# composite_u_matrix: Matrix formula to estimate the u ratio of a composite... In psychmeta: Psychometric Meta-Analysis Toolkit

## 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

 1 2 3 4 5 6 7 composite_u_matrix( ri_mat = NULL, ra_mat = NULL, u_vec, wt_vec = rep(1, length(u_vec)), sign_r_vec = 1 ) 

## 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:

\mjdeqn

u_composite=\sqrt\frac\left(\mathbfw\circ\mathbfu\right)^T\mathbfR_i\left(\mathbfw\circ\mathbfu\right)\mathbfw^T\mathbfR_a\mathbfwu_composite = sqrt((t(wt * u) R_i (wt * u) / (t(wt) R_a wt))

where \mjeqnu_compositeu_composite is the composite u ratio, \mjeqn\mathbfuu is a vector of u ratios, \mjeqn\mathbfR_iR_i is a range-restricted correlation matrix, \mjeqn\mathbfR_aR_a is an unrestricted correlation matrix, and \mjeqn\mathbfwwt is a vector of weights.

## Value

The estimated u ratio of the composite variable.

## Examples

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

psychmeta documentation built on June 1, 2021, 9:13 a.m.