Can One Pool Over Site in a Multi-Site Study With Categorical Item Measuring Instruments?: A Multiple Testing Procedure

We outline a procedure for examining collapsibility over site in multiple-location settings that are frequently utilized in contemporary educational and behavioral research. The method is based on a test of cross-site identity of the response distributions of polytomous items in multi-component measuring instruments, which implies the possibility to pool over study location. The approach is readily applicable in empirical studies using popular and widely circulated software and is generalizable to various types of items. The described procedure is illustrated with data from a child development survey.