psychmeta (version 2.6.4)

composite_rel_matrix: 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)))

Value

The estimated reliability of the composite variable.

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:

_XX=w^T(rs)+w^TSw-w^Tsw^TSwrel_composite = (t(wt^2) (rel_vec * var_vec) + S - var_sum) / (t(wt) S wt)

where _XXrel_composite is a composite reliability estimate, rrel_vec is a vector of reliability estimates, wwt is a vector of weights, SS is a covariance matrix, and svar_vec is a vector of variances (i.e., the diagonal elements of SS).

References

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.

Examples

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