1 The DemoKin package
2 Example 1: kin counts in stable populations
3 Example 2: population with changing rates
- 3.1 Period perspective
- 3.2 Cohort perspective
4 In the pipeline
5 Get involved!
6 Acknowledgement
7 Appendix: Obtaining U matrix from a life table
8 Session Information
References

Get the Rmd version of this file: https://github.com/alburezg/DemoKin_example

1 The `DemoKin` package

DemoKin uses matrix demographic methods to compute expected (average) kin counts from demographic rates under a range of scenarios and assumptions. The package is an R-language implementation of Caswell (2019; 2021) and draws on previous theoretical development by Goodman, Keyfitz and Pullum (1974).

Kin count estimation has a long history in mathematical demography, starting with the work of (Lotka 1931) on modeling orphanhood in theoretical populations across demographic regimes. To the best of our knowledge, Brass (1953) proposed the first kinship equation to estimate child survival over maternal age. Goodman et. al (1974) generalized this approach to sisters, granddaughters, cousins, etc., in stable and non-stable populations. The so-called Goodman-Keyfitz-Pullum Kinship Equations were popularized by Keyfitz and Caswell (2005) and Bongaarts (1987) used a similar approach to estimate descendants in his ‘Family Status Model’. More recently, Caswell (2019; 2021) introduce the matrix approach that DemoKin is based on.

1.1 Installation

You can install the development version from GitHub with:

Note that we made changes to the DemoKin package ahead of this presentation. If you had already installed the package, please uninstall it and and install it again.

# remove.packages("DemoKin")
# install.packages("devtools")
devtools::install_github("IvanWilli/DemoKin")
# devtools::install_github("IvanWilli/DemoKin", build_vignettes = TRUE)

1.2 The function `kin()`

DemoKin::kin() currently does most of the heavy lifting in terms of implementing matrix kinship models. This is what it looks like in action, in this case assuming demographic stability:

library(DemoKin)
library(tidyverse)

stable <- 
  kin(
    U = swe_surv
    , f = swe_asfr
    , stable = TRUE
    , focal_year = 1950
    )

1.2.1 Arguments

U matrix; numeric. A matrix of survival ratios with rows as ages and columns as years. The name of each col must be the year.
f numeric. A matrix of age-specific fertility rates with rows as ages and columns as years. The name of each col must be the year.
N numeric. A matrix of population with rows as ages and columns as years. The name of each col must be the year (only needed for non-stable computation)
pi numeric. A matrix with distribution of childbearing with rows as ages and columns as years. The name of each col must be the year.
stable logical. Stable assumption given year rates, taking focal_year in case is U and f are matrix.
focal_cohort integer. Year of birth of focal. Could be a vector. Should be within input data years range.
focal_year integer. Year of focal. Could be a vector. Should be within input data years range.
birth_female numeric; proportion of births that are female
selected_kin character. kin to return: “m” for mother, “d” for daughter… If NULL, return values for all relatives
living logical. Only living kin counts TRUE, or including death kin FALSE.

Note that DemoKin only requires period demographic rate data as input!

1.2.2 Details

Relatives for the selected_kin argument are identified by a unique code. Note that the relationship codes used in DemoKin differ from those in Caswell (2019). The equivalence between the two set of codes is given in the following table:

Table 1.1: Equivalence between relative codes between DemoKin and Caswell (2019).
DemoKin	Caswell	Label
coa	t	Cousins from older aunt
cya	v	Cousins from younger aunt
d	a	Daughter
gd	b	Grand-daughter
ggd	c	Great-grand-daughter
ggm	h	Great-grandmother
gm	g	Grandmother
m	d	Mother
nos	p	Nieces from older sister
nys	q	Nieces from younger sister
oa	r	Aunt older than mother
ya	s	Aunt younger than mother
os	m	Older sister
ys	n	Younger sister

1.3 Built-in data

The DemoKin package includes data from Sweden as an example. The data comes from the Human Mortality Database and Human Fertility Database. These datasets were loaded using theDemoKin::get_HMDHFD function. To list the data:

data(package="DemoKin")

