Package 'smoothAPC' reference manual

Package 'smoothAPC'

Title:	Smoothing of Two-Dimensional Demographic Data, Optionally Taking into Account Period and Cohort Effects
Description:	The implemented method uses for smoothing bivariate thin plate splines, bivariate lasso-type regularization, and allows for both period and cohort effects. Thus the mortality rates are modelled as the sum of four components: a smooth bivariate function of age and time, smooth one-dimensional cohort effects, smooth one-dimensional period effects and random errors.
Authors:	Alexander Dokumentov, Rob J Hyndman
Maintainer:	Alexander Dokumentov <[email protected]>
License:	GPL (>= 2)
Version:	0.3
Built:	2024-10-13 06:52:58 UTC
Source:	https://github.com/cran/smoothAPC

Title:

Smoothing of Two-Dimensional Demographic Data, Optionally Taking into Account Period and Cohort Effects

Description:

The implemented method uses for smoothing bivariate thin plate splines, bivariate lasso-type regularization, and allows for both period and cohort effects. Thus the mortality rates are modelled as the sum of four components: a smooth bivariate function of age and time, smooth one-dimensional cohort effects, smooth one-dimensional period effects and random errors.

Authors:

Alexander Dokumentov, Rob J Hyndman

Maintainer:

Alexander Dokumentov <[email protected]>

License:

GPL (>= 2)

Version:

0.3

Built:

2024-10-13 06:52:58 UTC

Source:

https://github.com/cran/smoothAPC

Help Index

Smooths demographic data using automatically estimated parameters and optionally taking into account period and cohort effects

Description

If period and cohort effects are taken into account (effects = TRUE) the method uses all available years and diagonals for estimation of the period and cohort effects.

Usage

autoSmoothAPC(data, effects = TRUE, cornerLength = 7,
  affdDiagonals = NULL, affdYears = NULL, lower = head(c(0.01, 0.01, 0.01,
  2, 0.001, 2, 0.001), 3 + effects * 4), upper = head(c(1.2, 1.8, 1.2, 12,
  0.4, 12, 0.4), 3 + effects * 4), init = head(c(0.1, 0.1, 0.2, 4, 0.001, 4,
  0.001), 3 + effects * 4), reltol = 0.001, parameters = NULL, trace = F,
  control = list(nnzlmax = 1e+06, nsubmax = 2e+06, tmpmax = 2e+05),
  weights = NULL)
autoSmoothAPC(data, effects = TRUE, cornerLength = 7,
  affdDiagonals = NULL, affdYears = NULL, lower = head(c(0.01, 0.01, 0.01,
  2, 0.001, 2, 0.001), 3 + effects * 4), upper = head(c(1.2, 1.8, 1.2, 12,
  0.4, 12, 0.4), 3 + effects * 4), init = head(c(0.1, 0.1, 0.2, 4, 0.001, 4,
  0.001), 3 + effects * 4), reltol = 0.001, parameters = NULL, trace = F,
  control = list(nnzlmax = 1e+06, nsubmax = 2e+06, tmpmax = 2e+05),
  weights = NULL)

Arguments

`data`	Demographic data (log mortality) presented as a matrix. Row numbers represent ages and column numbers represet time.
`effects`	Controls if the cohort and period effects are taken into account.
`cornerLength`	Sets the smallest length of a diagonal to be considered for cohort effects.
`affdDiagonals`	Diagonals to be used for cohort effects. The first diagonal is at the bottom left corner of the data matrix (maximal age and minimal time in the data matrix).
`affdYears`	Years to be used for period effects.
`lower`	Lowest possible values for the optimization procedure.
`upper`	Highest possible values for the optimization procedure.
`init`	Initial values for the optimization procedure.
`reltol`	Relative tolerance parameter to be supplied to `optim` function.
`parameters`	Optional model parameters. If not provided, they are estimated.
`trace`	Controls if tracing is on.
`control`	The control data passed directly to `rq.fit.sfn` function.
`weights`	Define how much every observation effect the resulting smooth surface. The parameter must have same dimentions as `data` parameter. Weights can be set to reciprocal of estimated standard deviation of the data.

Value

A list of four components: smooth surface, period effects, cohort effects and parameters used for smoothing (passed as a parameter or estimated).

