| Version: | 2.0 |
| Title: | Forecasting Mortality, Fertility, Migration and Population Data |
| Description: | Functions for demographic analysis including lifetable calculations; Lee-Carter modelling; functional data analysis of mortality rates, fertility rates, net migration numbers; and stochastic population forecasting. |
| Depends: | R (≥ 3.4), forecast (≥ 8.5) |
| Imports: | ftsa (≥ 4.8), rainbow, cobs, mgcv, strucchange, HMDHFDplus (≥ 2.0.0) |
| LazyData: | yes |
| ByteCompile: | TRUE |
| URL: | https://pkg.robjhyndman.com/demography/, https://github.com/robjhyndman/demography |
| BugReports: | https://github.com/robjhyndman/demography/issues |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2023-02-07 23:25:43 UTC; hyndman |
| Author: | Rob Hyndman  [aut,
cre, cph],
Heather Booth
[ctb],
Leonie Tickle
[ctb],
John Maindonald [ctb],
Simon Wood [ctb],
R Core Team [ctb] |
| Maintainer: | Rob Hyndman <Rob.Hyndman@monash.edu> |
| Repository: | CRAN |
| Date/Publication: | 2023-02-08 08:20:02 UTC |
Forecasting mortality and fertility data
Description
Functions for demographic analysis including lifetable calculations, Lee-Carter modelling and functional data analysis of mortality rates.
Author(s)
Rob J Hyndman with contributions from Heather Booth, Leonie Tickle, John Maindonald, Simon Wood and the R Core Team.
Maintainer: <Rob.Hyndman@monash.edu>
Coerce a demogdata object to a data.frame object
Description
Coerce a demogdata object to a data.frame object
Usage
## S3 method for class 'demogdata'
as.data.frame(x, ...)
Arguments
x |
Object to be coerced to a data frame. |
... |
Other arguments not used |
Value
A data.frame object.
Examples
# coerce demogdata object to data.frame ----
as.data.frame(fr.mort)
Australian fertility data
Description
Age-specific fertility rates and female child-bearing population for Australia.
Format
Object of class demogdata containing the following components:
- year
Vector of years
- age
Vector of ages
- rate
List containing one matrix with one age group per row and one column per year.
- pop
Population data in same form as
rate.- type
Type of object. In this case, “fertility”.
- label
Character string giving area from which data are taken. In this case, “Australia”.
Details
Australian fertility rates and populations (1921-2002) for age groups (<20, 20-24, 25-29, 30-34, 35-39, 40-44, 45+). Data taken from v3.2b of the Australian Demographic Data Bank released 10 February 2005.
Author(s)
Rob J Hyndman
Source
The Australian Demographic Data Bank (courtesy of Len Smith).
Examples
plot(aus.fert)
Monotonic interpolating splines
Description
Perform cubic spline monotonic interpolation of given data points, returning either a list of points obtained by the interpolation or a function performing the interpolation. The splines are constrained to be monotonically increasing (i.e., the slope is never negative).
Usage
cm.spline(x, y = NULL, n = 3 * length(x), xmin = min(x), xmax = max(x), ...)
cm.splinefun(x, y = NULL, ...)
Arguments
x, y |
vectors giving the coordinates of the points to be interpolated. Alternatively a single plotting structure can be specified: see |
n |
interpolation takes place at n equally spaced points spanning the interval [ |
xmin |
left-hand endpoint of the interpolation interval. |
xmax |
right-hand endpoint of the interpolation interval. |
... |
Other arguments are ignored. |
Details
These are simply wrappers to the splinefun function family from the stats package.
Value
cm.spline |
returns a list containing components |
cm.splinefun |
returns a function which will perform cubic spline interpolation of the given data points. This is often more useful than |
Author(s)
Rob J Hyndman
References
Forsythe, G. E., Malcolm, M. A. and Moler, C. B. (1977) Computer Methods for Mathematical Computations. Hyman (1983) SIAM J. Sci. Stat. Comput. 4(4):645-654. Dougherty, Edelman and Hyman 1989 Mathematics of Computation, 52: 471-494.
Examples
x <- seq(0,4,l=20)
y <- sort(rnorm(20))
plot(x,y)
lines(spline(x, y, n = 201), col = 2) # Not necessarily monotonic
lines(cm.spline(x, y, n = 201), col = 3) # Monotonic
Coherent functional demographic model for grouped data
Description
Fits a coherent functional model to demographic data as described in Hyndman,
Booth & Yasmeen (2012). If two of the series in data are named
male and female, then it will use these two groups. Otherwise
it will use all available groups.
Usage
coherentfdm(data, order1 = 6, order2 = 6, ...)
Arguments
data |
demogdata object containing at least two groups. |
order1 |
Number of basis functions to fit to the model for the geometric mean. |
order2 |
Number of basis functions to fit to the models for each ratio. |
... |
Extra arguments passed to |
Value
A list (of class fdmpr) consisting of two objects:
product (an fdm object containing a del for the
geometric mean of the data) and ratio (a list of fdm
objects, being the models for the ratio of each series with the geometric
mean).
Author(s)
Rob J Hyndman
References
Hyndman, R.J., Booth, H., and Yasmeen, F. (2012) Coherent mortality forecasting: the product-ratio method with functional time series models. Demography, to appear. https://robjhyndman.com/publications/coherentfdm/
See Also
Examples
fr.short <- extract.years(fr.sm,1950:2006)
fr.fit <- coherentfdm(fr.short)
summary(fr.fit)
plot(fr.fit$product, components=3)
Combine two demogdata objects into one demogdata object
Description
Function to combine demogdata objects containing different years but the same age structure into one demogdata object. The standard use for this function will be combining historical data with forecasts. The objects must be of the same type.
