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).
Bell, Richard C, Pattison, Philippa E & Withers, Graeme P. (1988). Conditional independence in a clustered item test. Applied Psychological Measurement, 12, 15-26. doi:10.1177/014662168801200103
Bell, Richard C.; Pattison, Philippa E.; Withers, Graeme P..
Conditional independence in a clustered item test.
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