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demography (version 1.18)

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

“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

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

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