Author(s)

Alexander Dokumentov

References

http://robjhyndman.com/publications/mortality-smoothing/

Examples



library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
plot(m)
sm <- autoSmoothAPC(m)
plot(sm)
plot(sm, "period")
plot(sm, "cohort")


library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
plot(m)
sm <- autoSmoothAPC(m)
plot(sm)
plot(sm, "period")
plot(sm, "cohort")

Presents matrix as a heatmap

Description

Presents matrix as a heatmap

Usage

## S3 method for class 'matrix'
plot(x, labs = c("X", "Y"), color.palette = c("default",
  "special"), main = "", ...)
## S3 method for class 'matrix'
plot(x, labs = c("X", "Y"), color.palette = c("default",
  "special"), main = "", ...)

Arguments

`x`	Matrix to plot.
`labs`	Vector of labels for X and Y axes.
`color.palette`	Character string `"default"` or `"special"` or a function accepting one argument and returning a color palette (for example `rainbow`).
`main`	Title for the plot.
`...`	Other parameters. They are currently ignored.

Author(s)

Alexander Dokumentov

Examples



plot(matrix(rnorm(100),10,10), main = "Noise")
plot(matrix(1:100,10,10), c("Dimension 1", "Dimension 2"), main = "Value")

library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
plot(m)
plot(m, color.palette = "special")
plot(m, color.palette = rainbow)

plot(matrix(rnorm(100),10,10), main = "Noise")
plot(matrix(1:100,10,10), c("Dimension 1", "Dimension 2"), main = "Value")

library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
plot(m)
plot(m, color.palette = "special")
plot(m, color.palette = rainbow)

Presents demographic data as a heatmap

Description

Presents demographic data as a heatmap

Usage

## S3 method for class 'smAPC'
plot(x, component = c("all", "surface", "period", "cohort",
  "residuals", "original"), labs = c("Age", "Time"),
  color.palette = c("default", "special"), main = "", ...)
## S3 method for class 'smAPC'
plot(x, component = c("all", "surface", "period", "cohort",
  "residuals", "original"), labs = c("Age", "Time"),
  color.palette = c("default", "special"), main = "", ...)

Arguments

`x`	Result of smoothing (object of class `smAPC`).
`component`	"smooth", "period", "cohort", "residuals" or "original".
`labs`	Vector of labels for X and Y axes.
`color.palette`	Character string `"default"` or `"special"` or a function accepting one argument and returning a color palette (for example `rainbow`).
`main`	Title for the plot.
`...`	Other parameters. They are currently ignored.

Author(s)

Alexander Dokumentov

Examples



library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
sm <- autoSmoothAPC(m)

plot(sm)
plot(sm, "surface")
plot(sm, "cohort")
plot(sm, "period")
plot(sm, "residuals")
plot(sm, "original", main = "Original data")


library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
sm <- autoSmoothAPC(m)

plot(sm)
plot(sm, "surface")
plot(sm, "cohort")
plot(sm, "period")
plot(sm, "residuals")
plot(sm, "original", main = "Original data")

Presents data as a 3D surface

Description

Presents data as a 3D surface

Usage

plot3d(x, ...)
plot3d(x, ...)

Arguments

`x`	Data to plot.
`...`	Other parameters.

Presents matrix as a 3D surface

Description

Presents matrix as a 3D surface

Usage

## S3 method for class 'matrix'
plot3d(x, labs = c("X", "Y", "Z"),
  color.palette = c("default", "special"), ...)
## S3 method for class 'matrix'
plot3d(x, labs = c("X", "Y", "Z"),
  color.palette = c("default", "special"), ...)

Arguments

`x`	Matrix to plot.
`labs`	Vector of labels for X, Y and Z axes.
`color.palette`	Character string `"default"` or `"special"` or a function accepting one argument and returning a color palette (for example `rainbow`).
`...`	Other parameters. They are currently ignored.