Item	Title
swe_asfr	Swedish age-specific fertility rates from 1900 to 2015
swe_pop	Female swedish population from 1900 to 2015
swe_surv	Female swedish survival ratios from 1900 to 2015

The in-built data sets are:

1.3.1 `swe_surv` matrix; survival ratio by age (DemoKin’s U argument)

The appendix shows how to obtain these survival matrices from standard life tables. This is what the data looks like:

swe_surv[1:4, 1:4]

##        1900      1901      1902      1903
## 2 0.9566306 0.9555890 0.9624144 0.9611063
## 3 0.9786518 0.9792724 0.9807146 0.9818320
## 4 0.9875967 0.9876130 0.9885345 0.9897997
## 5 0.9907708 0.9904054 0.9915360 0.9923815

And plotted over time and age:

library(fields)

image.plot(
  x = as.numeric(colnames(swe_surv))
  , y = 0:nrow(swe_surv)
  , z = t(as.matrix(swe_surv))
  , xlab = "Year"
  , ylab = "Survival ratio (U)"
  )

1.3.2 `swe_asfr` matrix; age specific fertility rate (DemoKin’s f argument)

This is what the data looks like:

swe_asfr[15:20, 1:4]

##       1900    1901    1902    1903
## 15 0.00013 0.00006 0.00008 0.00008
## 16 0.00053 0.00054 0.00057 0.00057
## 17 0.00275 0.00319 0.00322 0.00259
## 18 0.00932 0.00999 0.00965 0.00893
## 19 0.02328 0.02337 0.02347 0.02391
## 20 0.04409 0.04357 0.04742 0.04380

And plotted over time and age:

image.plot(
  x = as.numeric(colnames(swe_asfr))
  , y = 0:nrow(swe_asfr)
  , z = t(as.matrix(swe_asfr))
  , xlab = "Year"
  , ylab = "Age-specific fertility (f)"
  )

1.3.3 `swe_pop` matrix; population by age (DemoKin’s N argument)

This is what the data looks like:

swe_pop[1:4, 1:4]

## # A tibble: 4 x 4
##   `1900` `1901` `1902` `1903`
##    <dbl>  <dbl>  <dbl>  <dbl>
## 1  60917  62601  63337  63500
## 2  58927  57549  59573  60627
## 3  56823  57590  56426  58381
## 4  56473  55916  56887  55669

And plotted over time and age:

image.plot(
  x = as.numeric(colnames(swe_pop))
  , y = 0:nrow(swe_pop)
  , z = t(as.matrix(swe_pop))
  , xlab = "Year"
  , ylab = "Population counts by age (N)"
  )

1.4 Value

DemoKin::kin() returns a list containing two data frames: kin_full and kin_summary.

str(stable)

## List of 2
##  $ kin_full   :'data.frame': 142814 obs. of  7 variables:
##   ..$ year     : num [1:142814] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ cohort   : num [1:142814] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ age_focal: int [1:142814] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ kin      : chr [1:142814] "d" "d" "d" "d" ...
##   ..$ age_kin  : int [1:142814] 0 1 2 3 4 5 6 7 8 9 ...
##   ..$ alive    : chr [1:142814] "yes" "yes" "yes" "yes" ...
##   ..$ count    : num [1:142814] 0 0 0 0 0 0 0 0 0 0 ...
##  $ kin_summary: tibble[,7] [1,414 x 7] (S3: tbl_df/tbl/data.frame)
##   ..$ year     : num [1:1414] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ cohort   : num [1:1414] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ age_focal: int [1:1414] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ kin      : chr [1:1414] "coa" "cya" "d" "gd" ...
##   ..$ count    : num [1:1414] 0.402 0.134 0 0 0 ...
##   ..$ mean_age : num [1:1414] 10.18 5.04 NaN NaN NaN ...
##   ..$ sd_age   : num [1:1414] 7.42 4.42 NaN NaN NaN ...

