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).