Age decomposition of mortality: single decrement process

Age decomposition of mortality: single decrement process

Usage

decomp(mx1, mx2, sex = "m", age, method = "andreev", ax1 = NULL, ax2 = NULL)

Arguments

mx1

Numeric array with age specific mortality rates of population 1 (base population).

mx2

Numeric array with age specific mortality rates of population 2 (compared population).

sex

Character. Sex. "m" for males and "f" for females. By default, sex = "m".

age

Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))

method

Character. Decomposition method. "andreev" (1982), "arriaga" (1984) or "pollard" (1982) - slightly different in their results. By default, method = "andreev".

ax1

Optional. Numeric array with ax for the 1st population. By default, it is a the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).

ax2

Optional. Numeric array with ax for the 2nd population. By default, it is a the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).

Value

A data frame with one row per age group. It always contains age, ex12, and ex12_prc, where ex12 is the absolute age contribution to the life-expectancy difference and ex12_prc is the percentage contribution. Additional columns depend on method and contain intermediate life-table quantities used in the decomposition.

Details

Example of decomposition using Andreev (1982) formulas: $$\Delta_x = l_x^2(e_x^2 - e_x^1) - l_{x+n}^2(e_{x+n}^2 - e_{x+n}^1), \ \ \ x \neq \omega$$ $$\Delta_{\omega} = l_{\omega}^2(e_{\omega}^2 - e_{\omega}^1)$$ where \(\Delta_x\) is an absolute contribution of age \(x\) to difference in \(e_0\) between the second and the first population. \(e_x^i, l_x^i\) are life table functions for population \(i\). \(\omega\) is the last age group. Note, \(e_0^2 - e_0^1 = \sum_{x}^{\omega}\Delta_x\)

References

1. Arriaga, E. E. (1984). Measuring and explaining the change in life expectancies. Demography, 21, 83-96.

2. Andreev, E. M. (1982). Metod komponent v analize prodolzhitel'nosti zhizni. Vestnik statistiki, 9, 42-47.

3. Pollard, J. H. (1982). The expectation of life and its relationship to mortality. Journal of the Institute of Actuaries, 109(2), 225–240.

See also

mdecomp() for age and cause decomposition

Examples

age <- 0:5
mx1 <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
mx2 <- c(0.018, 0.009, 0.011, 0.014, 0.019, 0.028)
decomp(mx1, mx2, age = age)$ex12
#> [1] 0.08 0.03 0.04 0.03 0.04 2.21