smooth_vital function

Functions to smooth demographic data

These smoothing functions allow smoothing of a variable in a vital object. The vital object is returned along with some additional columns containing information about the smoothed variable: usually .smooth containing the smoothed values, and .smooth_se containing the corresponding standard errors.

smooth_spline(.data, .var, age_spacing = 1, k = -1)

smooth_mortality(.data, .var, age_spacing = 1, b = 65, power = 0.4, k = 30)

smooth_fertility(.data, .var, age_spacing = 1, lambda = 1e-10)

smooth_loess(.data, .var, age_spacing = 1, span = 0.2)

Arguments

• .data: A vital object
• .var: name of variable to smooth
• age_spacing: Spacing between ages for smoothed vital. Default is 1.
• k: Number of knots to use for penalized regression spline estimate.
• b: Lower age for monotonicity. Above this, the smooth curve is assumed to be monotonically increasing.
• power: Power transformation for age variable before smoothing. Default is 0.4 (for mortality data).
• lambda: Penalty for constrained regression spline.
• span: Span for loess smooth.

Returns

vital with added columns containing smoothed values and their standard errors

Details

smooth_mortality() use penalized regression splines applied to log mortality with a monotonicity constraint above age b. The methodology is based on Wood (1994). smooth_fertility() uses weighted regression B-splines with a concavity constraint, based on He and Ng (1999). The function smooth_loess() uses locally quadratic regression, while smooth_spline() uses penalized regression splines.

Examples

library(dplyr)
aus_mortality |>
        filter(State == "Victoria", Sex == "female", Year > 2000) |>
        smooth_mortality(Mortality)
aus_fertility |>
 filter(Year > 2000) |>
        smooth_fertility(Fertility)

References

Hyndman, R.J., and Ullah, S. (2007) Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis, 51, 4942-4956. https://robjhyndman.com/publications/funcfor/

Author(s)

Rob J Hyndman