composite_rel_matrix | R Documentation |

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

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

`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). |

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*).

The estimated reliability of the composite variable.

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.

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

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