1.4.1 `kin_full`

This data frame contains expected kin counts by year (or cohort), age of Focal and age of kin.

head(stable$kin_full)

##   year cohort age_focal kin age_kin alive count
## 1    0      0         0   d       0   yes     0
## 2    0      0         0   d       1   yes     0
## 3    0      0         0   d       2   yes     0
## 4    0      0         0   d       3   yes     0
## 5    0      0         0   d       4   yes     0
## 6    0      0         0   d       5   yes     0

1.4.2 `kin_summary`

This is a ‘summary’ data frame derived from kin_full. To produce it, we sum over all ages of kin to produce a data frame of expected kin counts by year or cohort and age of Focal (but not by age of kin). This is how the kin_summary object is derived:

kin_by_age_focal <- 
  stable$kin_full %>% 
  select(year, cohort, kin, age_focal, age_kin, count) %>% 
  group_by(year, cohort, kin, age_focal) %>% 
  summarise(count = sum(count)) %>% 
  ungroup()

## `summarise()` has grouped output by 'year', 'cohort', 'kin'. You can override using the `.groups` argument.

# Check that they are identical

kin_by_age_focal %>% 
  identical(
    stable$kin_summary %>% 
      select(year, cohort, kin, age_focal, count) %>% 
      arrange(year, cohort, kin, age_focal)
  )

## [1] TRUE

2 Example 1: kin counts in stable populations

Following Caswell (2019), we assume a female closed population in which everyone experiences the Swedish 1950 mortality and fertility rates at each age throughout their life. We then ask:

How can we characterize the kinship network of an average member of the population (call her ‘Focal’)?

For this exercise, we’ll use the Swedish data pre-loaded with DemoKin.

library(DemoKin)

system.time(
  stable <- 
  kin(
    focal_year = 1950
    , U = swe_surv
    , f = swe_asfr
    , stable = TRUE
    )
)

##    user  system elapsed 
##    0.71    0.06    0.77

2.1 ‘Keyfitz’ kinship diagram

We can visualize the implied kin counts for a Focal woman aged 35 yo in a stable population using a network or ‘Keyfitz’ kinship diagram (Keyfitz and Caswell 2005) using the plot_diagram function:

stable$kin_summary %>% 
  filter(age_focal == 35) %>% 
  select(kin, count) %>% 
  plot_diagram()

2.2 Expected kin counts for a Focal person surviving to each age

Before showing the results, we define a simple function to identify relatives based on their respective codes. The kinship codes (e.g., “gm”, “ggm”) are useful for filtering the data but confusing for visualization.

rename_kin <- function(df, consolidate = F){
  
  if(!consolidate){
    
    relatives <- c("Cousins from older aunt", "Cousins from younger aunt", "Daughter", "Grand-daughter", "Great-grand-daughter", "Great-grandmother", "Grandmother", "Mother", "Nieces from older sister", "Nieces from younger sister", "Aunt older than mother", "Aunt younger than mother", "Older sister", "Younger sister")
    names(relatives) <- c("coa", "cya", "d", "gd", "ggd", "ggm", "gm", "m", "nos", "nys", "oa", "ya", "os", "ys")
    
  } else if(consolidate){
    
    # Combine kin types irrespective of whether they come from older
    # or younger sibling lines
    consolidate <- c("c", "c", "d", "gd", "ggd", "ggm", "gm", "m", "n", "n", "a", "a", "s", "s")
    names(consolidate) <- c("coa", "cya", "d", "gd", "ggd", "ggm", "gm", "m", "nos", "nys", "oa", "ya", "os", "ys")
    
    # Rename kin types from codes to actual words
    relatives <- c("Cousins", "Daughter", "Grand-daughter", "Great-grand-daughter", "Great-grandmother", "Grandmother", "Mother", "Nieces", "Aunt", "Sister")
    names(relatives) <-  unique(consolidate)
    
    df <- 
      df %>% 
      mutate(kin = consolidate[kin]) %>%
      group_by(age_focal, kin) %>%
      summarise(count = sum(count)) %>% 
      ungroup() 
    
  }
  df$kin <- relatives[df$kin]
  df  
}

Now, let’s visualize how the expected number of daughters, siblings, cousins, etc., changes over the lifecourse of Focal.

stable$kin_summary %>%
  rename_kin(., consolidate = T) %>% 
  ggplot() +
  geom_line(aes(age_focal, count))  +
  geom_vline(xintercept = 35, color=2)+
  theme_bw() +
  labs(x = "Focal's age") +
  facet_wrap(~kin)

