MortCast (version 2.7-0)

logquad: Log-Quadratic Mortality Model

Description

Predict age-specific mortality rates using the Log-Quadratic Mortality Model (Wilmoth et al. 2012).

Usage

logquad(
  e0,
  sex = c("male", "female", "total"),
  my.coefs = NULL,
  q5ranges = c(1e-04, 0.9),
  k = 0,
  keep.lt = FALSE,
  ...
)
logquadj(e0m, e0f, ...)

Arguments

e0

Vector of target life expectancies.

sex

Which sex does the give e0 corresponds to.

my.coefs

Data frame with columns “sex”, “age”, “ax”, “bx”, “cx”, “vx”. The “sex” column should contain values “female”, “male” and/or “total”. The “age” column must be sorted so that it assures that rows correspond to ages in increasing order. Any NAs are internally converted to zeros. If not given, the dataset LQcoef is used.

q5ranges

A vector of size two, giving the min and max of 5q0 used in the bisection method.

k

Value of the \(k\) parameter.

keep.lt

Logical. If TRUE additional life table columns are kept in the resulting object.

…

Additional arguments passed to the underlying function.

e0m

A time series of target male life expectancy.

e0f

A time series of target female life expectancy.

Value

Function logquad returns a list with the following elements: a matrix mx with the predicted mortality rates. If keep.lt is TRUE, it also contains matrices sr (survival rates), and life table quantities Lx and lx. Function logquadj returns a list of objects, one for each sex.

Details

The LogQuad method in this implementation projects mortality rates using the equation $$\log(m_x) = a_x + b_x h + c_x h^2 + v_x k$$ where \(a_x\), \(b_x\), \(c_x\) and \(v_x\) are age-specific coefficients, \(h = \log( 5q0 )\) (i.e. reflects child mortality), and \(k\) should be chosen to match 45q15 (adult mortality) or set to 0 (default). The coefficients can be passed as inputs, or taken from the package default dataset LQcoef which are taken from https://u.demog.berkeley.edu/~jrw/LogQuad/.

For the given inputs and values of life expectancy e0, the function finds values of \(h\) that best match e0, using life tables and the bisection method. It returns the corresponding mortality schedule for each value of e0.

Function logquad is for one sex, while logquadj can be used for both sexes.

References

Wilmoth, J., Zureick, S., Canudas-Romo, V., Inoue, M., Sawyer, C. (2012). A Flexible Two-Dimensional Mortality Model for Use in Indirect Estimation. Population studies, 66(1), 1-28. doi:10.1080/00324728.2011.611411

See Also

LQcoef, mortcast.blend, mortcast, pmd, mlt

Examples

# NOT RUN {
data(e0Mproj, package = "wpp2017")
country <- "Brazil"
# get target e0
e0m <- as.numeric(subset(e0Mproj, name == country)[-(1:2)])
# project into future
pred <- logquad(e0m, sex = "male")
# plot first projection in black and the remaining ones in heat colors 
plot(pred$mx[,1], type = "l", log = "y", ylim = range(pred$mx),
    ylab = "male mx", xlab = "Age", main = country)
for(i in 2:ncol(pred$mx)) lines(pred$mx[,i], 
    col = heat.colors(20)[i])
    
# }