyp.12515

Best,
Phillip

> On 24 Sep 2015, at 22:42, Phillip Alday <Phillip.Alday at unisa.edu.au> wrote:
> 
> There is actually a fair amount of ERP literature using mixed-effects
> modelling, though you may have to branch out from the traditional
> psycholinguistics journals a bit (even just more "neurolinguistics" or
> language studies published in "psychology" would get you more!). But
> just in the traditional psycholinguistics journals, there is a wealth of
> literature, see for example the 2008 special issue on mixed models of
> the Journal of Memory and Language.
> 
> I would NOT encode the channels/ROIs/other topographic measures as
> random effects (grouping variables). If you think about the traditional
> ANOVA analysis of ERPs, you'll recall that ROI or some other topographic
> measure (laterality, saggitality) are included in the main effects and
> interactions. As a rule of thumb, this corresponds to a fixed effect in
> random effects models. More specifically, you generally care about
> whether the particular levels of the topographic measure (i.e. you care
> if an ERP component is located left-anterior or what not) and this is
> what fixed effects test. Random effects are more useful when you only
> care about the variance introduced by a particular term but not the
> specific levels (e.g. participants or items -- we don't care about a
> particular participant, but we do care about how much variance there is
> between participants, i.e. how the population of participants looks). 
> 
> Or, another thought: You may have seen ANOVA by-subjects and by-items,
> but I bet you've never seen an ANOVA by-channels. ANOVA "implicitly"
> collapses the channels within ROIs and you can do the same with mixed
> models. (That's an awkward statement technically, but it should help
> with the intuition.)
> 
> There is an another, related important point -- "nuisance parameters"
> aren't necessarily random effects. So even if you're not interested in
> the per-electrode distribution of the ERP component, that doesn't mean
> those should automatically be random effects. It *might* make sense to
> add a channel (as in per-electrode) random effect, if you care to model
> the variation within a given ROI (as you have done), but I haven't seen
> that yet. It is somewhat rare to include a per-channel fixed effect,
> just because you lose a lot of information that way and introduce more
> parameters into the model, but you could include a more fine-grained
> notion of saggital / lateral location based on e.g. the 10-20 system and
> make that into an ordered factor. (Or you could be extreme and even use
> the spherical coordinates that the 10-20 is based on and have continuous
> measures of electrode placement!) The big problem with including
> "channel" as a random-effect grouping variable is that the channels
> would have a very complicated covariance structure (because adjacent
> electrodes are very highly correlated with each other) and I'm not sure
> how to model this in a straightforward way with lme4.
> 
> More generally, in considering your random effects structure, you should
> look at Barr et al (2013, "Random effects structure for confirmatory
> hypothesis testing: Keep it maximal") and the recent reply by Bates et
> al (arXiv, "Parsimonious Mixed Models"). You should read up on the GLMM
> FAQ on testing random effects -- there are different opinions on this
> and not all think that testing them via likelihood-ratio tests makes
> sense.
> 
> That wasn't my most coherent response, but maybe it's still useful. And
> for questions like this on mixed models, do check out the R Special
> Interest Group on Mixed Models. :-)
> 
> Best,
> Phillip
> 
> On Thu, 2015-09-24 at 12:00 +0200, r-help-request at r-project.org wrote:
>> Message: 4
>> Date: Wed, 23 Sep 2015 12:46:46 +0200
>> From: Paolo Canal <paolo.canal at iusspavia.it>
>> To: r-help at r-project.org
>> Subject: [R] Appropriate specification of random effects structure for
>>        EEG/ERP data: including Channels or not?
>> Message-ID: <56028316.2050004 at iusspavia.it>
>> Content-Type: text/plain; charset="UTF-8"
>> 
>> Dear r-help list,
>> 
>> I work with EEG/ERP data and this is the first time I am using LMM to 
>> analyze my data (using lme4).
>> The experimental design is a 2X2: one manipulated factor is
>> agreement, 
>> the other is noun (agreement being within subjects and items, and
>> noun 
>> being within subjects and between items).
>> 
>> The data matrix is 31 subjects * 160 items * 33 channels. In ERP 
>> research, the distribution of the EEG amplitude differences (in a
>> time 
>> window of interest) are important, and we care about knowing whether
>> a 
>> negative difference is occurring in Parietal or Frontal electrodes.
