Evaluation of Reliability Coefficients for Two-Level Models via Latent Variable Analysis

Abstract

A latent variable analysis procedure for evaluation of reliability coefficients for 2-level models is outlined. The method provides point and interval estimates of group means' reliability, overall reliability of means, and conditional reliability. In addition, the approach can be used to test simple hypotheses about these parameters. The procedure is applicable with unconditional models as well as with conditional models including higher level explanatory variables. The proposed method is illustrated with an empirical example.

Notes

¹In the remaining discussion, σ² > 0 and τ₀₀ > 0 is also assumed, which is a rather mild if at all restrictive assumption in social and behavioral research. In this way, it is ensured that the ratios in the definitional equations for the reliability coefficients under consideration always exist, as do their later needed logit transforms.