composite_rel_matrix: Matrix formula to estimate the reliability of a weighted or...

Description Usage Arguments Details Value References Examples

View source: R/composites.R

Description

\loadmathjax

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

Usage

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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:

\mjdeqn\rho

_XX=\frac\mathbfw^T\left(\mathbfr\circ\mathbfs\right)+\mathbfw^T\mathbfS\mathbfw-\mathbfw^T\mathbfs\mathbfw^T\mathbfS\mathbfwrel_composite = (t(wt^2) (rel_vec * var_vec) + S - var_sum) / (t(wt) S wt)

where \mjeqn\rho_XXrel_composite is a composite reliability estimate, \mjeqn\mathbfrrel_vec is a vector of reliability estimates, \mjeqn\mathbfwwt is a vector of weights, \mjeqn\mathbfSS is a covariance matrix, and \mjeqn\mathbfsvar_vec is a vector of variances (i.e., the diagonal elements of \mjeqn\mathbfSS).

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

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

Example output

-----------------------------------------------------  psychmeta version 2.3.3  --

Please report any bugs to github.com/psychmeta/psychmeta/issues
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We work hard to produce these open-source tools for the R community, 
please cite psychmeta when you use it in your research: 
  Dahlke, J. A., & Wiernik, B. M. (2018). psychmeta: An R package for 
     psychometric meta-analysis. Applied Psychological Measurement. 
     Advance online publication. https://doi.org/10.1177/0146621618795933

Find info about psychmeta on the web at psychmeta.com and twitter.com/psychmetaR

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psychmeta documentation built on June 1, 2021, 9:13 a.m.