A Simplified Estimation of Latent State-Trait Parameters

The latent state-trait (LST) theory is an extension of the classical test theory that allows one to decompose a test score into a true trait, a true state residual, and an error component. For practical applications, the variances of these latent variables may be estimated with standard methods of structural equation modeling (SEM). These estimates allow one to decompose the coefficient of reliability into a coefficient of consistency (indicating true effects of the person) plus a coefficient of occasion specificity (indicating true effects of the situation and the person-situation interaction). One disadvantage of this approach is that the standard SEM analysis requires large sample sizes. This article aims to overcome this disadvantage by presenting a simple method that allows one to estimate the LST parameters algebraically from the observed covariance matrix. A Monte Carlo simulation suggests that the proposed method may be superior to the standard SEM analysis in small samples.