A statistical model for reliability generalization formulated as a mixture model

Abstract

In the type of meta-analysis known as reliability generalization (RG), the synthesized values are estimates of the reliability of a measurement tool. Traditionally, they have been analyzed using the classic random effects model, with the necessary adaptations to the specific ES index to which it refers (mainly, Cronbach's alpha coefficient of internal consistency). Some authors have pointed out that the classical random effects model incurs some defects and weaknesses, especially when the variance of the estimator is not independent of the ES index itself. The most notable case is the standardized mean difference, but the same circumstance occurs in some normalizing transformations of Cronbach's alpha. Suero et al (2023) have proposed an alternative formulation of the meta-analytical random effects model, based on the mixture models framework, which shows promising. In this paper we use this alternative formulation and its derived formulas to reanalyze data from a RG study of the fear to COVID scale. The results show that the formulas derived from the formulation as a mixture model is also promising for RG studies.