cosinor2 (version 0.2.1)

cosinor.detect: Rhythm Detection Test

Description

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

Usage

cosinor.detect(x)

Arguments

x

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

Details

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<U+00E9>lissen, 2014): $$F = \frac{\frac{\sum(\widehat{Y}_i - \bar{Y})^2}{2}}{\frac{\sum(Y_i - \bar{Y})^2}{N - 3}}$$ with \(df_1 = 2\) and \(df_2 = N - 3\) , where \(\widehat{Y}_i\) is the \(i\)th estimated value, \(Y_i\) is the \(i\)th 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: $$F = \frac{k(k-2)}{2(k-1)}\frac{1}{1-(\frac{\widehat{\sigma}_{\beta\gamma}}{\widehat{\sigma}_\beta \widehat{\sigma}_\gamma})^2}[\frac{\beta^2}{\widehat{\sigma}^2_\beta}-2\frac{\widehat{\sigma}_{\beta\gamma}}{\widehat{\sigma}_\beta \widehat{\sigma}_\gamma}\frac{\beta \gamma}{\widehat{\sigma}_\beta \widehat{\sigma}_\gamma}+\frac{\gamma^2}{\widehat{\sigma}^2_\gamma}]$$ with \(df_1 = 2\) and \(df_2 = k - 2\) , where \(k\) is the number of subjects in the population, \(\widehat{\sigma}_\beta\) and \(\widehat{\sigma}_\gamma\) are standard deviations of population \(\beta\) and \(\gamma\) coefficients and \(\widehat{\sigma}_{\beta\gamma}\) is the covariance of population \(\beta\) and \(\gamma\) coefficients.

References

Corn<U+00E9>lissen, G. (2014). Cosinor-Based Rhythmometry. Theoretical Biology and Medical Modeling, 11, Article 16.

Bingham, C., Arbogast, B., Guillaume Corn<U+00E9>lissen, G., Lee, J.K. & Halberg, F. (1982). Inferential Statistical Methods for Estimating and Comparing Cosinor Parameters. Chronobiologia, 9(4), 397-439.

Examples

# NOT RUN {
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)
# }