seBetaCor {fungible}

Standard Errors and CIs for Standardized Regression Coefficients from Correlations

Description

Computes Normal Theory and ADF Standard Errors and CIs for Standardized Regression Coefficients from Correlations

Usage

seBetaCor(R, rxy, Nobs, alpha = 0.05, digits = 3, covmat = "normal")

Arguments

R

A p x p predictor correlation matrix.

rxy

A p x 1 vector of predictor-criterion correlations

Nobs

Number of observations.

alpha

Desired Type I error rate; default = .05.

digits

Number of significant digits to print; default = 3.

covmat

String = 'normal' (the default) or a (p+1)p/2 x (p+1)p/2 covariance matrix of correlations. The default option computes an asymptotic covariance matrix under the assumption of multivariate normal data. Users can supply a covariance matrix under asymptotic distribution free (ADF) or elliptical distributions when available.

Value

cov.Beta

Covariance matrix of standardized regression coefficients.

se.Beta

Vector of standard errors for the standardized regression coefficients.

alpha

Type-I error rate.

CI.Beta

(1-alpha)% confidence intervals for standardized regression coefficients.

Author(s)

Jeff Jones and Niels Waller

References

Jones, J. A, and Waller, N. G. (2013). The Normal-Theory and asymptotic distribution-free (ADF) covariance matrix of standardized regression coefficients: Theoretical extensions and finite sample behavior.Technical Report (052913)[TR052913]

Nel, D.A.G. (1985). A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients. Linear Algebra and its Applications, 67, 137-145.

Yuan, K. and Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76(4), 670–690.

Examples

R <- matrix(c(1.0000, 0.3511, 0.3661,
	          0.3511, 1.0000, 0.4359,
	          0.3661, 0.4359, 1.0000), 3, 3) 

rxy <- c(0.5820, 0.6997, 0.7621)
Nobs <- 46
out <- seBetaCor(R = R, rxy = rxy, Nobs = Nobs) 

# 95% CIs for Standardized Regression Coefficients: 
#
#        lbound estimate ubound
# beta_1  0.107    0.263  0.419
# beta_2  0.231    0.391  0.552
# beta_3  0.337    0.495  0.653