fdm: Functional demographic model

In demography: Forecasting Mortality, Fertility, Migration and Population Data

Functional demographic model

Description

Fits a basis function model to demographic data. The function uses optimal orthonormal basis functions obtained from a principal components decomposition.

Usage

fdm(
  data,
  series = names(data$rate)[1],
  order = 6,
  ages = data$age,
  max.age = max(ages),
  method = c("classical", "M", "rapca"),
  lambda = 3,
  mean = TRUE,
  level = FALSE,
  transform = TRUE,
  ...
)

Arguments

data	demogdata object. Output from read.demogdata.
series	name of series within data holding rates (1x1).
order	Number of basis functions to fit.
ages	Ages to include in fit.
max.age	Maximum age to fit. Ages beyond this are collapsed into the upper age group.
method	Method to use for principal components decomposition. Possibilities are “M”, “rapca” and “classical”. See ftsm for details.
lambda	Tuning parameter for robustness when method="M".
mean	If TRUE, will estimate mean term in the model before computing basis terms. If FALSE, the mean term is assumed to be zero.
level	If TRUE, will include an additional (intercept) term that depends on the year but not on ages.
transform	If TRUE, the data are transformed with a Box-Cox transformation before the model is fitted.
...	Extra arguments passed to ftsm.

Value

Object of class “fdm” with the following components:

label	Name of country
age	Ages from data object.
year	Years from data object.
<series>	Matrix of demographic data as contained in data. It takes the name given by the series argument.
fitted	Matrix of fitted values.
residuals	Residuals (difference between observed and fitted).
basis	Matrix of basis functions evaluated at each age level (one column for each basis function). The first column is the fitted mean.
coeffs	Matrix of coefficients (one column for each coefficient series). The first column are all ones.
mean.se	Standard errors for the estimated mean function.
varprop	Proportion of variation explained by each basis function.
weights	Weight associated with each time period.
v	Measure of variation for each time period.
type	Data type (mortality, fertility, etc.)
y	The data stored as a functional time series object.

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/

See Also

ftsm, forecast.fdm

Examples

france.fit <- fdm(fr.mort)
summary(france.fit)
plot(france.fit)
plot(residuals(france.fit))

demography documentation built on Feb. 16, 2023, 7:02 p.m.