Unidimensional item response theory (IRT) has become
widely used in the analysis and equating of educational
achievement tests. If an IRT model is true,
item responses must be locally independent when the
trait is held constant. This paper presents several measures
of local dependence that are used in conjunction
with the three-parameter logistic model in the analysis
of unidimensional and two-dimensional simulated data
and in the analysis of three mathematics achievement
tests at Grades 3 and 6. The measures of local dependence
(called Q₂ and Q₃) were useful for identifying
subsets of items that were influenced by the same factors
(simulated data) or that had similar content (real
data). Item pairs with high Q₂ or Q₃ values tended to
have similar item parameters, but most items with
similar item parameters did not have high Q₂ or Q₃
values. Sets of locally dependent items tended to be
difficult and discriminating if the items involved an
accumulation of the skills involved in the easier items
in the rest of the test. Locally dependent items that
were independent of the other items in the test did not
have unusually high or low difficulties or discriminations.
Substantial unsystematic errors of equating were
found from the equating of tests involving collections
of different dimensions, but substantial systematic errors
of equating were only found when the two tests
measured quite different dimensions that were presumably taught sequentially.
Yen, Wendy M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145. doi:10.1177/014662168400800201
Yen, Wendy M..
Effects of local item dependence on the fit and equating performance of the three-parameter logistic model.
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