smooth_spline {vital}

Functions to smooth demographic data

Description

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.

Usage

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.

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.

Value

vital with added columns containing smoothed values and their standard errors

Author(s)

Rob J Hyndman

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/

Examples

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