EFA.dimensions (version 0.1.8.6)

CORRECTED_CORRELS: Corrected Pearson correlation coefficients

Description

Corrects Pearson correlation coefficients for attenuation due to unreliability and tests for overall differences between the original and corrected correlation matrices.

Usage

CORRECTED_CORRELS(cormat, Ncases = 100, alphas, 
                  systematic=FALSE, Nperms = 1000, verbose=TRUE)

Value

A list with the following elements:

cormat

The entered correlation matrix

alphas

The entered alphas

corxd

The matrix of corrected correlations

resids

The differences between the entered and corrected correlations

data_in_rows

The input data and results in row format

cor_spearman

The Spearman's rho correlation between the entered and corrected correlations

cor_kendall

The Kendall's tau correlation between the entered and corrected correlations

Steiger_test

Results of the Steiger test for equality of the entered and corrected correlation matrices

Jennrich_test

Results of the Jennrich test for equality of the entered and corrected correlation matrices

Arguments

cormat

A square correlation matrix.

Ncases

The number of cases upon which cormat is based.
Example: Ncases = 250

alphas

A vector of reliability coefficients (e.g., Cronbach alpha values) for the variables in cormat, in the same order as the variables in cormat.
Example: alphas <- c(.81, .95, .64, .49, .36)

systematic

The kind of permutations for the tests for significance differences between the uncorrected and corrected correlation matrices. The options are TRUE (for all possible permutations), or FALSE (the default), in which case random matrix permutations will be conducted.

Nperms

(optional) The number of random matrix permutation for when systematic = FALSE.
Example: Nperms = 1000

verbose

(optional) Should detailed results be displayed in console? TRUE (default) or FALSE

Author

Brian P. O'Connor

Details

This function uses the simple, traditional formula for correcting correlations for attentuation due to unreliability, as described in Schmidt and Hunter (1996), Schmitt (1996), and Trafimow (2016).

Spearman's rho and Kendall's tau correlations between the values in the entered and corrected correlation matrices are provided when there are three or more variables. These are rank correlations that do not assume that similarity increases are linear and which are more robust to outliers than are Pearson correlations. The corresponding permutation significance tests of overall equality between the entered and corrected correlation matrices are "Mantel" tests.

The Steiger (1980) and Jennrich (1970) tests of the overall equality of the entered and corrected correlation matrices are conducted using functions from the psych package (Revelle, 2023).

See the MatrixCorrelation package for additional tests of differences between correlation matrices.

References

Jennrich, R. I. (1970) An asymptotic test for the equality of two correlation matrices. Journal of the American Statistical Association, 65, 904-912.

Revelle, W. (2023). psych: Procedures for Psychological, Psychometric, and Personality Research. R package version 2.3.6, https://CRAN.R-project.org/package=psych

Schmidt, F. L., & Hunter, J. E. (1996). Measurement error in psychological research: Lessons from 26 research scenarios. Psychological Methods, 1(2), 199223.

Schmitt, N. (1996). Uses and abuses of coefficient alpha. Psychological Assessment, 8(4), 350353.

Steiger, J. H. (1980). Testing pattern hypotheses on correlation matrices: Alternative statistics and some empirical results. Multivariate Behavioral Research, 15, 335-352.

Trafimow, D. (2016). The attenuation of correlation coefficients: A statistical literacy issue. Teaching Statistics, 38(1), 2528.

Examples

# data from Schmitt (1996)
cormat <- '
 1.0
 .70  1.0
 .51  .47  1.0  
 .52  .55  .45  1.0
 .32  .35  .31  .28  1.0'
cormat_noms <- c('v1', 'v2', 'v3', 'v4', 'v5')
cormat <- data.matrix( read.table(text=cormat, fill=TRUE, col.names=cormat_noms, 
                                  row.names=cormat_noms ))
cormat[upper.tri(cormat)] <- t(cormat)[upper.tri(cormat)]

alphas <- c(.81, .95, .64, .49, .36)

CORRECTED_CORRELS(cormat=cormat, alphas=alphas, 
                  Nperms = 10000, systematic=FALSE, verbose=TRUE)