Usage
combine.demogdata(obj1, obj2)
Arguments
obj1 |
First demogdata object (e.g., historical data). |
obj2 |
Second demogdata object (e.g., forecasts). |
Value
Object of class “demogdata” with the following components:
year |
Vector of years |
age |
Vector of ages |
rate |
Matrix of rates with with one age group per row and one column per year. |
pop |
Matrix of populations in same form as |
type |
Type of object: “mortality”, “fertility” or “migration”. |
label |
Name of area from which the data are taken. |
Author(s)
Rob J Hyndman
See Also
Examples
fit <- fdm(fr.mort)
fcast <- forecast(fit, h=50)
france2 <- combine.demogdata(fr.mort,fcast)
plot(france2)
plot(life.expectancy(france2))
lines(rep(max(fr.mort$year)+0.5,2),c(0,100),lty=3)
Evaluation of demographic forecast accuracy
Description
Computes mean forecast errors and mean square forecast errors for each age level. Computes integrated squared forecast errors and integrated absolute percentage forecast errors for each year.
Usage
compare.demogdata(
data,
forecast,
series = names(forecast$rate)[1],
ages = data$age,
max.age = min(max(data$age), max(forecast$age)),
years = data$year,
interpolate = FALSE
)
Arguments
data |
Demogdata object such as created using
|
forecast |
Demogdata object such as created using
|
series |
Name of series to use. Default: the first matrix within
|
ages |
Ages to use for comparison. Default: all available ages. |
max.age |
Upper age to use for comparison. |
years |
Years to use in comparison. Default is to use all available years that are common between data and forecast. |
interpolate |
If TRUE, all zeros in data are replaced by interpolated estimates when computing the error measures on the log scale. Error measures on the original (rate) scale are unchanged. |
Value
Object of class "errorfdm" with the following components:
label |
Name of region from which data taken. |
age |
Ages from |
year |
Years from |
<error> |
Matrix of forecast errors on rates. |
<logerror> |
Matrix of forecast errors on log rates. |
mean.error |
Various measures of forecast accuracy averaged across years. Specifically ME=mean error, MSE=mean squared error, MPE=mean percentage error and MAPE=mean absolute percentage error. |
int.error |
Various measures of forecast accuracy integrated across ages. Specifically IE=integrated error, ISE=integrated squared error, IPE=integrated percentage error and IAPE=integrated absolute percentage error. |
life.expectancy |
If |
Note that the error matrices have different names indicating if the series forecast was male, female or total.
Author(s)
Rob J Hyndman
See Also
Examples
fr.test <- extract.years(fr.sm,years=1921:1980)
fr.fit <- fdm(fr.test,order=2)
fr.error <- compare.demogdata(fr.mort, forecast(fr.fit,20))
plot(fr.error)
par(mfrow=c(2,1))
plot(fr.error$age,fr.error$mean.error[,"ME"],
type="l",xlab="Age",ylab="Mean Forecast Error")
plot(fr.error$int.error[,"ISE"],
xlab="Year",ylab="Integrated Square Error")
Create demogdata object from raw data matrices
Description
Create demogdata object suitable for plotting using plot.demogdata and
fitting an LC or BMS model using lca or an FDA model using fdm.
Usage
demogdata(data, pop, ages, years, type, label, name, lambda)
Arguments
data |
Matrix of data: either mortality rates or fertility rates |
pop |
Matrix of population values of same dimension as data. These are population numbers as at 30 June of each year (i.e., the "exposures"). So, for example, the number of deaths is data*pop if data contains mortality rates. |
ages |
Vector of ages corresponding to rows of |
years |
Vector of years corresponding to columns of |
type |
Character string showing type of demographic series: either “mortality”, “fertility” or “migration”. |
label |
Character string of the name of area from which the data are taken. |
name |
Name of series: usually male, female or total. |
lambda |
Box-Cox transformation parameter. |
Value
Object of class “demogdata” with the following components:
year |
Vector of years |
age |
Vector of ages |
rate |
A list containing one or more rate matrices with one age group per row and one column per year. |
pop |
A list of the same form as |
type |
Type of object: “mortality”, “fertility” or “migration”. |
label |
label |
lambda |
lambda |
Author(s)
Rob J Hyndman
See Also
Extract some ages from a demogdata object
Description
Creates subset of demogdata object.
Usage
extract.ages(data, ages, combine.upper = TRUE)
Arguments
data |
Demogdata object such as created using |
ages |
Vector of ages to extract from data. |
combine.upper |
If TRUE, ages beyond the maximum of |
Value
Demogdata object with same components as data but with a subset of ages.
Author(s)
Rob J Hyndman
Examples
france.teens <- extract.ages(fr.mort,13:19,FALSE)
plot(france.teens)
Extract some years from a demogdata object
Description
Creates subset of demogdata object.
Usage
extract.years(data, years)
Arguments
data |
Demogdata object such as created using |
years |
Vector of years to extract from data. |
Value
Demogdata object with same components as data but with a subset of years.
Author(s)
Rob J Hyndman
Examples
france.1918 <- extract.years(fr.mort,1918)
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
|
lambda |
Tuning parameter for robustness when |
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 |
Value
Object of class “fdm” with the following components:
label |
Name of country |
age |
Ages from |
year |
Years from |
<series> |
Matrix of
demographic data as contained in |
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
Examples
france.fit <- fdm(fr.mort)
summary(france.fit)
plot(france.fit)
plot(residuals(france.fit))
Forecast functional demographic model.
Description
The coefficients from the fitted object are forecast using a univariate time series model. The forecast coefficients are then multiplied by the basis functions to obtain a forecast demographic rate curve.
Usage
## S3 method for class 'fdm'
forecast(
object,
h = 50,
level = 80,
jumpchoice = c("fit", "actual"),
method = "arima",
warnings = FALSE,
...
