tetcorQuasi {fungible}

Correlation between a Naturally and an Artificially Dichotomized Variable

Description

A function to compute Ulrich and Wirtz's correlation of a naturally and an artificially dichotomized variable.

Usage

tetcorQuasi(x, y = NULL)

Arguments

x

An N x 2 matrix or an N x 1 vector of binary responses coded 0/1.

y

An optional (if x is a vector) vector of 0/1 responses.

Value

A quasi tetrachoric correlation

...

Author(s)

Niels Waller

References

Ulrich, R. & Wirtz, M. (2004). On the correlation of a naturally and an artificially dichotomized variable. British Journal of Mathematical and Statistical Psychology, 57, 235-252.

Examples

set.seed(321)
Nsubj <- 5000

## Generate mvn data with rxy = .5
R <- matrix(c(1, .5, .5, 1), 2, 2)
X <- MASS::mvrnorm(n = Nsubj, mu = c(0, 0), Sigma = R, empirical = TRUE)

## dichotomize data
thresholds <- qnorm(c(.2, .3))
binaryData <- matrix(0, Nsubj, 2)

for(i in 1:2){
  binaryData[X[,i] <= thresholds[i],i] <- 1
}   

## calculate Pearson correlation
cat("\nPearson r: ", round(cor(X)[1,2], 2))

## calculate Pearson Phi correlation
cat("\nPhi r: ", round(cor(binaryData)[1,2], 2))

## calculate tetrachoric correlation
cat("\nTetrachoric r: ", round(tetcor(binaryData)$r[1,2], 2))

## calculate Quasi-tetrachoric correlation
cat("\nQuasi-tetrachoric r: ", round(tetcorQuasi(binaryData), 2))