demography (version 1.11)

fdm: 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 = 100, 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.
• 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.

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. http://robjhyndman.com/papers/funcfor

See Also

ftsm, forecast.fdm

Examples

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