)
Arguments
object |
Output from |
h |
Forecast horizon. |
level |
Confidence level for prediction intervals. |
jumpchoice |
If "actual", the forecasts are bias-adjusted by the difference between the fit and the last year of observed data. Otherwise, no adjustment is used. |
method |
Forecasting method to be used. |
warnings |
If TRUE, warnings arising from the forecast models for
coefficients will be shown. Most of these can be ignored, so the default is
|
... |
Other arguments as for |
Value
Object of class fmforecast with the following components:
label |
Name of region from which the data are taken. |
age |
Ages
from |
year |
Years from |
rate |
List of matrices containing forecasts, lower bound and upper bound of prediction intervals. Point forecast matrix takes the same name as the series that has been forecast. |
error |
Matrix of one-step errors for historical data |
fitted |
Matrix of one-step forecasts for historical data |
coeff |
List of objects of type |
coeff.error |
One-step errors for each of the coefficients. |
var |
List containing the various components of variance: model, error, mean, total and coeff. |
model |
Fitted model in |
type |
Type of data: “mortality”, “fertility” or “migration”. |
Author(s)
Rob J Hyndman
See Also
fdm, forecast.lca, forecast.ftsm.
Examples
france.fit <- fdm(fr.mort,order=2)
france.fcast <- forecast(france.fit,50)
plot(france.fcast)
models(france.fcast)
Forecast coherent functional demographic model.
Description
The product and ratio models from coherentfdm are forecast, and
the results combined to give forecasts for each group in the original data.
Usage
## S3 method for class 'fdmpr'
forecast(object, h = 50, level = 80, K = 100, drange = c(0, 0.5), ...)
Arguments
object |
Output from |
h |
Forecast horizon. |
level |
Confidence level for prediction intervals. |
K |
Maximum number of years to use in forecasting coefficients for ratio components. |
drange |
Range of fractional differencing parameter for the ratio coefficients. |
... |
Other arguments as for |
Value
Object of class fmforecast2 containing a list of objects each
of class fmforecast. The forecasts for each group in the original
data are given first. Then the forecasts from the product model, and
finally a list of forecasts from each of the ratio models.
Author(s)
Rob J Hyndman
See Also
Examples
fr.short <- extract.years(fr.sm,1950:2006)
fr.fit <- coherentfdm(fr.short)
fr.fcast <- forecast(fr.fit)
plot(fr.fcast$male)
plot(fr.fcast$ratio$male, plot.type='component', components=3)
models(fr.fcast)
Forecast demogdata data using Lee-Carter method.
Description
The kt coefficients are forecast using a random walk with drift. The forecast coefficients are then multiplied by bx to obtain a forecast demographic rate curve.
Usage
## S3 method for class 'lca'
forecast(
object,
h = 50,
se = c("innovdrift", "innovonly"),
jumpchoice = c("fit", "actual"),
level = 80,
...
)
Arguments
object |
Output from |
h |
Number of years ahead to forecast. |
se |
Method used for computation of standard error. Possibilities: “innovdrift” (innovations and drift) and “innovonly” (innovations only). |
jumpchoice |
Method used for computation of jumpchoice. Possibilities: “actual” (use actual rates from final year) and “fit” (use fitted rates). |
level |
Confidence level for prediction intervals. |
... |
Other arguments. |
Value
Object of class fmforecast with the following components:
label |
Region from which the data are taken. |
age |
Ages from |
year |
Years from |
rate |
List of matrices containing forecasts, lower bound and upper bound of prediction intervals. Point forecast matrix takes the same name as the series that has been forecast. |
fitted |
Matrix of one-step forecasts for historical data |
Other components included are
e0 |
Forecasts of life expectancies (including lower and upper bounds) |
kt.f |
Forecasts of coefficients from the model. |
type |
Data type. |
model |
Details about the fitted model |
Author(s)
Rob J Hyndman
See Also
Examples
france.lca <- lca(fr.mort, adjust="e0")
france.fcast <- forecast(france.lca, 50)
plot(france.fcast)
plot(france.fcast,'c')
French mortality data
Description
Age-specific mortality rates and population for France.
Format
Object of class demogdata containing the following components:
- year
Vector of years
- age
Vector of ages
- rate
List of matrices containing rates with with one age group per row and one column per year. Matrices:
total,female,male.- pop
Population data in same form as
rate.- type
Type of object. In this case, “mortality”.
- label
Character string giving area from which data are taken. In this case, “France”.
Details
fr.mort contains French mortality rates and populations (1899-2005) for ages 0-110. Data taken from the Human Mortality Database
on 20 February 2008. fr.sm contains a smoothed version of fr.mort obtained using the smooth.demogdata function.
Author(s)
Rob J Hyndman
Source
The Human Mortality Database (http://www.mortality.org).
Examples
plot(fr.mort,years=1950:1997)
plot(fr.mort,years=1990,type='p',pch=1)
lines(fr.sm,years=1990)
Read data from HMD and construct a mortality demogdata object
Description
hmd.mx reads "Mx" (1x1) data from the Human Mortality Database (HMD
https://www.mortality.org) and constructs a demogdata object suitable
for plotting using plot.demogdata and fitting an LC or BMS
model using lca or an FDA model using fdm.
hmd.pop reads "Population" (1x1) data from the HMD and constructs a
demogdata object suitable for plotting using plot.demogdata.
hmd.e0 reads life expectancy at birth from the HMD and returns the
result as a ts object.
Usage
hmd.mx(country, username, password, label = country)
hmd.e0(country, username, password)
hmd.pop(country, username, password, label = country)
Arguments
country |
Directory abbreviation from the HMD. For instance, Australia = "AUS". |
username |
HMD username (case-sensitive) |
password |
HMD password (case-sensitive) |
label |
Character string giving name of country from which the data are taken. |
Details
In order to read the data, users are required to create their account via the HMD website (https://www.mortality.org), and obtain a valid username and password.