Author(s)

Alexander Dokumentov

Examples



plot3d(matrix(rnorm(100),10,10))
plot3d(matrix(1:100,10,10), c("Dimension 1", "Dimension 2", "Value"))

library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
plot3d(m)
plot3d(m, color.palette = "special")
plot3d(m, color.palette = rainbow)

plot3d(matrix(rnorm(100),10,10))
plot3d(matrix(1:100,10,10), c("Dimension 1", "Dimension 2", "Value"))

library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
plot3d(m)
plot3d(m, color.palette = "special")
plot3d(m, color.palette = rainbow)

Presents demographic data as a 3D surface

Description

Presents demographic data as a 3D surface

Usage

## S3 method for class 'smAPC'
plot3d(x, component = c("all", "surface", "period", "cohort",
  "residuals", "original"), labs = c("Age", "Time", NA),
  color.palette = c("default", "special"), ...)
## S3 method for class 'smAPC'
plot3d(x, component = c("all", "surface", "period", "cohort",
  "residuals", "original"), labs = c("Age", "Time", NA),
  color.palette = c("default", "special"), ...)

Arguments

`x`	Result of smoothing (object of class `smAPC`).
`component`	"smooth", "period", "cohort", "residuals" or "original".
`labs`	Vector of labels for X, Y and Z axes.
`color.palette`	Character string `"default"` or `"special"` or a function accepting one argument and returning a color palette (for example `rainbow`).
`...`	Other parameters. They are currently ignored.

Author(s)

Alexander Dokumentov

Examples



library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
sm <- autoSmoothAPC(m)

plot3d(sm)
plot3d(sm, "surface", color.palette = "special")
plot3d(sm, "cohort")
plot3d(sm, "period")
plot3d(sm, "residuals")
plot3d(sm, "original", color.palette = rainbow)


library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
sm <- autoSmoothAPC(m)

plot3d(sm)
plot3d(sm, "surface", color.palette = "special")
plot3d(sm, "cohort")
plot3d(sm, "period")
plot3d(sm, "residuals")
plot3d(sm, "original", color.palette = rainbow)

Smooths demographic data using automatically estimated parameters and taking into account only significant period and cohort effects

Description

It is a heuristic procedure which tries to figure out positions of period and cohort effects in the data. It also uses a few steps to estimate model's parameters. The procedure is supposed to outperform autoSmoothAPC slightly.

Usage

signifAutoSmoothAPC(data, p.value = 0.05, cornerLength = 7,
  lower = c(0.01, 0.01, 0.01, 1, 0.001, 1, 0.001), upper = c(1.2, 1.8, 1.2,
  12, 0.4, 12, 0.4), init = c(0.1, 0.1, 0.2, 4, 0.001, 4, 0.001),
  reltol = 0.001, trace = F, control = list(nnzlmax = 1e+06, nsubmax =
  2e+06, tmpmax = 2e+05), weights = NULL)
signifAutoSmoothAPC(data, p.value = 0.05, cornerLength = 7,
  lower = c(0.01, 0.01, 0.01, 1, 0.001, 1, 0.001), upper = c(1.2, 1.8, 1.2,
  12, 0.4, 12, 0.4), init = c(0.1, 0.1, 0.2, 4, 0.001, 4, 0.001),
  reltol = 0.001, trace = F, control = list(nnzlmax = 1e+06, nsubmax =
  2e+06, tmpmax = 2e+05), weights = NULL)

Arguments

`data`	Demographic data (log mortality) presented as a matrix. Row numbers represent ages and column numbers represet time.
`p.value`	P-value used to test the period and the cohort effects for significance. The lower the value the fewer diagonals and years will be used to find cohort and period effects.
`cornerLength`	Minimal length of a diagonal to be considered for cohort effects.
`lower`	Lowest possible values for the optimization procedure.
`upper`	Highest possible values for the optimization procedure.
`init`	Initial values for the optimization procedure.
`reltol`	Relative tolerance parameter to be supplied to `optim` function.
`trace`	Controls if tracing is on.
`control`	The control data passed directly to `rq.fit.sfn` function.
`weights`	Define how much every observation effect the resulting smooth surface. The parameter must have same dimentions as `data` parameter. Weights can be set to reciprocal of estimated standard deviation of the data.

Value

A list of six components: smooth surface, period effects, cohort effects, parameters used for smoothing, diagonals used for cohort effects and years used for period effects.