## `summarise()` has grouped output by 'age_focal'. You can override using the `.groups` argument.

2.2.1 Family size

How does overall family size (and family composition) vary over life for an average woman who survives to each age?

counts <- 
  stable$kin_summary %>%
  group_by(age_focal) %>% 
  summarise(count = sum(count)) %>% 
  ungroup()

counts %>% 
  ggplot() +
  geom_line(aes(age_focal, count), size = 1)  +
  coord_cartesian(ylim = c(0, 6)) + 
  theme_bw() +
  labs(x = "Focal's age", y = "Number of living female relatives")

We can decompose this by relative type:

stable$kin_summary %>%
  select(age_focal, kin, count) %>% 
  rename_kin(., consolidate = T) %>% 
  ggplot(aes(x = age_focal, y = count)) +
  geom_area(aes(fill = kin), colour = "black") +
  geom_line(data = counts, size = 2) +
  labs(x = "Focal's age", y = "Number of living female relatives") +
  coord_cartesian(ylim = c(0, 6)) + 
  theme_bw() +
  theme(legend.position = "bottom")

## `summarise()` has grouped output by 'age_focal'. You can override using the `.groups` argument.

2.3 Deceased kin

We have focused on living kin, but what about relatives who have died? We can get the cumulative number of kin deaths experienced by an average Focal surviving to a given age by setting the parameter living = FALSE. This creates a new element kin_death_by_age_focal in the output value of kin():

stable_death <- 
  kin(
    focal_year = 1950
    , U = swe_surv
    , f = swe_asfr
    , stable = TRUE
    , living = FALSE
    )

2.3.1 Non-cumulative counts of kin deaths experienced by Focal

We start by considering the number of kin deaths that an average can expect to experience at each age. In other words, the non-cumulative number of deaths in the family that Focal experiences at a given age.

loss1 <- 
  stable_death$kin_summary %>%
  filter(alive =="no", age_focal>0) %>%
  group_by(age_focal) %>% 
  summarise(count = sum(count)) %>% 
  ungroup()

loss1 %>% 
  ggplot() +
  geom_line(aes(age_focal, count), size = 1)  +
  labs(x = "Focal's age", y = "Number of kin deaths experienced (non-cumulative)") +
  theme_bw()

How are these deaths distributed by type of relative? We can decompose this by kin type:

stable_death$kin_summary %>%
  filter(alive =="no", age_focal>0) %>%
  group_by(age_focal, kin) %>% 
  summarise(count = sum(count)) %>% 
  ungroup() %>% 
  rename_kin(., consolidate = T) %>% 
  ggplot(aes(x = age_focal, y = count)) +
  geom_area(aes(fill = kin), colour = "black") +
  geom_line(data = loss1, size = 2) +
  labs(x = "Focal's age", y = "Number of kin deaths experienced (cumulative)") +
  theme_bw() +
  theme(legend.position = "bottom")

## `summarise()` has grouped output by 'age_focal'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'age_focal'. You can override using the `.groups` argument.

2.3.2 Cumulative number of kin deaths

Now, we combine all kin types to show the cumulative burden of kin death for an average member of the population surviving to each age:

loss2 <- 
  stable_death$kin_summary %>%
  filter(alive =="no") %>%
  group_by(age_focal) %>% 
  summarise(count = sum(count_cum)) %>% 
  ungroup()

loss2 %>% 
  ggplot() +
  geom_line(aes(age_focal, count), size = 1)  +
  labs(x = "Focal's age", y = "Number of kin deaths experienced (cumulative)") +
  theme_bw()

A member of the population aged 15, 50, and 65yo will have experienced, on average, the death of 0.6, 2.6, 3.7 relatives, respectively. We can decompose this by relative type:

stable_death$kin_summary %>%
  filter(alive =="no") %>%
  group_by(age_focal, kin) %>% 
  summarise(count = sum(count_cum)) %>% 
  ungroup() %>% 
  rename_kin(., consolidate = T) %>% 
  ggplot(aes(x = age_focal, y = count)) +
  geom_area(aes(fill = kin), colour = "black") +
  geom_line(data = loss2, size = 2) +
  labs(x = "Focal's age", y = "Number of kin deaths experienced (cumulative)") +
  theme_bw() +
  theme(legend.position = "bottom")

## `summarise()` has grouped output by 'age_focal'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'age_focal'. You can override using the `.groups` argument.

2.4 Age distribution of relatives

How old are Focal’s relatives? Using the kin_full data frame, we can visualize the age distribution of Focal’s relatives throughout Focal’s life. As an example, let’s pick three points of Focal’s life: when she’s born (age=0) at the end of her reproductive life (age=50) and when she retires (age=65).

stable$kin_full %>%
  filter(age_focal %in% c(0, 50, 65)) %>% 
  filter(kin %in% c("m", "d", "os", "ys")) %>%
  mutate(age_focal = as.character(age_focal)) %>% 
  rename_kin() %>% 
  ggplot() +
  geom_line(aes(age_kin, count, colour = age_focal), size = 1) +
  scale_color_discrete("Focal's age") +
  labs(x = "Age of Focal's kin", y = "Age distribution") +
  theme_bw() +
  facet_wrap(~kin)

The output of the DemoKin::kin() function can also be used to easily determine the mean age Focal’s relatives by kin type. For simplicity, let’s focus on a Focal aged 35 yo and get the mean age (and standard deviation) of her relatives in our stable population.

ages_df <- 
  stable$kin_summary %>% 
  filter(age_focal == 35) %>% 
  select(kin, mean_age, sd_age)

ma <- 
  ages_df %>% 
  filter(kin=="m") %>% 
  pull(mean_age) %>% 
  round(1)

sda <- 
  ages_df %>% 
  filter(kin=="m") %>% 
  pull(sd_age) %>% 
  round(1)

We can say that the mother of a 35-yo Focal woman in our stable population is, on average, 61.8 years old, with a standard deviation of 5.9 years.

3 Example 2: population with changing rates

The real population is Sweden is not stable: individuals in it experience changing mortality and fertility rates throughout their life. Kinship structures in populations with changing rates can be computed following Caswell and Song (2021).

All the outputs that we showed for stable populations in the previous section are also available for non-stable populations (e.g., kin counts, deceased kin, and age distributions). In this section we’ll focus on outputs that are specific to time-varying kinship structures. In particular, we’ll show period, cohort, and age results for Sweden (Figure 5 from Caswell and Song (2021)).

Note that, in order to arrive a this results, we use a different set of input values. The objects U_caswell_2021, f_caswell_2021, and pi_caswell_2021 were extracted by Ivan from the supplementary materials provided by Caswell and Song (2021). They are included in DemoKin by default.

data(package="DemoKin")

Item	Title
U_caswell_2021	Historic and projected survival ratios from Sweden used in Caswell (2021)
f_caswell_2021	Historic and projected fertility ratios from Sweden used in Caswell (2021)
pi_caswell_2021	Historic and projected mother´s age distribution of childbearing from Sweden used in Caswell (2021)

3.1 Period perspective

Our first illustration refers to a period view of kin counts. Following Caswell, we consider a population that experienced the demographic rates given as input to DemoKin and ask:

How many living daughters would an average woman have at different ages, if we conducted a survey at a given point in time?

In order to provide these results, we re-run the kin() function with the stable = FALSE parameter and the input rates from Caswell and Song (2021). Note that we provide DemoKin with a vector of the period years for which we want to obtain the kin counts (i.e., in the focal_year argument).

system.time(
swe_period <- 
  kin(
    U = U_caswell_2021
    , f = f_caswell_2021
    , pi = pi_caswell_2021
    , stable = F
    , birth_female = 1
    # Note that we use the 'focal_year' parameters as input
    , focal_year = c(1891,1951,2050,2120)
    # We're only interested in certain kin ties
, selected_kin = c("d","gd","m","gm","os","ys")
)
)

## Assuming stable population before 1891.

##    user  system elapsed 
##   50.42    0.33   52.11

Now, we plot the expected number of daughters that Focal throughout her life at different points in time:

swe_period$kin_summary %>%
  filter(kin == "d") %>% 
  rename_kin() %>% 
  mutate(year = factor(year)) %>% 
  ggplot(aes(age_focal,count,color=year)) +
  geom_line(size=1)+
  labs(x = "Focal's age", y = "Number of daughters") + 
  theme_bw() +
  theme(legend.position = "bottom")

In a similar way, we can ask, how many grand-daughters, sisters, etc., would an average woman have at different points in time?

swe_period$kin_summary %>%
  rename_kin() %>% 
  mutate(year = factor(year)) %>% 
  ggplot(aes(age_focal,count,color=year)) +
  geom_line(size=1)+
  facet_wrap(~kin, scales = "free")+
  labs(x = "Focal's age", y = "Kin count") + 
  theme_bw() +
  theme(legend.position = "bottom")

3.2 Cohort perspective

We can also visualize the results from a cohort perspective. This would be useful if we were interested in knowing the number of daughters of women in a given cohort at different points in time. We could as, for example:

How many (living) daughters have women born in year 1951 accumulated by the year 2000, on average?

For a cohort perspective, we run the kin() function with the stable = FALSE parameter and with a vector of focal_year values:

system.time(
  swe_coh <- 
    kin(
      U = U_caswell_2021
      , f = f_caswell_2021
      , pi = pi_caswell_2021
      , stable = F
      , birth_female = 1
      # Note that we use the 'focal_cohort' parameters as input
      , focal_cohort = c(1891,1931,1971,2041)
      # We're only interested in certain kin ties
      , selected_kin = c("d","gd","m","gm")
    )
)

## Assuming stable population before 1891.

##    user  system elapsed 
##   66.38    0.25   67.61

Now, we can show the expected number of daughters that women born in different cohorts have at their disposal in any given year:

swe_coh$kin_summary %>%
  filter(kin == "d") %>% 
  rename_kin() %>% 
  mutate(cohort = factor(cohort)) %>% 
  ggplot(aes(year,count,color=cohort)) +
  scale_y_continuous(labels = seq(0,3,.2),breaks = seq(0,3,.2))+
  geom_line(size=1)+
  labs(x = "Year", y = "Number of daughters") + 
  theme_bw() +
  theme(legend.position = "bottom")

We can do the same thing for other kin types to show the expected number of kin for women born in a given cohort across time:

swe_coh$kin_summary %>%
  rename_kin() %>% 
  mutate(cohort = factor(cohort)) %>% 
  ggplot(aes(year,count,color=cohort)) +
  scale_y_continuous(labels = seq(0,3,.2),breaks = seq(0,3,.2))+
  geom_line(size=1)+
  facet_wrap(~kin,scales = "free")+
  labs(x = "Year", y = "Kin count") + 
  theme_bw() +
  theme(legend.position = "bottom")

4 In the pipeline

Hex logo for package
Implement multi-stage (Caswell 2020) and two-sex models (Caswell 2021)
Improve Keyfitz kinship diagrams
Improve documentation and vignette of package

5 Get involved!

DemoKin is giving its first steps. Please contact us via email, or create an issue or submit a pull request on GitHub. You can also get in touch directly:

GitHub:
- https://github.com/IvanWilli/DemoKin
Ivan:
- ivanwilliams1985[at]gmail.com
- https://twitter.com/ivanchowilliams
- https://github.com/IvanWilli
Diego
- alburezgutierrez[at]demogr.mpg.de
- https://twitter.com/d_alburez
- www.alburez.me

6 Acknowledgement

We thank Hal Caswell for sharing code and data from his Demographic Research papers. Mallika Snyder provided useful comments on an earlier version of this handout. For a list of DemoKin contributions, see https://github.com/IvanWilli/DemoKin#citation

7 Appendix: Obtaining U matrix from a life table

Here, we show how to estimate the argument U from DemoKin::kin() (survival ratio by age from a life table) from a standard life table. The code is part of the function DemoKin::get_HMDHFD(). For this example, we use Swedish period life tables from the Human Mortality Database.

library(tidyverse)

lt <- read.table("fltper_1x10.txt", header = T, skip = 2) 

lt$Age[lt$Age == "110+"] <- 110
lt$Age <- as.numeric(lt$Age)

age = 0:100
ages = length(age)
w = last(age)

