# correct.cor: Find dis-attenuated correlations given correlations and... In psych: Procedures for Psychological, Psychometric, and Personality Research

## Description

Given a raw correlation matrix and a vector of reliabilities, report the disattenuated correlations above the diagonal.

## Usage

 `1` ```correct.cor(x, y) ```

## Arguments

 `x` A raw correlation matrix `y` Vector of reliabilities

## Details

Disattenuated correlations may be thought of as correlations between the latent variables measured by a set of observed variables. That is, what would the correlation be between two (unreliable) variables be if both variables were measured perfectly reliably.

This function is mainly used if importing correlations and reliabilities from somewhere else. If the raw data are available, use `score.items`, or `cluster.loadings` or `cluster.cor`.

Examples of the output of this function are seen in `cluster.loadings` and `cluster.cor`

## Value

Raw correlations below the diagonal, reliabilities on the diagonal, disattenuated above the diagonal.

## Author(s)

Maintainer: William Revelle revelle@northwestern.edu

## References

Revelle, W. (in preparation) An Introduction to Psychometric Theory with applications in R. Springer. at https://personality-project.org/r/book/

`cluster.loadings` and `cluster.cor`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```# attitude from the datasets package #example 1 is a rather clunky way of doing things a1 <- attitude[,c(1:3)] a2 <- attitude[,c(4:7)] x1 <- rowSums(a1) #find the sum of the first 3 attitudes x2 <- rowSums(a2) #find the sum of the last 4 attitudes alpha1 <- alpha(a1) alpha2 <- alpha(a2) x <- matrix(c(x1,x2),ncol=2) x.cor <- cor(x) alpha <- c(alpha1\$total\$raw_alpha,alpha2\$total\$raw_alpha) round(correct.cor(x.cor,alpha),2) # #much better - although uses standardized alpha clusters <- matrix(c(rep(1,3),rep(0,7),rep(1,4)),ncol=2) cluster.loadings(clusters,cor(attitude)) # or clusters <- matrix(c(rep(1,3),rep(0,7),rep(1,4)),ncol=2) cluster.cor(clusters,cor(attitude)) # #best keys <- make.keys(attitude,list(first=1:3,second=4:7)) scores <- scoreItems(keys,attitude) scores\$corrected #However, to do the more general case of correcting correlations for reliabilty #corrected <- cor2cov(x.cor,1/alpha) #diag(corrected) <- 1 ```