Compute the disattenuation correction for measurement error

Estimates the true correlation between two variables by correcting the observed correlation for attenuation due to measurement error in both variables.

Usage

compute_dissatenuation(variable1, error1, variable2, error2)

Arguments

variable1

Numeric vector. True scores for the first variable.

error1

Numeric vector. Measurement error for variable1. Must be the same length as variable1.

variable2

Numeric vector. True scores for the second variable.

error2

Numeric vector. Measurement error for variable2. Must be the same length as variable2.

Value

A numeric scalar. The disattenuated (corrected) correlation between variable1 and variable2.

Details

The observed correlation is computed from the error-contaminated scores (variable + error). Reliability for each variable is estimated as the ratio of true score variance to total observed variance. The disattenuated correlation is then: $$\rho = \frac{r_{obs}}{\sqrt{R_1 \cdot R_2}}$$ where \(R_1\) and \(R_2\) are the reliability estimates.

Examples

set.seed(1)
compute_dissatenuation(rnorm(10), rnorm(10), rnorm(10), rnorm(10))
#> [1] 0.1306254