Inverse-normal (rank-based) transformation

Applies a rank-based inverse-normal transformation (INT) to a numeric vector, placing empirical quantiles onto a standard normal scale.

int_transform(x, ties = "average")

Arguments

x

Numeric vector. NAs are preserved.

ties

Method passed to base::rank(). Default "average".

Value

A numeric vector of the same length as x, with NAs in the same positions and non-missing values transformed to approximate normality.

Details

The Blom-style formula used is: $$\Phi^{-1}\!\left(\frac{r_i - 0.5}{n}\right)$$ where \(r_i\) is the rank of observation \(i\) and \(n\) is the number of non-missing observations. This is the standard transformation used in SOLAR Eclipse and most variance-components heritability software.

Examples

set.seed(1)
x <- rexp(200, rate = 0.5)   # right-skewed
hist(x,              main = "Raw")

hist(int_transform(x), main = "INT")