Functional Linear Model of the 24-Hour Activity Profile

Fits the averaged 24-hour activity profile with a periodic basis expansion (Fourier by default, B-spline alternative) by weighted least squares, giving a smooth functional form of the daily activity pattern. The single-component cosinor is the one-harmonic special case; adding harmonics fits the non-sinusoidal shape of a real rest-activity profile. This follows the functional form of Wang et al. (2011), as implemented for actigraphy by pyActigraphy.

Usage

circadian.flm(
  counts,
  timestamps,
  basis = c("fourier", "bspline"),
  n_harmonics = 4,
  nbasis = 9,
  spline_order = 4,
  period = 24,
  wear_time = NULL,
  min_valid_hours = 10,
  weights = c("n", "none"),
  n_eval = 1440
)

Arguments

counts: Numeric activity vector.
timestamps: POSIXct timestamps, one per value.
basis: Basis type: "fourier" (default) or "bspline".
n_harmonics: Number of Fourier harmonics (default 4, giving a 9-term expansion as in Wang et al. (2011)).
nbasis: Number of B-spline basis functions (default 9).
spline_order: B-spline order (default 4, cubic).
period: Profile period in hours (default 24).
wear_time: Optional logical wear-time mask.
min_valid_hours: Minimum valid hours per day (default 10).
weights: Profile weighting: "n" (square root of the per-hour observation count, default, matching cosinor.analysis) or "none" (plain least squares, matching pyActigraphy).
n_eval: Length of the dense within-day evaluation grid (default 1440).

Value

An object of class actiRhythm_flm: the fitted coefficients, the smooth daily curve (smooth_curve), the fitted profile, per-harmonic amplitudes and acrophases (harmonics, Fourier only), the peak and trough, and the fit statistics (r_squared, aic, f_statistic, p_value). The function never errors; on insufficient data it returns the same structure with r_squared NA.

References

Wang J, Xian H, Licis A, Deych E, Ding J, McLeland J, Toedebusch C, Li T, Duntley S, Shannon W (2011). “Measuring the impact of apnea and obesity on circadian activity patterns using functional linear modeling of actigraphy data.” Journal of Circadian Rhythms, 9, 11. doi:10.1186/1740-3391-9-11 .

Ramsay JO, Silverman BW (2005). Functional Data Analysis, 2nd edition. Springer. doi:10.1007/b98888 .

Hammad G, Reyt M, Beliy N, Baillet M, Deantoni M, Lesoinne A, Muto V, Schmidt C (2021). “pyActigraphy: open-source python package for actigraphy data visualization and analysis.” PLOS Computational Biology, 17(10), e1009514. doi:10.1371/journal.pcbi.1009514 .

Examples

ts <- seq(as.POSIXct("2024-01-01", tz = "UTC"), by = 60, length.out = 4 * 1440)
h  <- as.numeric(format(ts, "%H")) + as.numeric(format(ts, "%M")) / 60
counts <- 100 + 60 * cos(2 * pi * (h - 14) / 24) + 25 * cos(2 * pi * (h - 6) / 12)
circadian.flm(counts, ts)
#> Functional Linear Model (24-hour activity profile)
#> 
#>   Basis:        fourier (order 4, 9 terms)
#>   Period:       24 hours
#>   Days / profile points: 4 / 24
#> 
#>   Model fit:
#>     R-squared:   1.0000
#>     AIC:         -1371.37
#>     F-statistic: 13059180580519173999266600266066.00 (p = <2e-16)
#> 
#>   Dominant harmonic: H1, amplitude 59.83, acrophase 14.01 h
#> 
#>   Peak 165.0 at 16.5 h; trough 20.5 at 0.8 h
#> 
#>   Basis fit follows Wang et al. (2011); F/p are ordinary regression
#>   statistics (not Wang's between-subject permutation test).
#>