lt_a_un: UN a(x) estimates from either M(x), q(x), or both

In timriffe/DemoTools: Standardize, Evaluate, and Adjust Demographic Data

UN a(x) estimates from either M(x), q(x), or both

Description

The UN a(x) formula uses Coale-Demeny for ages 0, and 1-4, values of 2.5 for ages 5-9 and 10-14, and the Greville formula for higher ages. In the original sources these are referred to as separation factors.

Usage

lt_a_un(
  nMx,
  nqx,
  lx,
  IMR = NA,
  Age,
  AgeInt,
  a0rule = "ak",
  Sex = "m",
  region = "w",
  SRB = 1.05,
  tol = .Machine$double.eps,
  maxit = 1000,
  mod = TRUE,
  extrapLaw = "kannisto",
  extrapFrom = max(Age),
  extrapFit = Age[Age >= 60],
  ...
)

Arguments

nMx	numeric. Event exposure mortality rates.
nqx	numeric. Vector of age specific death probabilities in standard abridged age groups.
lx	numeric. Vector of lifetable survivorship in standard abridged age groups.
IMR	numeric. Optional. q0, the death probability in first year of life, in case available separately.
Age	integer. A vector of ages of the lower integer bound of the age classes.
AgeInt	integer. Vector of age interval widths.
a0rule	character. Either "ak" (default) or "cd".
Sex	character. "m", "f" or "b" for male, female, or both.
region	character. "n", "e", "s" or "w" for North, East, South, or West.
SRB	numeric. The sex ratio at birth (boys/girls), default 1.05.
tol	numeric. The tolerance for the qx-based iterative method. Default .Machine$double.eps.
maxit	integer. The maximum number of iterations for the qx-based iterative method. Default 1000.
mod	logical. Whether or not to use Gerland's modification for ages 5-14. Default TRUE.
extrapLaw	character. If extrapolating, which parametric mortality law should be invoked? Options include "Kannisto", "Kannisto_Makeham", "Makeham","Gompertz", "GGompertz", "Beard", "Beard_Makeham", "Quadratic". Default "Kannisto". See details.
extrapFrom	integer. Age from which to impute extrapolated mortality.
extrapFit	integer vector. Ages to include in model fitting. Defaults to all ages > =60.
...	Other arguments to be passed on to the MortalityLaw function.

Details

a(x) for age 0 and age group 1-4 are based on Coale-Demeny q₀-based lookup tables. If the main input is nMx, and if IMR is not given, we first approximate q₀ for the Coale-Demeny approach before applying the formula. The final a(x) value is closed out using the lt_a_closeout() method (reciprocal and Mortpak methods are deprecated). For nMx inputs this method is rather direct, but for q_X or l(x) inputs it is iterative. Age groups must be standard abridged. No check on age groups are done.

Value

nax average contribution to exposure of those dying in the interval.

References

\insertRef

greville1977shortDemoTools \insertRefun1982modelDemoTools \insertRefarriaga1994populationDemoTools \insertRefmortpak1988DemoTools

Examples

# example data from UN 1982 Model Life Tables for Developing Countries.
# first Latin American model table for males (p. 34).
Mx <- c(.23669,.04672,.00982,.00511,.00697,.01036,.01169,
		.01332,.01528,.01757,.02092,.02517,.03225,.04241,.06056,
		.08574,.11840,.16226,.23745)
ax <- c(0.330,1.352,2.500,2.500,2.633,2.586,2.528,2.528,
		2.526,2.529,2.531,2.538,2.542,2.543,2.520,2.461,2.386,2.295,4.211)

AgeInt     <- inferAgeIntAbr(vec = Mx)
Age <- int2age(AgeInt)
nAx1       <- lt_a_un(nMx = Mx,
                   Age = Age,
		                AgeInt = AgeInt,
		                a0rule = "cd",
		                Sex = "m",
				          region = "w",
		                mod = FALSE)
nAx2       <- lt_a_un(nMx = Mx,
                   Age = Age,
		                AgeInt = AgeInt,
		                a0rule = "cd",
		                Sex = "m",
				          region = "w",
		                mod = TRUE)
# this is acceptable...
round(nAx2,3) - ax # only different in ages 5-9 and 10-14, and last two ages
# ignore open age, which is treated differently
N <- length(ax)
# default unit test...
stopifnot(all(round(nAx1[Age<80],3) - ax[Age<80] == 0)) # spot on

# another example:

nMx <- c(0.11621,0.02268,0.00409,0.00212,0.00295,
         0.00418,0.00509,0.00609,0.00714,0.00808,
         0.00971,0.0125,0.0175,0.02551,0.03809,
         0.05595,0.0809,0.15353,0.2557)
AgeInt <- inferAgeIntAbr(vec = nMx)
Age    <- int2age(AgeInt)
nAx1   <- lt_a_un(nMx, 
                  Age = Age,
                  AgeInt = AgeInt, 
                  a0rule = "ak",
                  mod = TRUE, 
                  closeout = TRUE)

nqx    <- lt_id_ma_q(nMx = nMx, 
                     nax = nAx1, 
                     AgeInt = AgeInt, 
                     closeout = FALSE)
nAx2 <- lt_a_un(nqx = nqx, 
                Age = Age,
                AgeInt = AgeInt, 
                a0rule = "ak", 
                mod= TRUE, 
                closeout = TRUE)

stopifnot(all(abs(nAx1[Age<75] - nAx2[Age<75]) < 1e-7))

timriffe/DemoTools documentation built on Oct. 14, 2024, 12:53 p.m.