Value
hmd.mx returns an object of class demogdata with the following components:
year |
Vector of years |
age |
Vector of ages |
rate |
A list containing one or more rate matrices with one age group per row and one column per year. |
pop |
A list of the same form as |
type |
Type of object: “mortality”, “fertility” or “migration”. |
label |
label |
hmd.pop returns a similar object but without the rate component.
hmd.e0 returns an object of class ts with columns male, female and total.
Author(s)
Rob J Hyndman
See Also
demogdata,read.demogdata,plot.demogdata, life.expectancy
Examples
## Not run:
norway <- hmd.mx("NOR", username, password, "Norway")
summary(norway)
## End(Not run)
Integrated Squared Forecast Error for models of various orders
Description
Computes ISFE values for functional time series models of various orders.
Usage
isfe(...)
## S3 method for class 'demogdata'
isfe(
data,
series = names(data$rate)[1],
max.order = N - 3,
N = 10,
h = 5:10,
ages = data$age,
max.age = max(ages),
method = c("classical", "M", "rapca"),
fmethod = c("arima", "ar", "arfima", "ets", "ets.na", "struct", "rwdrift", "rw"),
lambda = 3,
...
)
Arguments
... |
Additional arguments control the fitting procedure. |
data |
demogdata object. |
series |
name of series within data holding rates (1x1) |
max.order |
Maximum number of basis functions to fit. |
N |
Minimum number of functional observations to be used in fitting a model. |
h |
Forecast horizons over which to average. |
ages |
Ages to include in fit. |
max.age |
Maximum age to fit. |
method |
Method to use for principal components decomposition. Possibilities are “M”, “rapca” and “classical”. |
fmethod |
Method used for forecasting. Current possibilities are “ets”, “arima”, “ets.na”, “struct”, “rwdrift” and “rw”. |
lambda |
Tuning parameter for robustness when |
Value
Numeric matrix with (max.order+1) rows and length(h) columns
containing ISFE values for models of orders 0:max.order.
Author(s)
Rob J Hyndman
References
Hyndman, R.J., and Ullah, S. (2007) Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis, 51, 4942-4956. https://robjhyndman.com/publications/funcfor/
See Also
Model mortality or fertility data using Lee-Carter approach
Description
Lee-Carter model of mortality or fertility rates. lca produces a
standard Lee-Carter model by default, although many other options are
available. bms is a wrapper for lca and returns a model based
on the Booth-Maindonald-Smith methodology.
Usage
lca(
data,
series = names(data$rate)[1],
years = data$year,
ages = data$age,
max.age = 100,
adjust = c("dt", "dxt", "e0", "none"),
chooseperiod = FALSE,
minperiod = 20,
breakmethod = c("bai", "bms"),
scale = FALSE,
restype = c("logrates", "rates", "deaths"),
interpolate = FALSE
)
bms(
data,
series = names(data$rate)[1],
years = data$year,
ages = data$age,
max.age = 100,
minperiod = 20,
breakmethod = c("bms", "bai"),
scale = FALSE,
restype = c("logrates", "rates", "deaths"),
interpolate = FALSE
)
Arguments
data |
demogdata object of type “mortality” or “fertility”. Output from read.demogdata. |
series |
name of series within data containing mortality or fertility values (1x1) |
years |
years to include in fit. Default: all available years. |
ages |
ages to include in fit. Default: all available ages up to
|
max.age |
upper age to include in fit. Ages beyond this are collapsed into the upper age group. |
adjust |
method to use for adjustment of coefficients |
chooseperiod |
If TRUE, it will choose the best fitting period. |
minperiod |
Minimum number of years to include in fitting period if chooseperiod=TRUE. |
breakmethod |
method to use for identifying breakpoints if
chooseperiod=TRUE. Possibilities are “bai” (Bai's method computed
using |
scale |
If TRUE, it will rescale bx and kt so that kt has drift parameter = 1. |
restype |
method to use for calculating residuals. Possibilities are “logrates”, “rates” and “deaths”. |
interpolate |
If TRUE, it will estimate any zero mortality or fertility rates using the same age group from nearby years. |
Details
All mortality or fertility data are assumed to be in matrices of
mortality or fertility rates within data$rate. Each row is one age group
(assumed to be single years). Each column is one year. The
function produces a model for the series mortality or fertility rate matrix
within data$rate. Forecasts from this model can be obtained using forecast.lca.
Value
Object of class “lca” with the following components:
label |
Name of region |
age |
Ages from |
year |
Years from |
<series> |
Matrix of mortality or fertility data as contained in |
ax |
Average deathrates across fitting period |
bx |
First principal component in Lee-Carter model |
kt |
Coefficient of first principal component |
residuals |
Functional time series of residuals. |
fitted |
Functional time series containing estimated mortality or fertility rates from model |
varprop |
Proportion of variance explained by model. |
y |
The data stored as a functional time series object. |
mdev |
Mean deviance of total and base lack of fit, as described in Booth, Maindonald and Smith. |
Author(s)
Heather Booth, Leonie Tickle, John Maindonald and Rob J Hyndman.
References
Booth, H., Maindonald, J., and Smith, L. (2002) Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56, 325-336.
Lee, R.D., and Carter, L.R. (1992) Modeling and forecasting US mortality. Journal of the American Statistical Association, 87, 659-671.
See Also
forecast.lca, plot.lca, summary.lca, fdm
Examples
## Not run:
france.LC1 <- lca(fr.mort, adjust="e0")
plot(france.LC1)
par(mfrow=c(1,2))
plot(fr.mort,years=1953:2002,ylim=c(-11,1))
plot(forecast(france.LC1,jumpchoice="actual"),ylim=c(-11,1))
france.bms <- bms(fr.mort, breakmethod="bai")
fcast.bms <- forecast(france.bms)
par(mfrow=c(1,1))
plot(fcast.bms$kt)
## End(Not run)
Estimate life expectancy from mortality rates
Description
All three functions estimate life expectancy from lifetable.
