How to estimate absolute-error components in structural equation models of generalizability theory

Structural equation modeling (SEM) has been proposed to estimate generalizability theory (GT) variance components, primarily focusing on estimating relative error to calculate generalizability coefficients. Proposals for estimating absolute-error components have given the impression that a separate SEM must be fitted to a transposed data matrix. This paper uses real and simulated data to demonstrate how a single SEM can be specified to estimate absolute error (and thus dependability) by placing appropriate constraints on the mean structure, as well as thresholds (when used for ordinal measures). Using the R packages lavaan and gtheory, different estimators are compared for normal and discrete measurements. Limitations of SEM for GT are demonstrated using multirater data from a planned missing-data design, and an important remaining area for future development is discussed.