Latent structure and reliability

A large-scale Monte Carlo study

Abstract

There are numerous reliability coefficients and α is the most popular. It is known that different coefficients can be appropriate in specific conditions and that α should not be used indiscriminately. However, some coefficients and conditions, particularly regarding the latent structure, lacked attention in previous research. In four Monte Carlo simulations, this study compared α, λ₂, maximized λ₄, λ₄ based on locally optimal splits, μ₂, Gilmer-Feldt, Kaiser-Caffrey α, Heise-Bohrnstedt Ω, Joreskog's ρ, ω_total, algebraic greatest lower bound, greatest lower bound based on minimum rank factor analysis in every condition and also hierarchical ω and asymptotic ω hierarchical in multidimensional conditions. Findings suggest each of these coefficients can be useful at least in some conditions. Most differences in performance were observed in congeneric conditions and conditions with up to moderate loadings. Some coefficients were found to be more useful than previously considered. Results are discussed in the context of existing theory and previous Monte Carlo studies.