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)))The estimated reliability of the composite variable.
Vector of reliabilities associated with variables in the composite to be formed.
Correlation matrix from which the composite is to be computed.
Vector of standard deviations associated with variables in the composite to be formed.
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:
$$\rho_{XX}=\frac{\mathbf{w}^{T}\left(\mathbf{r}\circ\mathbf{s}\right)+\mathbf{w}^{T}\mathbf{S}\mathbf{w}-\mathbf{w}^{T}\mathbf{s}}{\mathbf{w}^{T}\mathbf{S}\mathbf{w}}$$
where \(\rho_{XX}\) is a composite reliability estimate, \(\mathbf{r}\) is a vector of reliability estimates, \(\mathbf{w}\) is a vector of weights, \(\mathbf{S}\) is a covariance matrix, and \(\mathbf{s}\) is a vector of variances (i.e., the diagonal elements of \(\mathbf{S}\)).
Mosier, C. I. (1943). On the reliability of a weighted composite. Psychometrika, 8(3), 161–168. tools:::Rd_expr_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. tools:::Rd_expr_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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