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.
composite_u_matrix(
ri_mat = NULL,
ra_mat = NULL,
u_vec,
wt_vec = rep(1, length(u_vec)),
sign_r_vec = 1
)The estimated u ratio of the composite variable.
Range-restricted correlation matrix from which the composite is to be computed (if NULL, ri_mat is estimated from ra_mat).
Unrestricted correlation matrix from which the composite is to be computed (if NULL, ra_mat is estimated from ri_mat).
Vector of u ratios associated with variables in the composite to be formed.
Weights to be used in forming the composite (by default, all variables receive equal weight).
The signs of the relationships between the variables in the composite and the variable by which range restriction was induced.
This is computed as:
$$u_{composite}=\sqrt{\frac{\left(\mathbf{w}\circ\mathbf{u}\right)^{T}\mathbf{R}_{i}\left(\mathbf{w}\circ\mathbf{u}\right)}{\mathbf{w}^{T}\mathbf{R}_{a}\mathbf{w}}}$$
where \(u_{composite}\) is the composite u ratio, \(\mathbf{u}\) is a vector of u ratios, \(\mathbf{R}_{i}\) is a range-restricted correlation matrix, \(\mathbf{R}_{a}\) is an unrestricted correlation matrix, and \(\mathbf{w}\) is a vector of weights.
composite_u_matrix(ri_mat = matrix(c(1, .3, .3, 1), 2, 2), u_vec = c(.8, .8))
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