psychmeta (version 2.6.4)

composite_u_matrix: Matrix formula to estimate the u ratio of a composite variable

Description

This function estimates the u ratio of a composite variable when at least one matrix of correlations (restricted or unrestricted) among the variables is available.

Usage

composite_u_matrix(
  ri_mat = NULL,
  ra_mat = NULL,
  u_vec,
  wt_vec = rep(1, length(u_vec)),
  sign_r_vec = 1
)

Value

The estimated u ratio of the composite variable.

Arguments

ri_mat

Range-restricted correlation matrix from which the composite is to be computed (if NULL, ri_mat is estimated from ra_mat).

ra_mat

Unrestricted correlation matrix from which the composite is to be computed (if NULL, ra_mat is estimated from ri_mat).

u_vec

Vector of u ratios associated with variables in the composite to be formed.

wt_vec

Weights to be used in forming the composite (by default, all variables receive equal weight).

sign_r_vec

The signs of the relationships between the variables in the composite and the variable by which range restriction was induced.

Details

This is computed as:

u_composite=(wu)^TR_i(wu)w^TR_awu_composite = sqrt((t(wt * u) R_i (wt * u) / (t(wt) R_a wt))

where u_compositeu_composite is the composite u ratio, uu is a vector of u ratios, R_iR_i is a range-restricted correlation matrix, R_aR_a is an unrestricted correlation matrix, and wwt is a vector of weights.

Examples

composite_u_matrix(ri_mat = matrix(c(1, .3, .3, 1), 2, 2), u_vec = c(.8, .8))