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Dear Tom, dear all,
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<div class="">Let met reply to this e-mail on the discussion list, ’ter lering ende vermaak’ of - hopefully - many.</div>
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">From:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Tom Marshall <<a href="mailto:tom.marshall@psy.ox.ac.uk" class="">tom.marshall@psy.ox.ac.uk</a>><br class="">
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">Subject:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class=""><b class="">fieldtrip cluster stats on circular data?</b><br class="">
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">Date:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">30 November 2020 at 17:50:13 CET<br class="">
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">To:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">"Schoffelen, J.M. (Jan Mathijs)" <<a href="mailto:jan.schoffelen@donders.ru.nl" class="">jan.schoffelen@donders.ru.nl</a>><br class="">
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Hi JM,<o:p class=""></o:p></div>
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Is there support for using the fieldtrip cluster-stat functions if the axis I want to cluster over is<span class="Apple-converted-space"> </span><i class="">circular</i>?<o:p class=""></o:p></div>
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E.g., say I have spike counts at evenly-spaced phase bins of an oscillation, in two conditions, and I want to test the hypothesis of a difference between the way the spikes phase-cluster in condition A vs condition B. So instead of a time-axis, my data have
a<span class="Apple-converted-space"> </span><i class="">phase</i>-axis that spans 0-2pi.<span class="Apple-converted-space"> </span><span style="font-size: 11pt;" class=""><font color="#a811d1" class="">It seems like you could use cluster-based permutation
to test that hypothesis. In fact you could just hack those data into a fieldtrip structure and plug them into ft_timelockstatistics right away. But ft_timelockstatistics would then not identify clusters if they cross the arbitrary 0/2pi point (because 0 is
at the beginning of the vector and 2pi at the end); you would be biased towards finding clusters in certain parts of the phase-space and not others by ignoring its circularity.</font></span></div>
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<div>Well, the first thing that comes to mind, is that you could - rather than framing this in terms of a ’statfun’ - look into computing spike-field coherence <a href="https://www.fieldtriptoolbox.org/tutorial/spikefield/" class="">https://www.fieldtriptoolbox.org/tutorial/spikefield/</a>.
That is, spike-field coherence (or a similar measure that quantifies the extent to which the timing of point-process are aligned to a preferred phase of an oscillatory process. Then, what you’re after is to statistically compare the spike-field coherence across
conditions (provided you control for difference in overall spike rate, and the SNR of the oscillation signal.</div>
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<div>Alternatively, and that’s what you asked about, one can think of designing a ’statfun’ that takes the circularity of the independent variable into account. So, in such a context, one would have a bunch of observed (dependent variables) values (e.g. spike
rate), which are paired with an independent variable (i.e. the phase of an oscillation at which the spike rate was estimated). What I have done in the past was to operationalize your question into a test-statistic that quantified (least-squares) the amplitude
of a cosine function to the data points, as a function of phase. As a matter of fact, following up on a related discussion I recently had in house, I just created a FAQ about this: <a href="https://www.fieldtriptoolbox.org/faq/how_can_i_test_whether_a_behavioral_measure_is_phasic/" class="">https://www.fieldtriptoolbox.org/faq/how_can_i_test_whether_a_behavioral_measure_is_phasic/</a></div>
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<div>In this FAQ I pasted the code for a statufn (ft_statfun_cosinefit), which basically estimates the amplitude of the best-fitting cosine wave, determined by the phase values in the design. By default, it does not care about the optimal phase (although the
function allows for the constraint to fit a cosine wave with a fixed (specified) phase). One could of course think of other - perhaps more appropriate - test statistics, e.g. the concentration parameter of a von Mises distribution (or the goodness-of-fit of
a (mixture of) von Mises distributions, which also would address the question as to whether there’s a single preferred phase to begin with).</div>
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<div>The tricky bit would be to think of an appropriate randomization scheme, in order to test a null hypothesis at the first level.</div>
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<div>Yet, in your case, it seems you want to do a second level test (i.e. is the amplitude of the cosinefit in condition A systematically larger than in condition B), so the permutation only comes into play when you start permuting across conditions (in which
case you can just use a depsamplesT based test statistic.</div>
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<div>Best wishes,</div>
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<div>JM</div>
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So question part A: Has anyone implemented this before and if so is there code for it?</div>
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Yes, and yes. See above.</div>
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Part B: <wild guesses welcome> Do you think adapting the cluster-stats code would be a big/difficult job for a moderately-experienced coder who knows the fieldtrip source a bit (i.e., me)? Which low-level functions are the right place to start looking? And
would this be useful for the fieldtrip user base? If so I’d happily try to implement it and submit a PR.</div>
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<div>Thanks. Let’s follow this up if you were thinking of another solution as the one outlined above.</div>
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