Author(s)

Alexander Dokumentov

References

http://robjhyndman.com/publications/mortality-smoothing/

Examples



library(demography)
m <- log(fr.mort$rate$female[1:30, 120:139])
plot(m)
sm <- signifAutoSmoothAPC(m)
plot(sm)
plot(sm, "surface")
plot(sm, "period")
plot(sm, "cohort")


library(demography)
m <- log(fr.mort$rate$female[1:30, 120:139])
plot(m)
sm <- signifAutoSmoothAPC(m)
plot(sm)
plot(sm, "surface")
plot(sm, "period")
plot(sm, "cohort")

Smooths demographic data optionally taking into account period and cohort effects

Description

Smooths demographic data optionally taking into account period and cohort effects

Usage

smoothAPC(data, lambda = 1, lambdaaa = 1, lambdayy = 1, lambdaay = 1,
  lambdaYearsEffect = 5, thetaYearsEffect = 0.1 * lambda,
  lambdaCohortEffect = 5, thetaCohortEffect = 0.1 * lambda,
  cornerLength = 7, effects = TRUE, affdDiagonals = NULL,
  affdYears = NULL, control = list(nnzlmax = 1e+06, nsubmax = 2e+06, tmpmax
  = 2e+05), weights = NULL)
smoothAPC(data, lambda = 1, lambdaaa = 1, lambdayy = 1, lambdaay = 1,
  lambdaYearsEffect = 5, thetaYearsEffect = 0.1 * lambda,
  lambdaCohortEffect = 5, thetaCohortEffect = 0.1 * lambda,
  cornerLength = 7, effects = TRUE, affdDiagonals = NULL,
  affdYears = NULL, control = list(nnzlmax = 1e+06, nsubmax = 2e+06, tmpmax
  = 2e+05), weights = NULL)

Arguments

`data`	Demographic data (log mortality) presented as a matrix. Row numbers represent ages and column numbers represet time.
`lambda`	Controls "general flexibility" of the smooth surface.
`lambdaaa`	Controls "flexibility" of the smooth surface in age direction (first dimension).
`lambdayy`	Controls "flexibility" of the smooth surface in years direction (second dimension).
`lambdaay`	Controls "flexibility" of the smooth surface in age and years directions.
`lambdaYearsEffect`	Controls "flexibility" of the period effects.
`thetaYearsEffect`	Reduces the likelihood of period effects.
`lambdaCohortEffect`	Controls "flexibility" of the cohort effects.
`thetaCohortEffect`	Reduces the likelihood of cohort effects.
`cornerLength`	Sets the smallest length of a diagonal to be considered for cohort effects.
`effects`	Controls if the cohort and period effects are taken into account.
`affdDiagonals`	Diagonals to be used for cohort effects.
`affdYears`	Years to be used for period effects.
`control`	Control data passed directly to `rq.fit.sfn` function..
`weights`	Define how much every observation effect the resulting smooth surface. The parameter must have same dimentions as `data` parameter. Weights can be set to reciprocal of estimated standard deviation of the data.

Value

List of three components: smooth surface, period effects, cohort effects.

Author(s)

Alexander Dokumentov

References

http://robjhyndman.com/publications/mortality-smoothing/

Examples



library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
sm <- smoothAPC(m, lambdaaa = 0.2, lambdayy = 0.1, lambdaay = 0.4, effects = FALSE)
plot(sm, "original")
plot(sm)


library(demography)
m <- log(fr.mort$rate$female[1:30, 150:160])
sm <- smoothAPC(m, lambdaaa = 0.2, lambdayy = 0.1, lambdaay = 0.4, effects = FALSE)
plot(sm, "original")
plot(sm)

Package 'smoothAPC'

Help Index

Smooths demographic data using automatically estimated parameters and optionally taking into account period and cohort effects

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Presents matrix as a heatmap

Description

Usage

Arguments

Author(s)

Examples

Presents demographic data as a heatmap

Description

Usage

Arguments

Author(s)

Examples

Presents data as a 3D surface

Description

Usage

Arguments

Presents matrix as a 3D surface

Description

Usage

Arguments

Author(s)

Examples

Presents demographic data as a 3D surface

Description

Usage

Arguments

Author(s)

Examples

Smooths demographic data using automatically estimated parameters and taking into account only significant period and cohort effects

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Smooths demographic data optionally taking into account period and cohort effects

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples