Quick model about name-gender associations

gistfile1.txt

library(ggplot2)

# Here, I use 'Kim' as shorthand for all names that differ in gender association between the local and immigrant population
# For simplicity I assume Kim is an equally common name in both countries
expand.grid(
  p_kim_local = c(0.001, 0.01, 0.05, 0.1), # True proportion of locally-born people named Kim
  p_male_kim_immigrants = 0.90, # pTrue roportion males among foreign-born people named Kim:
  p_male_kim_locals = 0.10, # True proportion males among locally-born people named Kim:
  p_male_kim_GENDERIZE = seq(0.1, 0.9, length = 11), # worldwide estimate for gender of people named Kim from Genderize.io
  p_immigrants = seq(0, 0.5, length = 11), # True proportion of researchers who are immigrants
  p_immigrants_male = 0.8, # True proportion of males among immigrant researchers not named Kim
  p_residents_male = 0.6 # True proportion of males among non-immigrant researchers not named Kim
) -> parameters
parameters$p_kim_foreign <- parameters$p_kim_local 

# Calculate the real proportion of males, across immigrants and non-immigrants in the focal country
parameters$real_pMale <-
  with(parameters,
       (1 - p_immigrants) * p_kim_local * p_male_kim_locals + # pMale among non-immigrants named Kim
         p_immigrants * p_kim_foreign * p_male_kim_immigrants +  # pMale among immigrants named Kim
         (1 - p_immigrants) * (1 - p_kim_local) * p_residents_male + # pMale among non-immigrants NOT named Kim
         p_immigrants * (1 - p_kim_local) * p_immigrants_male  # pMale among immigrants NOT named Kim
  )

# Estimate pMale, if we ignore country and use the world-wide estimate from Genderize.io
parameters$estimated_pMale_worldwide <-
  with(parameters,
       (1 - p_immigrants) * p_kim_local * p_male_kim_GENDERIZE + # pMale among non-immigrants named Kim
         p_immigrants * p_kim_foreign * p_male_kim_GENDERIZE +  # pMale among immigrants named Kim
         (1 - p_immigrants) * (1 - p_kim_local) * p_residents_male + # pMale among non-immigrants NOT named Kim
         p_immigrants * (1 - p_kim_local) * p_immigrants_male  # pMale among immigrants NOT named Kim
  )

# Estimate pMale, if we DO NOT ignore country, and use the country-specific estimate from Genderize.io
# I assume this ends up mis-classifying more immigrants, but improves classification of non-immigrants
parameters$estimated_pMale_local <-
  with(parameters,
       (1 - p_immigrants) * p_kim_local * p_male_kim_locals + # pMale among non-immigrants named Kim
         p_immigrants * p_kim_foreign * p_male_kim_locals +  # pMale among immigrants named Kim
         (1 - p_immigrants) * (1 - p_kim_local) * p_residents_male + # pMale among non-immigrants NOT named Kim
         p_immigrants * (1 - p_kim_local) * p_immigrants_male  # pMale among immigrants NOT named Kim
  )

# Calculate the difference in the absolute error when estimating the % men
# Positive numbers mean it is better to use the local name-gender associations, as done by Holman et al
parameters$difference_in_error <- with(parameters,
                               100*abs(estimated_pMale_worldwide - real_pMale) - 
  100*abs(estimated_pMale_local - real_pMale)
)

# Blue areas are places where it is best to use the country-specific associations
# Red areas show where it is best to ignore them, and use the world-wide estimate
ggplot(parameters, 
                aes(p_immigrants, 
                    p_male_kim_GENDERIZE, 
                    fill = difference_in_error)) + 
  geom_tile() + 
  scale_fill_gradient2(name = "Error in estimate\nof % males") + 
  facet_wrap(~p_kim_local) + 
  xlab("Proportion of researchers who are immigrants") + 
  ylab("Worldwide frequency of men\namong people named Kim") +
  labs(title = "Blue means it's best to not ignore the country information",
          subtitle = "Facets show frequency of people named Kim")