Seeking tau: A comparison of six methods

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Abstract
Six methods for measuring the period of circadian rhythms (tau) have been compared using real and artificial data. The modified periodogram technique estimates tau by fitting a data‐specific form estimate to time series data with a period that minimizes the variance of data around the form estimate. The onset periodogram converts raw data to new values that reflect rapid increases of data magnitude, then fits a form estimate to these new values. Iterative cosinor determines the period of the single cosine curve that best describes the data. The iterative harmonic derives a form estimate, consisting of a cosine function plus a series of true harmonics, which most closely describes the data. Other methods measure the slope of the line fitting each day's acrophase (regressive cosinor) or subjectively selected phase markers (eyefitting). Our analyses indicate that the estimated value of tau can vary depending on the method used. Periodogram and iterative harmonic methods provided the most consistently satisfactory estimates of tau from all sets of data examined. Eyefitting and onset periodogram methods accurately estimated tau from artificial data based on hamster activity rhythms, but were less useful for estimating temperature tau. The eyefitting procedure was less replicable than the automated methods for estimating tau. The choice of analysis method ultimately depends upon the character of the data to be analyzed and the nature of the hypotheses to be tested.