The function flife.expectancy is primarily designed for forecast life expectancies and will optionally
produce prediction intervals. Where appropriate, it will package the results as a forecast object
which makes it much easier to product nice plots of forecast life expectancies.
The e0 function is a shorthand wrapper for flife.expectancy with age=0.
Usage
life.expectancy(
data,
series = names(data$rate)[1],
years = data$year,
type = c("period", "cohort"),
age = min(data$age),
max.age = min(100, max(data$age))
)
flife.expectancy(
data,
series = NULL,
years = data$year,
type = c("period", "cohort"),
age,
max.age = NULL,
PI = FALSE,
nsim = 500,
...
)
e0(
data,
series = NULL,
years = data$year,
type = c("period", "cohort"),
max.age = NULL,
PI = FALSE,
nsim = 500,
...
)
Arguments
data |
Demogdata object of type “mortality” such as obtained from |
series |
Name of mortality series to use. Default is the first demogdata series in data. |
years |
Vector indicating which years to use. |
type |
Either |
age |
Age at which life expectancy is to be calculated. |
max.age |
Maximum age for life table calculation. |
PI |
If TRUE, produce a prediction interval. |
nsim |
Number of simulations to use when computing a prediction interval. |
... |
Other arguments passed to |
Value
Time series of life expectancies (one per year), or a forecast object of life expectancies (one per year).
Author(s)
Rob J Hyndman
See Also
Examples
plot(life.expectancy(fr.mort),ylab="Life expectancy")
france.LC <- lca(fr.mort,adjust="e0",years=1950:1997)
france.fcast <- forecast(france.LC,jumpchoice="actual")
france.e0.f <- life.expectancy(france.fcast)
france.fdm <- fdm(extract.years(fr.mort,years=1950:2006))
france.fcast <- forecast(france.fdm)
## Not run:
e0.fcast <- e0(france.fcast,PI=TRUE,nsim=200)
plot(e0.fcast)
## End(Not run)
life.expectancy(fr.mort,type='cohort',age=50)
Construct lifetables from mortality rates
Description
Computes period and cohort lifetables from mortality rates for multiple years.
Usage
lifetable(
data,
series = names(data$rate)[1],
years = data$year,
ages = data$age,
max.age = min(100, max(data$age)),
type = c("period", "cohort")
)
Arguments
data |
Demogdata object such as obtained from |
series |
Name of series to use. Default is the first series in |
years |
Vector indicating which years to include in the tables. |
ages |
Vector indicating which ages to include in table. |
max.age |
Age for last row. Ages beyond this are combined. |
type |
Type of lifetable: |
Details
For period lifetables, all years and all ages specified are included in the tables. For cohort lifetables,
if ages takes a scalar value, then the cohorts are taken to be of that age in each year contained in years.
But if ages is a vector of values, then the cohorts are taken to be of those ages in the first year contained in years.
For example, if ages=0 then lifetables of the birth cohorts for all years in years are computed. On the other hand,
if ages=0:100 and years=1950:2010, then lifetables of each age cohort in 1950 are computed.
In all cases, q_x = m_x/(1+[(1-a_x)m_x]) as per Chiang (1984).
Warning: the code has only been tested for data based on single-year age groups.
Value
Object of class “lifetable” containing the following components:
label |
Name of region from which data are taken. |
series |
Name of series |
age |
Ages for lifetable |
year |
Period years or cohort years |
mx |
Death rate at age x. |
qx |
The probability that an individual of exact age x will die before exact age x+1. |
lx |
Number of survivors to exact age x. The radix is 1. |
dx |
The number of deaths between exact ages x and x+1. |
Lx |
Number of years lived between exact age x and exact age x+1. |
Tx |
Number of years lived after exact age x. |
ex |
Remaining life expectancy at exact age x. |
Note that the lifetables themselves are not returned, only their components. However, there is a print method that constructs (and returns) the lifetables from the above components.
Author(s)
Heather Booth, Leonie Tickle, Rob J Hyndman, John Maindonald and Timothy Miller
References
Chiang CL. (1984) The life table and its applications. Robert E Krieger Publishing Company: Malabar.
Keyfitz, N, and Caswell, H. (2005) Applied mathematical demography, Springer-Verlag: New York.
Preston, S.H., Heuveline, P., and Guillot, M. (2001) Demography: measuring and modeling population processes. Blackwell
See Also
Examples
france.lt <- lifetable(fr.mort)
plot(france.lt)
lt1990 <- print(lifetable(fr.mort,year=1990))
france.LC <- lca(fr.mort)
france.fcast <- forecast(france.LC)
france.lt.f <- lifetable(france.fcast)
plot(france.lt.f)
# Birth cohort lifetables, 1900-1910
france.clt <- lifetable(fr.mort,type="cohort",age=0, years=1900:1910)
# Partial cohort lifetables for 1950
lifetable(fr.mort, years=1950)
Mean and median functions for data of class demogdata
Description
Computes mean or median of demographic rates for each age level.
Usage
## S3 method for class 'demogdata'
mean(x, series = names(x$rate)[1], transform = TRUE, na.rm = TRUE, ...)
## S3 method for class 'demogdata'
median(
x,
na.rm = FALSE,
series = names(x$rate)[1],
transform = TRUE,
method = c("hossjercroux", "coordinate"),
...
)
Arguments
x |
Demogdata object such as created using |
series |
Name of demogdata series to plot.. |
transform |
Should transform of data be taken first? |
na.rm |
a logical value indicating whether NA values should be stripped before the computation proceeds. |
... |
Other arguments. |
method |
Method for computing the median. Either "coordinate" for a coordinate-wise median, or "hossjercroux" for the L1-median using the Hossjer-Croux algorithm. |
Value
A list containing x=ages and y=mean or median rates.
