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

 composite_u_matrix R Documentation

## 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
)
```

### 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 = sqrt((t(wt * u) R_i (wt * u) / (t(wt) R_a wt))

where u_composite is the composite u ratio, u is a vector of u ratios, R_i is a range-restricted correlation matrix, R_a is an unrestricted correlation matrix, and wt is a vector of weights.

### Value

The estimated u ratio of the composite variable.

### Examples

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

psychmeta documentation built on Aug. 26, 2022, 5:14 p.m.