# composite_rel_matrix: Matrix formula to estimate the reliability of a weighted or... In psychmeta: Psychometric Meta-Analysis Toolkit

 composite_rel_matrix R Documentation

## Matrix formula to estimate the reliability of a weighted or unweighted composite variable

### Description

This function computes the reliability of a variable that is a weighted or unweighted composite of other variables.

### Usage

```composite_rel_matrix(rel_vec, r_mat, sd_vec, wt_vec = rep(1, length(rel_vec)))
```

### Arguments

 `rel_vec` Vector of reliabilities associated with variables in the composite to be formed. `r_mat` Correlation matrix from which the composite is to be computed. `sd_vec` Vector of standard deviations 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).

### Details

This function treats measure-specific variance as reliable.

The Mosier composite formula is computed as:

rel_composite = (t(wt^2) (rel_vec * var_vec) + S - var_sum) / (t(wt) S wt)

where rel_composite is a composite reliability estimate, rel_vec is a vector of reliability estimates, wt is a vector of weights, S is a covariance matrix, and var_vec is a vector of variances (i.e., the diagonal elements of S).

### Value

The estimated reliability of the composite variable.

### References

Mosier, C. I. (1943). On the reliability of a weighted composite. Psychometrika, 8(3), 161–168. doi: 10.1007/BF02288700

Schmidt, F. L., & Hunter, J. E. (2015). Methods of meta-analysis: Correcting error and bias in research findings (3rd ed.). Thousand Oaks, CA: Sage. doi: 10.4135/9781483398105. pp. 441 - 447.

### Examples

```composite_rel_matrix(rel_vec = c(.8, .8),
r_mat = matrix(c(1, .4, .4, 1), 2, 2), sd_vec = c(1, 1))
```

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