Author(s)
Rob J Hyndman
References
Hossjer, O., and Croux, C. (1995) Generalized univariate signed rank statistics for testing and estimating a multivariate location parameter. Nonparametric Statistics, 4, 293-308.
Examples
plot(fr.mort)
lines(mean(fr.mort),lwd=2)
lines(median(fr.mort),lwd=2,col=2)
Show model information for the forecast coefficients in FDM models.
Description
The models for the time series coefficients used in forecasting fdm models are shown.
Usage
models(object, ...)
## S3 method for class 'fmforecast'
models(object, select = 0, ...)
## S3 method for class 'fmforecast2'
models(object, ...)
Arguments
object |
Output from |
... |
Other arguments. |
select |
Indexes of coefficients to display. If select=0, all coefficients are displayed. |
Author(s)
Rob J Hyndman
See Also
Examples
## Not run:
fr.short <- extract.years(fr.sm,1950:2006)
fr.fit <- fdm(fr.short,series="male")
fr.fcast <- forecast(fr.fit)
models(fr.fcast)
fr.fit <- coherentfdm(fr.short)
fr.fcast <- forecast(fr.fit)
models(fr.fcast,select=1:3)
## End(Not run)
Calculate net migration from mortality and fertility data
Description
Function to compute the net number of migrants in each year and for each age, based on the total population numbers, deaths and births in each year.
Usage
netmigration(mort, fert, startyearpop=mort, mfratio = 1.05)
Arguments
mort |
Demogdata object of type |
fert |
Demogdata object of type |
startyearpop |
Demogdata object containing population data for first year of calculation. |
mfratio |
Male-female ratio to be used in simulating births. |
Value
Object of class “demogdata” with the following components:
year |
Vector of years |
age |
Vector of ages |
rate |
List containing matrices of net migration numbers (not "rates") with with one age group per
row and one column per year. Names of matrices are the same as for |
pop |
List containing matrices of populations in same form as |
type |
Type of object. In this case, “migration”. |
label |
label from |
Author(s)
Rob J Hyndman
See Also
Examples
## Not run:
require(addb)
aus.mig <- netmigration(australia,aus.fertility)
plot(aus.mig)
## End(Not run)
Plot age-specific demographic functions
Description
If plot.type="functions", then years are plotted using a rainbow palette so the
earliest years are red, followed by orange, yellow, green, blue
and indigo with the most recent years plotted in violet.
If plot.type="time", then each age is shown as a separate time series in a time plot.
Usage
## S3 method for class 'demogdata'
plot(
x,
series = ifelse(!is.null(x$rate), names(x$rate)[1], names(x$pop)[1]),
datatype = ifelse(!is.null(x$rate), "rate", "pop"),
years = x$year,
ages = x$age,
max.age = max(x$age),
transform = (x$type == "mortality"),
plot.type = c("functions", "time", "depth", "density"),
type = "l",
main = NULL,
xlab,
ylab,
...
)
## S3 method for class 'demogdata'
lines(
x,
series = ifelse(!is.null(x$rate), names(x$rate)[1], names(x$pop)[1]),
datatype = ifelse(!is.null(x$rate), "rate", ""),
years = x$year,
ages = x$age,
max.age = max(x$age),
transform = (x$type == "mortality"),
plot.type = c("functions", "time", "depth", "density"),
...
)
## S3 method for class 'demogdata'
points(..., pch = 1)
Arguments
x |
Demogdata object such as created using |
series |
Name of series to plot. Default: the first matrix within |
datatype |
Name of demogdata object which contains series. Default “rate”. Alternative: “pop”. |
years |
Vector indicating which years to plot. Default: all available years. |
ages |
Vector indicating which ages to plot. Default: all available ages. |
max.age |
Maximum age to plot. Default: all available ages. |
transform |
Should a transformation of the data be plotted? Default is TRUE if the object contains mortality data and datatype="rate", and FALSE otherwise. |
plot.type |
Type of plot: either “functions” or “time”. |
type |
What type of plot should be drawn. See |
main |
Main title for the plot. |
xlab |
Label for x-axis. |
ylab |
Label for y-axis. |
... |
Other plotting parameters. In |
pch |
Plotting character. |
Value
None. Function produces a plot
Author(s)
Rob J Hyndman
Examples
plot(fr.mort)
par(mfrow=c(1,2))
plot(aus.fert,plot.type="time")
plot(aus.fert,plot.type="functions")
Plot differences between actuals and estimates from fitted demographic model
Description
Function produces a plot of errors from a fitted demographic model.
Usage
## S3 method for class 'errorfdm'
plot(x, transform = TRUE, ...)
Arguments
x |
Object of class |
transform |
Plot errors on transformed scale or original scale? |
... |
Plotting parameters. |
Author(s)
Rob J Hyndman
See Also
Examples
fr.fit <- lca(extract.years(fr.mort,years=1921:1980))
fr.error <- compare.demogdata(fr.mort, forecast(fr.fit,20))
plot(fr.error)
Plot forecasts from a functional demographic modell
Description
Type of plot depends on value of plot.type:
plot.type="function"produces a plot of the forecast functions;
plot.type="components"produces a plot of the basis functions and coefficients with forecasts and prediction intervals for each coefficient;
plot.type="variance"produces a plot of the variance components.
Usage
## S3 method for class 'fmforecast'
plot(
x,
plot.type = c("function", "component", "variance"),
vcol = 1:4,
mean.lab = "Mean",
xlab2 = "Year",
h = 1,
...
)
## S3 method for class 'lca'
plot(x, ...)
