[R-sig-ME] (G)LMM for radian/phase data

ian m s white i.m.s.white at ed.ac.uk
Thu Sep 5 12:51:11 CEST 2013

Would analysing the cosine of the phase difference solve some of your problems?

On 5 Sep 2013, at 09:17, Tobias Heed <tobias.heed at uni-hamburg.de> wrote:

> Hello to everyone,
> I would like to analyze a dependent variable that is in radians/degrees.
> Experiment/data:
> Specifically, the data is from a coordination task in which I test whether the synchrony of repetitive movements with the two hands changes with a number of conditions.
> The data I have is the phase difference between the movements of the two hands in each repetition of the movement.
> Thus, a value of 359° is almost the same as a value of 1° (with 359 meaning that the second hand is leading by 1°, and 1 meaning it is following by 1°).
> Movements are mostly "exactly opposite" (imagine tapping with the two index fingers, first the one, than the other, numerous times), so that I have what looks like a normal distribution around 180° phase difference, but due to the type of data, I have long tails that are cut off at 0 and 360. But, there is also a small peak around 0 (would mean here that sometimes people accidentally tap the fingers together rather than successively), evident in small peaks at the end of the two tails (because "around 0" means it could be both 359 and 1, for example).
> My hypothesis is that synchrony is affected by some experimental conditions (coded as factors). This is evident in a wider distribution of the values around 180° in the conditions in which synchrony is worse.
> Previous studies have binned phase differences and run an ANOVA over the % of phase differences (accumulated over all trials) in a bin considered "quite according to instruction". Here, for example, they would consider all phase differences from 130-230° as correct (near enough to 180°). The advantage of this is that I can also bin data around the second peak (0°) by using 310-360° and 0-50° (which gets me around the problem that the data wrap around at 360°).
> Questions:
> I am wondering how to correctly analyze these data with a (G)LMM:
> 1. is there a GLMM link function for such data, or is there a transformation I can use to convert the dependent variable and run an LMM?
> 2, It seems problematic to me that if I were to use the degree values (or some transform of them), then the effect is in a change of data spread rather than in a change of mean. I am not sure how a predictor should code for this, and therefore I wonder whether I can use the degree values like this at all. 
> 3, I have converted the degree value of each trial as "correct"/"incorrect" (as described above) and run a GLMM with a binomial link function. It works well, and the results make sense, but would this be considered an adequate approach?
> I am thankful for replies.
> Best,
> Tobias
> -- 
> --------------------------------------------------------------------------------------------------------------
> Tobias Heed, PhD
> Biological Psychology and Neuropsychology  |  University of Hamburg
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> Phone: (49) 40 - 42838 5831  |  Fax:   (49) 40 - 42838 6591
> tobias.heed at uni-hamburg.de  |  Website  |  Google Scholar  |  ResearcherID
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