Conditional Independence in a Clustered Item Test

Although the assumption of local independence un derlies 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 ex amine the conditional independence of items both within and between clusters. In general, although rela tionships between items were usually positive (as re quired for theories involving monotone item trace lines), conditional independence was not found. De partures 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).