# survival probabilities
L <- lt %>%
  filter(Age<=w) %>%
  mutate(Lx = ifelse(Age==w, Tx, Lx)) %>%
  select(Year, Age, Lx) %>%
  spread(Year, Lx) %>%
  select(-Age)

U <- rbind(L[c(-1,-101),]/L[-c(100:101),],
           L[101,]/(L[100,]+L[101,]),
           L[101,]/(L[100,]+L[101,]))
   
rownames(U) <- age
colnames(U) <- unique(lt$Year)
U[is.na(U)] <- 0

U[1:4, 1:4]

##   1751-1759 1760-1769 1770-1779 1780-1789
## 0 0.8990951 0.8959954 0.8954728 0.9046334
## 1 0.9494330 0.9520463 0.9402367 0.9476692
## 2 0.9662034 0.9679407 0.9606561 0.9650853
## 3 0.9737870 0.9734861 0.9685377 0.9726419

8 Session Information

sessionInfo()

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19044)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United Kingdom.1252 
## [2] LC_CTYPE=English_United Kingdom.1252   
## [3] LC_MONETARY=English_United Kingdom.1252
## [4] LC_NUMERIC=C                           
## [5] LC_TIME=English_United Kingdom.1252    
## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] igraph_1.2.6       fields_11.6        spam_2.6-0         dotCall64_1.0-1   
##  [5] knitr_1.31         forcats_0.5.1      stringr_1.4.0      dplyr_1.0.5       
##  [9] purrr_0.3.4        readr_1.4.0        tidyr_1.1.3        tibble_3.1.0      
## [13] ggplot2_3.3.3      tidyverse_1.3.0    DemoKin_0.0.0.9000
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.7         lubridate_1.7.10   visNetwork_2.0.9   assertthat_0.2.1  
##  [5] digest_0.6.28      utf8_1.2.1         R6_2.5.0           cellranger_1.1.0  
##  [9] backports_1.2.1    reprex_1.0.0       evaluate_0.14      highr_0.8         
## [13] httr_1.4.2         pillar_1.5.1       rlang_0.4.10       readxl_1.3.1      
## [17] rstudioapi_0.13    jquerylib_0.1.4    rmarkdown_2.7      DiagrammeR_1.0.6.1
## [21] labeling_0.4.2     htmlwidgets_1.5.3  munsell_0.5.0      broom_0.7.5       
## [25] compiler_4.0.2     modelr_0.1.8       xfun_0.21          pkgconfig_2.0.3   
## [29] htmltools_0.5.1.1  tidyselect_1.1.0   bookdown_0.21      fansi_0.4.2       
## [33] crayon_1.4.1       dbplyr_2.1.0       withr_2.4.1        jsonlite_1.7.2    
## [37] gtable_0.3.0       lifecycle_1.0.0    DBI_1.1.1          magrittr_2.0.1    
## [41] scales_1.1.1       cli_2.3.1          stringi_1.5.3      farver_2.1.0      
## [45] fs_1.5.0           xml2_1.3.2         bslib_0.2.5        ellipsis_0.3.1    
## [49] generics_0.1.0     vctrs_0.3.7        RColorBrewer_1.1-2 tools_4.0.2       
## [53] glue_1.4.2         maps_3.3.0         hms_1.0.0          yaml_2.2.1        
## [57] colorspace_2.0-0   rvest_1.0.0        haven_2.3.1        sass_0.4.0

References

Bongaarts, John. 1987. “The Projection of Family Composition over the Life Course with Family Status Life Tables.” In Family Demography: Methods and Their Application, edited by John Bongaarts and Thomas Burch. Oxford: IUSSP Series, Oxford Univer- sity Pres.

Brass, W. 1953. “The Derivation of Fertility and Reproduction Rates from Restricted Data on Reproductive Histories.” Population Studies 7 (2): 137. https://doi.org/10.2307/2172029.

Caswell, Hal. 2021. “The Formal Demography of Kinship. IV. Two-Sex Kinship Models.” (In Preparation).

———. 2019. “The Formal Demography of Kinship: A Matrix Formulation.” Demographic Research 41 (September): 679–712. https://doi.org/10.4054/DemRes.2019.41.24.

