Conditional independence in a clustered item test

Abstract

Although the assumption of local independence underlies all latent trait theories in mental testing, it has rarely been empirically examined. In this study of a clustered item test (the Australian Scholastic Aptitude Test), a loglinear modeling approach was used to examine the conditional independence of items both within and between clusters. In general, although relationships between items were usually positive (as required for theories involving monotone item trace lines), conditional independence was not found. Departures from independence were more marked in items within clusters rather than between clusters, and also among items based on mathematical rather than verbal material. Another finding was the tendency for departures from independence to increase with ability (as measured by the score on other items).