This function computes the reliability of a variable that is a unit-weighted composite of other variables.
composite_rel_scalar(mean_rel, mean_intercor, k_vars)
The mean reliability of variables in the composite.
The mean correlation among the variables in the composite.
The number of variables in the composite.
The Mosier composite formula is computed as:
rel_composite = (mean_rel * k_vars + k_vars * (k_vars-1) * mean_intercor) / (k_vars + k_vars * (k_vars-1) * mean_intercor)
where mean_rel is the mean reliability of variables in the composite, mean_intercor is the mean intercorrelation among variables in the composite, and k is the number of variables in the composite.
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_scalar(mean_rel = .8, mean_intercor = .4, k_vars = 2)
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