composite_rel_scalar: Scalar formula to estimate the reliability of a composite...

In psychmeta/psychmeta: Psychometric Meta-Analysis Toolkit

Scalar formula to estimate the reliability of a composite variable

Description

This function computes the reliability of a variable that is a unit-weighted composite of other variables.

Usage

composite_rel_scalar(mean_rel, mean_intercor, k_vars)

Arguments

mean_rel	The mean reliability of variables in the composite.
mean_intercor	The mean correlation among the variables in the composite.
k_vars	The number of variables in the composite.

Details

The Mosier composite formula is computed as:

\rho_{XX}=\frac{\bar{\rho}_{x_{i}x_{i}}k+k\left(k-1\right)\bar{\rho}_{x_{i}x_{j}}}{k+k\left(k-1\right)\bar{\rho}_{x_{i}x_{j}}}

where \bar{\rho}_{x_{i}x_{i}} is the mean reliability of variables in the composite, \bar{\rho}_{x_{i}x_{j}} is the mean intercorrelation among variables in the composite, and k is the number of variables in the composite.

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.4135/9781483398105")}. pp. 441 - 447.

Examples

composite_rel_scalar(mean_rel = .8, mean_intercor = .4, k_vars = 2)

psychmeta/psychmeta documentation built on Feb. 12, 2024, 1:21 a.m.