cosinor.detect: Rhythm Detection Test
In cosinor2: Extended Tools for Cosinor Analysis of Rhythms

Description Usage Arguments Details References Examples

Performs the rhythm detection test, a global test for the significance of the estimated model for single cosinor and population-mean cosinor.

1	cosinor.detect(x)

`x`	An object of the `cosinor.lm` or `population.cosinor.lm` class.

The rhythm detection test, also called the zero-amplitude test, tests the overall significance of the cosinor model. The test is actually an F-ratio and is calculated as following (according to the procedure described in Corn<c3><a9>lissen, 2014):

F = \frac{\frac{∑(\widehat{Y}_i - \bar{Y})^2}{2}}{\frac{∑(Y_i - \bar{Y})^2}{N - 3}}

with df_1 = 2 and df_2 = N - 3 , where \widehat{Y}_i is the ith estimated value, Y_i is the ith observed value, \bar{Y} is the arithmetic mean of observed values and N is the number of timepoints. For the population-mean cosinor model, the test is calculated according to the procedure described in Bingham et al. (1982) as follows:

F = \frac{k(k-2)}{2(k-1)}\frac{1}{1-(\frac{\widehat{σ}_{βγ}}{\widehat{σ}_β \widehat{σ}_γ})^2}[\frac{β^2}{\widehat{σ}^2_β}-2\frac{\widehat{σ}_{βγ}}{\widehat{σ}_β \widehat{σ}_γ}\frac{β γ}{\widehat{σ}_β \widehat{σ}_γ}+\frac{γ^2}{\widehat{σ}^2_γ}]

with df_1 = 2 and df_2 = k - 2 , where k is the number of subjects in the population, \widehat{σ}_β and \widehat{σ}_γ are standard deviations of population β and γ coefficients and \widehat{σ}_{βγ} is the covariance of population β and γ coefficients.

Corn<c3><a9>lissen, G. (2014). Cosinor-Based Rhythmometry. Theoretical Biology and Medical Modeling, 11, Article 16.

Bingham, C., Arbogast, B., Guillaume Corn<c3><a9>lissen, G., Lee, J.K. & Halberg, F. (1982). Inferential Statistical Methods for Estimating and Comparing Cosinor Parameters. Chronobiologia, 9(4), 397-439.

fit.temperature<-cosinor.lm(Temperature~time(Time), period = 24, data = temperature_zg)
cosinor.detect(fit.temperature)

fit.november<-population.cosinor.lm(data = PANAS_november, time = PANAS_time,
period = 7)
cosinor.detect(fit.november)

Loading required package: cosinor
            F df1 df2            p
[1,] 681.1604   2  45 2.282638e-34
     MESOR Amplitude Acrophase
1 1.435419 0.2662682 -5.544496
            F df1 df2          p
[1,] 4.732237   2  17 0.02323689