Mortality models for mx approximation

Usage

mort.approx(mx, age, model = c("Brass", "Gompertz"), standard.mx = NULL, ...)

Arguments

mx: Numeric vector of age specific mortality rates.
age: Numeric vector of ages.
model: Character. Model name to be estimated. Now "Gompertz" and "Brass" are supported.
standard.mx: Numeric vector of age specific mortality rates for standard population. Default is NULL.
...: Used only for Brass model. Other parameters for the function LT() including ax (by default, the middle of the interval), sex (by default = "m" - males), l0 (by default = 1).

Value

A list with two components: model, the fitted lm or nls object; and predicted, a data frame with columns age and mx.pred containing the fitted mortality schedule.

Details

This function runs least squares optimization of the selected mortality function using Gauss-Newton algorithm algorithm with 2000 maximum iterations and 1e-07 as tolerance parameter. For "Gompertz" usual OLS estimator is used.

Gompertz model

The model is as follows: $$m(age) = \alpha e^{\beta age}$$

Brass model

The model is as follows: $$y(age) = \alpha + \beta y^{S}(age)$$ where $$y(age) = \frac{1}{2} ln[\frac{q(age)}{1-q(age)}]$$ and subscript S defines that function is for standard population. To get mx from qx usual formula is used: $$m(age) = \frac{q(age)}{n-q(age)(n-a(age))}$$ where n is the size of age interval and a(x) is a parameter from life table.

References

Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell Publishers.

Examples

age <- seq(40, 80, 10)
mx <- c(0.003, 0.005, 0.009, 0.018, 0.036)
standard.mx <- c(0.0025, 0.004, 0.007, 0.014, 0.03)
mort.approx(mx = mx, age = age, model = "Gompertz")
#> $model
#> 
#> Call:
#> stats::lm(formula = log(mx) ~ age)
#> 
#> Coefficients:
#> (Intercept)          age  
#>    -8.38237      0.06251  
#> 
#> 
#> $predicted
#>   age     mx.pred
#> 1  40 0.002789002
#> 2  50 0.005210930
#> 3  60 0.009736027
#> 4  70 0.018190652
#> 5  80 0.033987150
#> 
mort.approx(mx = mx, age = age, model = "Brass", standard.mx = standard.mx)
#> $model
#> Nonlinear regression model
#>   model: 0.5 * log((qx/(1 - qx))) ~ a + b * stand.logit
#>    data: parent.frame()
#>     a     b 
#> 0.189 1.050 
#>  residual sum-of-squares: 0.0001375
#> 
#> Number of iterations to convergence: 1 
#> Achieved convergence tolerance: 2.517e-08
#> 
#> $predicted
#>   age     mx.pred
#> 1  40 0.003037349
#> 2  50 0.004955936
#> 3  60 0.008879215
#> 4  70 0.018178505
#> 5  80 0.030000300
#>