lt_rule_1a0_cd: Coale-Demeny a(0) as function of m(0), region, and sex.

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

Coale-Demeny a(0) as function of m(0), region, and sex.

Description

Coale-Demeny a(0) from Manual X Table 164. This is a rule of thumb. In this and some other older texts, a(0) is known as a 'separation factor'.

Usage

lt_rule_1a0_cd(M0, IMR = NA, Sex = "m", region = "w")

Arguments

M0	numeric. Event exposure infant mortality rate.
IMR	numeric. Optional. q0, the death probability in first year of life, in case available separately.
Sex	character. "m" or "f" for male or female,
region	character. "n", "e", "s" or "w" for North, East, South, or West.

Details

If IMR is not given, then M0 is converted to q(0) using the following approximation:

1. Find \alpha , \beta. Look up the appropriate slope and intercept for the given sex and region.

2. calculate a as: a = M₀ * β

3. calculate b as: b = 1 + M₀ *(1- α)

4. approximate q₀ as: q₀ = (b²- √ [b -4*a*M₀]) / (2*a)

5. use q₀ as IMR, and applied directly to the Coale-Demeny piecewise linear formula.

If IMR is given, then M0 is disregarded, and transitivity is therefore not guaranteed. In this case, one has the option to use lt_id_qm_a() to derive a(0), however discrepancies between these two parameters could force implausible results in a(0), whereas the CD rule always gives something plausible.

Value

The average age at death in the first year of life a(0).

References

\insertRef

united1983manualDemoTools \insertRefPASDemoTools

Examples

m0 <- seq(.001, .2, by = .001)
## Not run: 
plot(m0, sapply(m0, lt_rule_1a0_cd, Sex = "m", region = "e"), ylab = "a0",
		type = 'l', ylim = c(0,.36), lty = 2, col = "blue")
lines(m0,sapply(m0, lt_rule_1a0_cd, Sex = "m", region = "w"), col = "blue")
lines(m0,sapply(m0, lt_rule_1a0_cd, Sex = "f", region = "e"), lty = 2, col = "red")
lines(m0,sapply(m0, lt_rule_1a0_cd, Sex = "f", region = "w"), col = "red")
text(.15, lt_rule_1a0_cd(.15,Sex = "m", region = "e"),"males E",font=2)
text(.15, lt_rule_1a0_cd(.15,Sex = "m", region = "w"),"males N,W,S",font=2)
text(.15, lt_rule_1a0_cd(.15,Sex = "f", region = "e"),"females E",font=2)
text(.15, lt_rule_1a0_cd(.15,Sex = "f", region = "w"),"females N,W,S",font=2)

# compare with the Preston approximation
# constants identical after m0 = .107
m0 <- seq(.001,.107,by =.001)
a0CDm0 <- sapply(m0, lt_rule_1a0_cd, Sex = "m", region = "w")
a0CDpr <- 0.045 + 2.684 * m0
plot(m0, a0CDm0, type = 'l', lty = 2, col = "red")
lines(m0, a0CDpr)
plot(m0, (a0CDm0 - a0CDpr) * 365, main = "difference (days)", ylab = "days")

## End(Not run)

timriffe/DemoTools documentation built on Jan. 28, 2024, 5:13 a.m.