# [FieldTrip] Performing statistics based on phase/amplitude correlation

Karl Doron karl.doron at gmail.com
Sat Mar 19 03:40:38 CET 2011

```Eelke,

I haven't used  cfg.output = 'fourier'; but if it returns complex numbers,
your lines of code below won't give phase information. Matlab's real( )
function gives the real part of the complex pair --I believe it would be the
signal filtered by the wavelet transform ( the a part of a + b*i ). *The
angle( ) function will give phase angles. Maybe someone who thinks in polar
coordinates (not my specialty) can comment?

Once you get phase angles, you'll need a circular-linear correlation (phase
is circular; amplitude is linear). Check out the CircStat toolbox for
Matlab. * *

% extract freqs X samples matrices to compute correlations on
>    phSig = real(squeeze(tfrPh.fourierspctrm(1,match_str(tfrPh.label,
> chansPh(k)), :, :)));

-karl doron

On Fri, Mar 18, 2011 at 5:25 AM, Eelke Spaak <eelke.spaak at donders.ru.nl>wrote:

> Hmm, actually my own suggestion of switching around the time and trial
> dimensions seems to be very promising (and makes intuitive sense I
> guess, having thought about it some more).
>
> Best,
> Eelke
>
> 2011/3/18 Eelke Spaak <eelke.spaak at donders.ru.nl>:
> > Dear FieldTrip community,
> >
> > At the moment, I am analysing some data to see whether a correlation
> > exists between phase and amplitude over different frequencies, and in
> > different channels. Computing the signals of interest (i.e., the phase
> > and amplitude time series) works fine, and computing the correlation
> > is also easily done with Matlab's corrcoef function. Now comes the
> > tricky part. I would like to use the FT statistics framework to assess
> > the significance of the found correlation, and use clustering in
> > frequency-frequency space to correct for multiple comparisons. I
> > understand that this requires a statfun_correlationPearson (or
> > something like it), and I do not think I'll encounter any problems
> > implementing this. Before I start doing so, however, I am not sure how
> > to pass the design and the data to the higher-level statistics
> > functions, such as ft_freqstatistics.
> >
> > My data structure is custom-imported, and contains a single 100s-long
> > trial, on which the phase/amplitude analysis should be conducted:
> >
> > data =
> >        hdr: [1x1 struct]
> >    fsample: 1000
> >      trial: {[24x100000 double]}
> >       time: {[1x100000 double]}
> >      label: {24x1 cell}
> >        cfg: [1x1 struct]
> >
> > The phase and amplitude time series are generated by convolution with
> > Morlet wavelets using ft_freqanalysis:
> >
> >    % perform wavelet convolution for amplitude data
> >    cfg = [];
> >    cfg.channel = chansAmpl;
> >    cfg.method = 'wavelet';
> >    cfg.output = 'fourier';
> >    cfg.keeptrials = 'yes';
> >    cfg.width = 7;
> >    cfg.gwidth = 4;
> >    cfg.foi = freqAmpl;
> >    cfg.toi = data.time{1}; % compute estimate for each sample
> >    tfr = ft_freqanalysis(cfg, data);
> >
> >    % perform wavelet convolution for phase data
> >    cfg.channel = chansPh;
> >    cfg.foi = freqPh;
> >    tfrPh = ft_freqanalysis(cfg, data);
> >
> > where chansAmpl = {'CH10'}, chansPh = {'CH17'}, freqAmpl = 3:5:98,
> > freqPh = 2:2:30. Simply computing the correlation of interest is done
> > in the following manner:
> >
> >    % extract freqs X samples matrices to compute correlations on
> >    phSig = real(squeeze(tfrPh.fourierspctrm(1,match_str(tfrPh.label,
> > chansPh(k)), :, :)));
> >    amplSig = abs(squeeze(tfr.fourierspctrm(1,match_str(tfr.label,
> > chansAmpl(l)), :, :)));
> >
> >    % compute correlations
> >    r = corr(phSig', amplSig', 'rows', 'pairwise'); % use only non-NaN
> rows
> >
> > The correlation matrix r I get out of this nicely corresponds to the
> > results I found by using algorithms implemented elsewhere: so far so
> > good. My (unsuccessful) attempts to use the statistics framework have
> > been variations on the following:
> >
> >    % add amplitude spectrum to the TFR (which now only has fourierspctrm)
> >    tfr.amplspctrm = abs(tfr.fourierspctrm);
> >
> >    cfg = [];
> >    cfg.method = 'montecarlo';
> >    cfg.statistic = 'corr'; % I have made a (now empty) statfun_corr
> >    cfg.parameter = 'amplspctrm';
> >    cfg.numrandomization = 100;
> >    cfg.design = real(tfrPh.fourierspctrm);
> >    stat = ft_freqstatistics(cfg, tfr);
> >
> > For your information, the tfr and cfg fields look like this before the
> > call to ft_freqstatistics:
> >
> > cfg =
> >              method: 'montecarlo'
> >           statistic: 'corr'
> >           parameter: 'amplspctrm'
> >    numrandomization: 100
> >              design: [4-D double]
> >
> > tfr =
> >            label: {'CH10'}
> >           dimord: 'rpttap_chan_freq_time'
> >             freq: [3 8 13 18 23 28 33 38 43 48 53 58 63 68 73 78 83 88 93
> 98]
> >             time: [1x100000 double]
> >    fourierspctrm: [4-D double]
> >        cumtapcnt: [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
> >              cfg: [1x1 struct]
> >       amplspctrm: [4-D double]
> >
> > The statfun_corr gets a dat variable, that appears to be a column
> > vector constructed by concatenating all the samples in the amplitude
> > spectrum. How should my function treat this? I am aware that
> > specifying a 4D design matrix is a bit odd, but it does contain my 15
> > regressors X 100000 samples (X 2 singleton dimensions that correspond
> > to the 1 trial and 1 channel that I analysed). If I squeeze() the
> > matrix before calling ft_freqstatistics, I get an error 'the size of
> > the design matrix does not match the number of observations in the
> > data'.
> >
> > I realize my question is a bit vague, but I am somewhat lost as to how
> > to proceed. In short, what I want is this: (1) compute a correlation
> > (across samples) for each phase time series with each amplitude time
> > series (each time series corresponds to a single frequency); (2)
> > shuffle the phase time series around, computing correlations on the
> > shuffled data to assess significance of the observed correlation; (3)
> > prune away correlations that are isolated in frequency-frequency
> > space, retain only large clusters of correlations.
> >
> > All the documentation about the cluster-based statistics is focused on
> > comparing variables that differ across trials and/or subjects, and my
> > 'problem' might be that I only have a single trial. Chopping up the
> > data into 100000 trials, each 1 sample long, is maybe a possibility?
> > But it seems a bit artificial.
> >
> > (It would actually probably not be very difficult to implement my
> > desired functionality 'by hand', but I guess it should be possble
> > within FT's statistics framework. That would have quite some
> >
> > Many thanks in advance for any input you can offer.
> >
> > Best,
> >
> > Eelke
> >
>
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