>> At 
>> the same time information from single channel is often too noisy and 
>> channels are organized in topographic factors for evaluating
>> differences 
>> in distribution. In the present case I have assigned each channel to
>> one 
>> of three levels of two factors, i.e., Longitude (Anterior, Central, 
>> Parietal) and Medial (Left, Midline, Right): for instance, one
>> channel 
>> is Anterior and Left. With traditional ANOVAs channels from the same 
>> level of topographic factors are averaged before variance is
>> evaluated 
>> and this also has the benefit of reducing the noise picked up by the 
>> electrodes.
>> 
>> I have troubles in deciding the random structure of my model. Very
>> few 
>> examples on LMM on ERP data exist (e.g., Newman, Tremblay, Nichols, 
>> Neville & Ullman, 2012) and little detail is provided about the 
>> treatment of channel. I feel it is a tricky term but very important
>> to 
>> optimize fit. Newman et al say "data from each electrode within an
>> ROI 
>> were treated as repeated measures of that ROI". In Newman et al, the 
>> ROIs are the 9 regions deriving from Longitude X Medial
>> (Anterior-Left, 
>> Anterior-Midline, Anterior-Right, Central-Left ... and so on), so in
>> a 
>> way they treated each ROI separately and not according to the
>> relevant 
>> dimensions of Longitude and Medial.
>> 
>> We used the following specifications in lmer:
>> 
>> [fixed effects specification: ?V ~ Agreement * Noun * Longitude *
>> Medial 
>> * (cov1 + cov2 + cov3 + cov4)] (the terms within brackets are a
>> series 
>> of individual covariates, most of which are continuous variables)
>> 
>> [random effects specification: (1+Agreement*Type of Noun | subject) + 
>> (1+Agreement | item) + (1|longitude:medial:channel)]
>> 
>> What I care the most about is the last term 
>> (1|longitude:medial:channel). I chose this specification because I 
>> thought that allowing each channel to have different intercepts in
>> the 
>> random structure would affect the estimation of the topographic fixed 
>> effects (Longitude and Medial) in which channel is nested.
>> Unfortunately 
>> a reviewer commented that since "channel is not included in the fixed 
>> effects I would probably leave that out".
>> 
>> But each channel is a repeated measure of the eeg amplitude inside
>> the 
>> two topographic factors, and random terms do not have to be in the
>> fixed 
>> structure, otherwise we would also include subjects and items in the 
>> fixed effects structure. So I kind of feel that including channels as 
>> random effect is correct, and having them nested in longitude:medial 
>> allows to relax the assumption that the effect in the EEG has always
>> the 
>> same longitude:medial distribution. But I might be wrong.
>> 
>> I thus tested differences in fit (ML) with anova() between 
>> (1|longitude:medial:channel) and the same model without the term, and
>> a 
>> third model with the model with a simpler (1|longitude:medial).
>> 
>> Fullmod vs Nochannel:
>> 
>> Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
>> modnoch 119 969479 970653 -484621 969241
>> fullmod 120 968972 970156 -484366 968732 508.73 1 < 2.2e-16 ***
>> 
>> Differences in fit is remarkable (no variance components with
>> estimates 
>> close to zero; no correlation parameters with values close to ?1).
>> 
>> Fullmod vs SimplerMod:
>> 
>>   Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
>> 
>> fullmod 120 968972 970156 -484366 968732
>> simplermod 120 969481 970665 -484621 969241 0 0 1
>> 
>> Here the number of parameters to estimate in fullmod and simplermod
>> is 
>> the same but the increase in fit is very consistent (-509 BIC). So I 
>> guess although the chisquare is not significant we do have a string 
>> increase in fit. As I understand this, a model with better fit will
>> find 
>> more accurate estimates, and I would be inclined to keep the fullmod 
>> random structure.
>> 
>> But perhaps I am missing something or I am doing something wrong.
>> Which 
>> is the correct random structure to use?
>> 
>> Feedbacks are very much appreciated. I often find answers in the
>> list, 
>> and this is the first time I post a question.
>> Thanks,
>> Paolo
>> 
>> 
>> 
>> 
>