Arguments
x |
Output from |
plot.type |
Type of plot. See details. |
vcol |
Colors to use if |
mean.lab |
Label for mean component. |
xlab2 |
x-axis label for coefficient time series. |
h |
If |
... |
Other arguments are passed to |
Value
None. Function produces a plot
Author(s)
Rob J Hyndman
See Also
Examples
france.fcast <- forecast(fdm(fr.mort))
plot(france.fcast)
plot(france.fcast,"c")
plot(france.fcast,"v")
Plot life expectancy from lifetable
Description
plots life expectancy for each age and each year as functional time series.
Usage
## S3 method for class 'lifetable'
plot(
x,
years = x$year,
main,
xlab = "Age",
ylab = "Expected number of years left",
...
)
## S3 method for class 'lifetable'
lines(x, years = x$year, ...)
Arguments
x |
Output from |
years |
Years to plot. Default: all available years. |
main |
Main title. |
xlab |
Label for x-axis. |
ylab |
Label for y-axis. |
... |
Additional arguments passed to |
Author(s)
Rob J Hyndman
See Also
Examples
france.lt <- lifetable(fr.mort)
plot(france.lt)
france.LC <- lca(fr.mort)
france.fcast <- forecast(france.LC)
france.lt.f <- lifetable(france.fcast)
plot(france.lt.f,years=2010)
Population simulation
Description
Simulate future sample paths of a population using functional models for mortality, fertility and migration.
Usage
pop.sim(
mort,
fert = NULL,
mig = NULL,
firstyearpop,
N = 100,
mfratio = 1.05,
bootstrap = FALSE
)
Arguments
mort |
Forecasts of class |
fert |
Forecasts of class |
mig |
Forecasts of class |
firstyearpop |
Population for first year of simulation. |
N |
Number of sample paths to simulate. |
mfratio |
Male-female ratio used in distributing births. |
bootstrap |
If TRUE, simulation uses resampled errors rather than normally distributed errors. |
Value
A list of two arrays containing male and female future simulated population values. The arrays are of dimension (p,h,N) where p is the number of age groups, h is the forecast horizon and N is the number of simulated sample paths.
Author(s)
Rob J Hyndman
See Also
simulate.fmforecast, simulate.fmforecast2.
Examples
## Not run:
require(addb)
# Construct data objects
mort.sm <- smooth.demogdata(set.upperage(extract.years(australia,1950:2002),100))
fert.sm <- smooth.demogdata(extract.years(aus.fertility,1950:2002))
aus.mig <- netmigration(set.upperage(australia,100),aus.fertility,mfratio=1.0545)
# Fit models
mort.fit <- coherentfdm(mort.sm)
fert.fit <- fdm(fert.sm)
mig.fit <- coherentfdm(aus.mig)
# Produce forecasts
mort.fcast <- forecast(mort.fit)
fert.fcast <- forecast(fert.fit)
mig.fcast <- forecast(mig.fit)
# Simulate
aus.sim <- pop.sim(mort.fcast,fert.fcast,mig.fcast,australia)
## End(Not run)
Read demographic data and construct demogdata object
Description
Read data from text files and construct a demogdata object suitable for
plotting using plot.demogdata and fitting an LC or BMS model
using lca or an FDA model using fdm.
Usage
read.demogdata(
file,
popfile,
type,
label,
max.mx = 10,
skip = 2,
popskip = skip,
lambda,
scale = 1
)
Arguments
file |
Filename containing demographic rates. |
popfile |
Filename containing population numbers. |
type |
Character string showing type of demographic series: either “mortality”, “fertility” or “migration”. |
label |
Name of area from which the data are taken. |
max.mx |
Maximum allowable value for demographic rate. All values greater than max.mx will be set to max.mx. |
skip |
Number of lines to skip at the start of |
popskip |
Number of lines to skip at the start of |
lambda |
Box-Cox transformation parameter to be used in modelling and plotting. If missing, default values are 0 (for mortality), 0.4 (for fertility) and 1 (for migration). |
scale |
Number of people in the rate definition. |
Details
All data are assumed to be tab-delimited text files with the first column
containing the year of observation and the second column containing the age
level. All remaining columns are assumed to be demographic rates for sections
of the population. The first row of the text file is assumed to contain the
names of each column. Population data are assumed to have the same format but
with population numbers in place of rates. The columns names in the two
files should be identical. Note that this format is what is used by the Human
Mortality Database http://www.mortality.org. If popfile contains
the Exposures and file contains the Mx rates from the HMD, then
everything will work seamlessly.
Value
Object of class “demogdata” with the following components:
year |
Vector of years |
age |
Vector of ages |
rate |
A list containing one or more rate matrices with one age group per row and one column per year. |
pop |
A list of the same form as |
type |
Type of object: “mortality”, “fertility” or “migration”. |
label |
label |
Author(s)
Rob J Hyndman
See Also
Examples
## Not run: norway <- read.demogdata("Mx_1x1.txt",
"Exposures_1x1.txt", type="mortality", label="Norway")
## End(Not run)
Compute residuals and fitted values from functional demographic model or Lee-Carter model
Description
After fitting a Lee-Carter model or functional demographic model, it is useful to inspect the residuals or plot the fitted values. These functions extract the relevant information from the fit object.
Usage
## S3 method for class 'fdm'
residuals(object, ...)
## S3 method for class 'fdm'
fitted(object, ...)
## S3 method for class 'lca'
fitted(object, ...)
## S3 method for class 'lca'
residuals(object, ...)
Arguments
object |
|
... |
Other arguments. |
Value
residuals.fdm and residuals.lca produce an object of
class “fmres” containing the residuals from the model.
fitted.fdm and fitted.lca produce an object of class
“fts” containing the fitted values from the model.
Author(s)
Rob J Hyndman.
See Also
Examples
fit1 <- lca(fr.mort)
plot(residuals(fit1))
plot(fitted(fit1))
Combine the upperages of a demogdata object.
Description
Computes demographic rates by combining age groups.
Usage
set.upperage(data, max.age)
Arguments
data |
Demogdata object such as created using |
max.age |
Upper age group. Ages beyond this are combined into the upper age group. |
Value
Demogdata object with same components as data but with a subset of ages.