———. 2020. “The Formal Demography of Kinship II: Multistate Models, Parity, and Sibship.” Demographic Research 42 (June): 1097–1146. https://doi.org/10.4054/DemRes.2020.42.38.

Caswell, Hal, and Xi Song. 2021. “The Formal Demography of Kinship. III. Kinship Dynamics with Time-Varying Demographic Rates.” Demographic Research 45: 517–46.

Goodman, Leo A. 1974. “Family Formation and the Frequency of Various Kinship Relationships.” Theoretical Population Biology, 27. https://doi.org/10.1016/0040-5809(74)90049-5.

Keyfitz, Nathan, and Hal Caswell. 2005. Applied Mathematical Demography. New York: Springer.

Lotka, Alfred J. 1931. “Orphanhood in Relation to Demographic Factors.” Metron 9 (2): 37–109.

DemoKin: An R package to compute kinship networks in stable and non-stable populations

Ivan Williams (Universidad de Buenos Aires)
Diego Alburez-Gutierrez* (Max Planck Institute for Demographic Research)

Formal Demography Working Group - Feb 25 2022

1 The `DemoKin` package

1.1 Installation

1.2 The function `kin()`

1.2.1 Arguments

1.2.2 Details

1.3 Built-in data

1.3.1 `swe_surv` matrix; survival ratio by age (DemoKin’s U argument)

1.3.2 `swe_asfr` matrix; age specific fertility rate (DemoKin’s f argument)

1.3.3 `swe_pop` matrix; population by age (DemoKin’s N argument)

1.4 Value

1.4.1 `kin_full`

1.4.2 `kin_summary`

2 Example 1: kin counts in stable populations

2.1 ‘Keyfitz’ kinship diagram

2.2 Expected kin counts for a Focal person surviving to each age

2.2.1 Family size

2.3 Deceased kin

2.3.1 Non-cumulative counts of kin deaths experienced by Focal

2.3.2 Cumulative number of kin deaths

2.4 Age distribution of relatives

3 Example 2: population with changing rates

3.1 Period perspective

3.2 Cohort perspective

4 In the pipeline

5 Get involved!

6 Acknowledgement

7 Appendix: Obtaining U matrix from a life table

8 Session Information

References

DemoKin: An R package to compute kinship networks in stable and non-stable populations

Ivan Williams (Universidad de Buenos Aires) Diego Alburez-Gutierrez* (Max Planck Institute for Demographic Research)

Formal Demography Working Group - Feb 25 2022

1 The DemoKin package

1.1 Installation

1.2 The function kin()

1.2.1 Arguments

1.2.2 Details

1.3 Built-in data

1.3.1 swe_surv matrix; survival ratio by age (DemoKin’s U argument)

1.3.2 swe_asfr matrix; age specific fertility rate (DemoKin’s f argument)

1.3.3 swe_pop matrix; population by age (DemoKin’s N argument)

1.4 Value

1.4.1 kin_full

1.4.2 kin_summary

2 Example 1: kin counts in stable populations

2.1 ‘Keyfitz’ kinship diagram

2.2 Expected kin counts for a Focal person surviving to each age

2.2.1 Family size

2.3 Deceased kin

2.3.1 Non-cumulative counts of kin deaths experienced by Focal

2.3.2 Cumulative number of kin deaths

2.4 Age distribution of relatives

3 Example 2: population with changing rates

3.1 Period perspective

3.2 Cohort perspective

4 In the pipeline

5 Get involved!

6 Acknowledgement

7 Appendix: Obtaining U matrix from a life table

8 Session Information

References

Ivan Williams (Universidad de Buenos Aires)
Diego Alburez-Gutierrez* (Max Planck Institute for Demographic Research)

1 The `DemoKin` package

1.2 The function `kin()`

1.3.1 `swe_surv` matrix; survival ratio by age (DemoKin’s U argument)

1.3.2 `swe_asfr` matrix; age specific fertility rate (DemoKin’s f argument)

1.3.3 `swe_pop` matrix; population by age (DemoKin’s N argument)

1.4.1 `kin_full`

1.4.2 `kin_summary`