Are there some commonly used statistical methods, for example cosinor analysis, well-suited to rhythm analysis using binary data? The data consist of events: awake versus asleep in minute bins; I would be searching for ultradian rhythms in 'awakenings' during the night. I was hoping to avoid coercing the data into a more continuous form.
I am still thinking about that.
But, maybe you can obtain the mean pattern for each subject obtaining a value between 0 and 1 for each bin. I know You can loose the ultradian rhythm if it is not phase stable.
For correct that you can perform a Zeitgeber Time using sleep onset as time=0.
It could work but I am not sure.
I hope It gives you some idea.
Good luck
The same transformation you apply to the time variable in a cosinor analysis could be used with any method other than linear regression, at least in principle. This could probably be extended to a logistic regression model or generalized estimating equations. It sounds like the latter might be more appropriate here, as you seem to suggest that you have repeated measures over each individual for each bin - that way, you would be able to get an idea of how time as the independent variable influences the sleep/wake state adjusting for the previous bin's state.
These suggestions sound interesting; my literature searches seem to suggest maximum entropy spectral analysis as a common method of describing ultradian rhythms, but its still not quite clear to me if this method is applicable to binary data, or if I would have to make my data more continuous..
Do you know intradaily variability from Van Someren? It is a very simple formula to calculate if your wave is sinusoidal or gausian noise. In the middle you can find ultradian patterns. I checked it and it works like Fourier analysis (they are correlated).
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