Work due to Junker and more recently due to Junker and Ellis characterized desired latent properties of an educational testing procedure in terms of a collection of other manifest properties. This is important because one can only propose tests for manifest quantities, not latent ones. Here, we complete the conversion of a pair of latent properties to equivalent conditions in terms of four manifest quantities and identify a general method for producing tests for manifest properties.
"Manifest characterization and testing for certain latent properties." Ann. Statist. 29 (3) 876 - 898, June 2001. https://doi.org/10.1214/aos/1009210693