Correlation of a weighted composite with an external variable — fuse

Implements the standard formula \(r_{C,Y} = (w' \rho_{XY}) / \sqrt{w' R_{XX} w}\) for the correlation between a weighted composite of items and an external criterion Y, where the items have correlations R_XX and individual validities \rho_{XY} (Lord & Novick, 1968, Ch. 4).

Usage

fuse_validity(weights, item_cor, item_validities)

Arguments

weights: Composite weights.
item_cor: Predictor (item) correlation matrix.
item_validities: Item-level correlations with the external variable.

Value

Scalar correlation.

Examples

R <- matrix(c(1, .3, .3, 1), 2, 2)
fuse_validity(c(.5, .5), R, item_validities = c(.30, .25))
#> [1] 0.3410955