weighted mean

weighted_mean.r

# Number of individuals in the population
npop <- 100000

# Distribution of variable in the population
x <- rnorm(npop)

# Individuals selected into sample with high x value
s <- rbinom(npop, 1, plogis(x * 0.4))

# Population mean of x
mean(x)

# Mean of x in selected sample
mean(x[s==1])

# Mean of x in unselected sample
mean(x[s==0])

# Estimate probability of being selected into sample
# Ordinarily might use a range of different variables to construct a predictor
mod <- glm(s ~ x, family="binomial")

# Get probabilities of being selected into sample
f <- fitted.values(mod)

# Generate weights
weight <- 1/f[s==1]

# Estimate mean of x in population by weighting the sample
sum(x[s==1] * weight) / sum(weight)

# Compare to population mean
mean(x)