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Tidy Analysis Tools for Mortality, Fertility, Migration and Population Data
robjhyndman/vital
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The goal of vital is to allow analysis of demographic data using tidytools.
You can install thestable version fromCRAN:
pak::pak("vital")
You can install thedevelopment version fromGithub:
pak::pak("robjhyndman/vital")
First load the necessary packages.
library(vital)library(tsibble)library(dplyr)library(ggplot2)
The basic data object is avital, which is time-indexed tibble thatcontains vital statistics such as births, deaths, population counts, andmortality and fertility rates.
Here is an example of avital object containing mortality data forNorway.
norway_mortality<-norway_mortality|> collapse_ages(max_age=100)
We can use functions to see which variables are index, key or vital:
index_var(norway_mortality)#> [1] "Year"key_vars(norway_mortality)#> [1] "Age" "Sex"vital_vars(norway_mortality)#> age sex deaths population#> "Age" "Sex" "Deaths" "Population"
norway_mortality|> filter(Sex!="Total",Year<1980,Age<90)|> autoplot(Mortality)+ scale_y_log10()
# Life table for Norwegian males in 2000norway_mortality|> filter(Sex=="Male",Year==2000)|> life_table()#> # A vital: 101 x 13 [?]#> # Key: Age x Sex [101 x 1]#> Year Age Sex mx qx lx dx Lx Tx ex rx nx#> <int> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>#> 1 2000 0 Male 4.26e-3 4.24e-3 1 4.24e-3 0.996 76.0 76.0 0.996 1#> 2 2000 1 Male 5.93e-4 5.93e-4 0.996 5.90e-4 0.995 75.0 75.3 0.999 1#> 3 2000 2 Male 2.29e-4 2.29e-4 0.995 2.28e-4 0.995 74.0 74.3 1.000 1#> 4 2000 3 Male 1.57e-4 1.57e-4 0.995 1.56e-4 0.995 73.0 73.3 1.000 1#> 5 2000 4 Male 2.21e-4 2.21e-4 0.995 2.20e-4 0.995 72.0 72.3 1.000 1#> 6 2000 5 Male 1.89e-4 1.89e-4 0.995 1.88e-4 0.994 71.0 71.4 1.000 1#> 7 2000 6 Male 1.28e-4 1.28e-4 0.994 1.27e-4 0.994 70.0 70.4 1.000 1#> 8 2000 7 Male 1.27e-4 1.27e-4 0.994 1.26e-4 0.994 69.0 69.4 1.000 1#> 9 2000 8 Male 9.40e-5 9.40e-5 0.994 9.34e-5 0.994 68.0 68.4 1.000 1#> 10 2000 9 Male 2.17e-4 2.17e-4 0.994 2.16e-4 0.994 67.0 67.4 1.000 1#> # ℹ 91 more rows#> # ℹ 1 more variable: ax <dbl>
# Life expectancynorway_mortality|> filter(Sex!="Total")|> life_expectancy()|> ggplot(aes(x=Year,y=ex,color=Sex))+ geom_line()
Several smoothing functions are provided:smooth_spline(),smooth_mortality(),smooth_fertility(), andsmooth_loess(), eachsmoothing across the age variable for each year.
# Smoothed datanorway_mortality|> filter(Sex!="Total",Year==1967)|> smooth_mortality(Mortality)|> autoplot(Mortality)+ geom_line(aes(y=.smooth),col="#0072B2")+ ylab("Mortality rate")+ scale_y_log10()
Several mortality models are available including variations onLee-Carter models (Lee & Carter, JASA, 1992), and functional data models(Hyndman & Ullah, CSDA, 2007).
fit<-norway_mortality|> filter(Sex!="Total")|> model(lee_carter= LC(log(Mortality)),fdm= FDM(log(Mortality)) )fit#> # A mable: 2 x 3#> # Key: Sex [2]#> Sex lee_carter fdm#> <chr> <model> <model>#> 1 Female <LC> <FDM>#> 2 Male <LC> <FDM>
Models are fitted for all combinations of key variables excluding age.
fit|> select(lee_carter)|> filter(Sex=="Female")|> report()#> Series: Mortality#> Model: LC#> Transformation: log(Mortality)#>#> Options:#> Adjust method: dt#> Jump choice: fit#>#> Age functions#> # A tibble: 101 × 3#> Age ax bx#> <int> <dbl> <dbl>#> 1 0 -4.33 0.0155#> 2 1 -6.16 0.0223#> 3 2 -6.77 0.0193#> 4 3 -7.14 0.0187#> 5 4 -7.18 0.0165#> # ℹ 96 more rows#>#> Time coefficients#> # A tsibble: 124 x 2 [1Y]#> Year kt#> <int> <dbl>#> 1 1900 115.#> 2 1901 109.#> 3 1902 103.#> 4 1903 109.#> 5 1904 106.#> # ℹ 119 more rows#>#> Time series model: RW w/ drift#>#> Variance explained: 66.33%
fit|> select(lee_carter)|> autoplot()
fit|> select(lee_carter)|> age_components()#> # A tibble: 202 × 4#> Sex Age ax bx#> <chr> <int> <dbl> <dbl>#> 1 Female 0 -4.33 0.0155#> 2 Female 1 -6.16 0.0223#> 3 Female 2 -6.77 0.0193#> 4 Female 3 -7.14 0.0187#> 5 Female 4 -7.18 0.0165#> 6 Female 5 -7.41 0.0174#> 7 Female 6 -7.45 0.0165#> 8 Female 7 -7.48 0.0155#> 9 Female 8 -7.37 0.0125#> 10 Female 9 -7.39 0.0124#> # ℹ 192 more rowsfit|> select(lee_carter)|> time_components()#> # A tsibble: 248 x 3 [1Y]#> # Key: Sex [2]#> Sex Year kt#> <chr> <int> <dbl>#> 1 Female 1900 115.#> 2 Female 1901 109.#> 3 Female 1902 103.#> 4 Female 1903 109.#> 5 Female 1904 106.#> 6 Female 1905 110.#> 7 Female 1906 101.#> 8 Female 1907 106.#> 9 Female 1908 105.#> 10 Female 1909 99.6#> # ℹ 238 more rows
fit|> forecast(h=20)#> # A vital fable: 8,080 x 6 [1Y]#> # Key: Age x (Sex, .model) [101 x 4]#> Sex .model Year Age Mortality .mean#> <chr> <chr> <dbl> <int> <dist> <dbl>#> 1 Female lee_carter 2024 0 t(N(-6.8, 0.0088)) 0.00110#> 2 Female lee_carter 2025 0 t(N(-6.9, 0.018)) 0.00106#> 3 Female lee_carter 2026 0 t(N(-6.9, 0.027)) 0.00103#> 4 Female lee_carter 2027 0 t(N(-6.9, 0.036)) 0.00100#> 5 Female lee_carter 2028 0 t(N(-7, 0.045)) 0.000972#> 6 Female lee_carter 2029 0 t(N(-7, 0.055)) 0.000944#> 7 Female lee_carter 2030 0 t(N(-7, 0.064)) 0.000916#> 8 Female lee_carter 2031 0 t(N(-7.1, 0.074)) 0.000889#> 9 Female lee_carter 2032 0 t(N(-7.1, 0.084)) 0.000863#> 10 Female lee_carter 2033 0 t(N(-7.1, 0.094)) 0.000838#> # ℹ 8,070 more rows
The forecasts are returned as a distribution column (here transformednormal because of the log transformation used in the model). The.meancolumn gives the point forecasts equal to the mean of the distributioncolumn.
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Tidy Analysis Tools for Mortality, Fertility, Migration and Population Data
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