Create smooth demogdata functions

Smooth demogdata data using one of four methods depending on the value of method

Usage

smooth.demogdata(
  data,
  method = switch(data$type, mortality = "mspline", fertility = "cspline", migration =
    "loess"),
  age.grid,
  power = switch(data$type, mortality = 0.4, fertility = 1, migration = 1),
  b = 65,
  k = 30,
  span = 0.2,
  lambda = 1e-10,
  interpolate = FALSE,
  weight = data$type != "migration",
  obs.var = "empirical"
)

Arguments

data

Demogdata object such as created using read.demogdata.

method

Method of smoothing. Possibilities: "mspline" (monotonic regression splines), "cspline" (concave regression splines), "spline" (unconstrained regression splines), "loess" (local quadratic using loess).

age.grid

Ages to use for smoothed curves. Default is single years over a slightly greater range than the unsmoothed data.

power

Power transformation for age variable before smoothing. Default is 0.4 for mortality data and 1 (no transformation) for fertility or migration data.

b

Lower age for monotonicity if method=="mspline". Above this, the smooth curve is assumed to be monotonically increasing.

k

Number of knots to use for penalized regression spline estimate. Ignored if method=="loess".

span

Span for loess smooth if method=="loess".

lambda

Penalty for constrained regression spline if method=="cspline".

interpolate

If interpolate==TRUE, a linear interpolation is used instead of smoothing.

weight

If TRUE, uses weighted smoothing.

obs.var

Method for computing observational variance. Possible values: “empirical” or “theoretical”.

Value

Demogdata object identical to data except all rate matrices are replaced with smooth versions and pop matrices are replaced with disaggregated population estimates obtained using monotonic spline interpolation applied to the cumulative population data. Weight matrices are also added to the object showing the inverse variances of the estimated smooth curves.

Details

The value of method determines the type of smoothing used.

method="mspline"

Weighted penalized regression splines with a monotonicity constraint. The curves are monotonically increasing for age greater than b. Smoothness controlled by k. Methodology based on Wood (1994). Code calls gam for the basic computations.

method="cspline"

Weighted regression B-splines with a concavity constraint. Smoothness controlled by lambda. Methodology based on He and Ng (1999). Code calls cobs for the basic computations.

method="spline"

Unconstrained weighted penalized regression splines. Equivalent to "mspline" but with b=Inf.

method="loess"

Weighted locally quadratic regression. Smoothness controlled by span. Code calls loess for the basic computations.

Author

Rob J Hyndman

Examples

france.sm <- smooth.demogdata(extract.years(fr.mort, 1980:1997))
plot(france.sm)

plot(fr.mort, years = 1980, type = "p", pch = 1)
lines(france.sm, years = 1980, col = 2)