tetrachoric under different scenarios

tetrachoric.r

library(mvtnorm)
library(psych)

n <- 100000
dn <- rmvnorm(n, c(0,0), matrix(c(1,0.5, 0.5,1), 2))

# 50% prevalence
d <- dn
d[,1] <- rbinom(n, 1, pnorm(d[,1]))
d[,2] <- rbinom(n, 1, pnorm(d[,2]))

tetrachoric(table(d[,1], d[,2]))


# Sample liability but 5% prevalence
d <- dn
d[,1] <- rbinom(n, 1, pnorm(d[,1])/10)
d[,2] <- rbinom(n, 1, pnorm(d[,2])/10)

tetrachoric(table(d[,1], d[,2]))


# Ascertain data - aim for sample size with 50% cases and controls for trait 1

d <- dn
d[,1] <- rbinom(n, 1, pnorm(d[,1])/10)
d[,2] <- rbinom(n, 1, pnorm(d[,2])/10)

d <- rbind(
	d[d[,1] == 1,],
	d[d[,1] == 0, ][1:sum(d[,1] == 1),]
)

tetrachoric(table(d[,1], d[,2]))