Residual Circadian Spectrum

Removes the fitted cosinor mean and estimates the spectrum of what is left, the residual circadian spectrum, integrating it into frequency bands. It measures the ultradian and noise structure that the cosinor does not fit (Krafty et al. 2019), so two recordings with the same 24-hour rhythm but different residual fragmentation are told apart.

Usage

residual.spectrum(
  counts,
  timestamps,
  period = 24,
  bands = list(ultradian = c(2, 8), high_freq = c(0.5, 2))
)

Arguments

counts

Numeric activity vector.

timestamps

POSIXct timestamps, one per value.

period

Cosinor period in hours (default 24).

bands

Named list of c(low_hours, high_hours) period bands for the residual power; defaults to ultradian (2-8 h) and high-frequency (0.5-2 h).

Value

An object of class actiRhythm_rcs: the residual variance, a per-band power table, and the spectrum. Never errors.

References

Krafty RT, Fu H, Graves JL, Bruce SA, Hall MH, Smagula SF (2019). “Measuring variability in rest-activity rhythms from actigraphy with application to characterizing symptoms of depression.” Statistics in Biosciences, 11, 314–333. doi:10.1007/s12561-018-09230-2 .

Examples

ts <- seq(as.POSIXct("2024-01-01", tz = "UTC"), by = 600, length.out = 6 * 144)
th <- as.numeric(difftime(ts, ts[1], units = "hours"))
residual.spectrum(100 + 80 * cos(2 * pi * th / 24) + 20 * sin(2 * pi * th / 4), ts,
                  period = 24)
#> Residual Circadian Spectrum
#> 
#>   Residual variance: 200.2
#> 
#>       band low_h high_h power fraction
#>  ultradian   2.0      8 86400        1
#>  high_freq   0.5      2     0        0
#>