vector.alpha: Alpha Replicability of a Vector (pattern) of Correlations
In multicon: Multivariate Constructs

Description Usage Arguments Details Value Author(s) References See Also Examples

A function for compute the alpha replicability of a vector of linear coefficients (e.g. correlations, covariances) between a single variable (x) and a set of other variables (set).

1	vector.alpha(x, set, type = "cor", CI = 0.95, CItype = "xci", minval = -1)

`x`	A numeric vector of the same length as nrow(set).
`set`	A data.frame or matrix of which each column is to be related with x.
`type`	A character string specifying the type of linear coefficients between x and set to be computed. The default "cor" computes the replicability for the correlations between x and set. The option "cov" computes the replicability for covariances. The option "XY" computes the replicability for the betas when X predicts Y. The option "YX" computes the replicability for the betas when Y predicts X.
`CI`	A numeric between .00 and 1.00 indicating the desired confidence level.
`CItype`	A character string of either "xci" or "aci" specifying the the type of confidence interval to compute based on Koning & Franses (2003).
`minval`	A numeric indicating the minimum level of replicability to be returned.

Sherman and Wood (2014) suggest that one way to estimate the replicability of a vector of correlation coefficients between a variable of interest (x) and a set of other variables (set) is to 1) Z-score all variables, 2) multiply the Z-scored variable of interest by the Z-scores for each of the variables in set, 3) transpose the resultant matrix of cross-products and compute cronbach's alpha on this matrix. This function does just that and includes options for getting replicability coefficients for regression slopes and covariances.

`N`	The sample size
`Average R`	The average magnitude of correlations between x and set
`Alpha`	The estimated alpha reliability
`Upper Limit`	The Upper Limit of the CI around the split-half reliability
`Lower Limit`	The Lower Limit of the CI around the split-half reliability

Ryne A. Sherman

Sherman, R. A. & Wood, D. (2014). Estimating the expected replicability of a pattern of correlations and other measures of association. Multivariate Behavioral Research. 49(1), 17-40. Koning, A. J. & Franses, P. H. (2003). Confidence Intervals for Cronbach's Alpha Coefficient values. ERIM Report Series Reference No. ERS-2003-041-MKT. Available at SSRN: http//ssrn.com/abstract=423658

vector.splithalf splithalf.r

data(RSPdata)
	# Is the pattern of relationships between self reported 
	#extraversion and behavior replicable?
RSPdata$sEXT
data(beh.comp)
head(beh.comp)
vector.alpha(RSPdata$sEXT, beh.comp) #alpha = .666
	# Might also try vector.splithalf
vector.splithalf(RSPdata$sEXT,beh.comp) # split-half reliability = .684