Author(s)
Rob J Hyndman
Examples
france.short <- set.upperage(fr.mort, 85)
Compute sex ratios from mortality rates
Description
Calculates the Male/Female ratios from historical or forecasted mortality rates.
Usage
sex.ratio(data)
Arguments
data |
Demogdata object of type “mortality” such as obtained from |
Value
Functional time series of sex ratios.
Author(s)
Rob J Hyndman
Examples
plot(sex.ratio(fr.mort),ylab="Sex ratios (M/F)")
Simulate future sample paths from functional demographic model forecasts.
Description
This function will simulate future sample paths given forecasting models
from a functional demographic model such as those obtained using forecast.fdm or forecast.fdmpr.
Usage
## S3 method for class 'fmforecast'
simulate(
object,
nsim = 100,
seed = NULL,
bootstrap = FALSE,
adjust.modelvar = TRUE,
...
)
## S3 method for class 'fmforecast2'
simulate(object, ...)
Arguments
object |
Object of class |
nsim |
Number of sample paths to simulate. |
seed |
Either NULL or an integer that will be used in a call to set.seed before simulating the time seriers. The default, NULL will not change the random generator state. |
bootstrap |
If TRUE, simulation uses resampled errors rather than normally distributed errors. |
adjust.modelvar |
If TRUE, will adjust the model variance by the ratio of the empirical and theoretical variances for one-step forecasts. |
... |
Other arguments passed to |
Value
An array containing the future simulated values (in the case of a fmforecast object),
or a list of arrays containing the future simulated values (in the case of a fmforecast2 object).
Author(s)
Rob J Hyndman
See Also
forecast.fdm, forecast.lca, forecast.ftsm.
Examples
## Not run:
france.fit <- fdm(fr.mort,order=2)
france.fcast <- forecast(france.fit,50,method="ets")
france.sim <- simulate(france.fcast,nsim=100)
france.fit2 <- coherentfdm(fr.sm)
france.fcast2 <- forecast(france.fit2,50)
france.sim2 <- simulate(france.fcast2,nsim=100)
## End(Not run)
Create smooth demogdata functions
Description
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 |
method |
Method of smoothing. Possibilities: |
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 |
k |
Number of knots to use for penalized regression spline estimate. Ignored if |
span |
Span for loess smooth if |
lambda |
Penalty for constrained regression spline if |
interpolate |
If |
weight |
If TRUE, uses weighted smoothing. |
obs.var |
Method for computing observational variance. Possible values: “empirical” or “theoretical”. |
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 callsgamfor 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 callscobsfor 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
loessfor the basic computations.
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.
Author(s)
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)
Summary for functional demographic model or Lee-Carter model
Description
Summarizes a basis function model fitted to age-specific demographic rate data. It returns various measures of goodness-of-fit.
Usage
## S3 method for class 'fdm'
summary(object, ...)
## S3 method for class 'lca'
summary(object, ...)
Arguments
object |
|
... |
Other arguments. |
Author(s)
Rob J Hyndman
See Also
fdm, lca, bms,
compare.demogdata
Examples
fit1 <- lca(fr.mort)
fit2 <- bms(fr.mort,breakmethod="bai")
fit3 <- fdm(fr.mort)
summary(fit1)
summary(fit2)
summary(fit3)
Compute total fertility rate from fertility rates
Description
Compute total fertility rates from age-specific fertility rates contained in
a demogdata object.
Usage
tfr(data, PI = FALSE, nsim = 500, ...)
Arguments
data |
Demogdata object of type |
PI |
If TRUE, produce a prediction interval. |
nsim |
Number of simulations to use when computing a prediction interval. |
... |
Other arguments passed to |
Value
If data are of class demogdata, the function returns a time
series of fertility rates. If data are from forecast.fdm, the
function returns an object of class forecast containing point
forecasts and (optionally) prediction intervals.
Author(s)
Rob J Hyndman
See Also
Examples
plot(tfr(aus.fert))
ausfert.fcast <- forecast(fdm(aus.fert))
plot(tfr(ausfert.fcast,PI=TRUE,nsim=400))
Updating functional demographic models and coherent functional demographic models.
Description
update.fmforecast() updates fdm forecasts. The argument object is the output from forecast.fdm which has been subsequently modified with new coefficient forecasts. These new forecasts are used when re-calculating the forecast of the mortality or fertility rates, or net migration numbers.
update.fmforecast2() updates fdmpr forecasts. The argument object is the output from forecast.fdmpr which has been subsequently modified with new coefficient forecasts.
Usage
## S3 method for class 'fmforecast'
update(object, ...)
## S3 method for class 'fmforecast2'
update(object, ...)
Arguments
object |
Output from either |
... |
Extra arguments currently ignored. |
Value
A list of the same class as object.
Author(s)
Rob J Hyndman.
See Also
Examples
## Not run:
france.fit <- fdm(fr.mort,order=2)
france.fcast <- forecast(france.fit,50)
# Replace first coefficient model with ARIMA(0,1,2)+drift
france.fcast$coeff[[2]] <- forecast(Arima(france.fit$coeff[,2],
order=c(0,1,2), include.drift=TRUE), h=50, level=80)
france.fcast <- update(france.fcast)
fr.short <- extract.years(fr.sm,1950:2006)
fr.fit <- coherentfdm(fr.short)
fr.fcast <- forecast(fr.fit)
par(mfrow=c(1,2))
plot(fr.fcast$male)
# Replace first coefficient model in product component with a damped ETS model:
fr.fcast$product$coeff[[2]] <- forecast(ets(fr.fit$product$coeff[,2], damped=TRUE),
h=50, level=80)
fr.fcast <- update(fr.fcast)
plot(fr.fcast$male)
## End(Not run)