Level‐specific reliability coefficients from the perspective of latent state‐trait theory

The growing popularity of the ecological momentary assessment method in psychological research requires adequate statistical models for intensive longitudinal data (ILD), with multilevel latent state-trait (ML-LST) models based on the latent state-trait theory revised (LST-R theory) as one possible alternative. Besides the traditional LST-R coefficients reliability, consistency and occasion-specificity, ML-LST models are also suitable for estimating reliability at Level 1 ("within-subject reliability") and Level 2 ("between-subject reliability"). However, these level-specific coefficients have not yet been defined in LST-R theory and, therefore, their interpretation has been unclear from the perspective of LST-R theory. In the current study, we discuss the interpretation and identification of these coefficients based on the (multilevel) versions of the Multistate-Singletrait (MSST), the Multistate-Indicator-specific trait (MSIT) and the Multistate-Singletrait model with M-1 correlated method factors (MSST-M-1). We show that, in the MSST-M-1 model, the between-subject coefficient is a measure of the indicator-unspecificity of an item (i.e. the portion of between-level variance that a specific item shares with a common trait) or the unidimensionality of a scale. Moreover, we highlight differences between occasion-specificity and within-subject reliability. The performance of the ML-MSST-M-1 model and the corresponding theoretical findings are illustrated using data from an experience sampling study on the within-person fluctuations of narcissistic admiration (Heyde et al., 2023).