Computer programs for fitting latent trait models to
data provide indices of item misfit. An analysis of the
consistency of item misfit determination is presented.
Two content-equivalent forms of 71 items representing
the behavioral domain of arithmetic skills were generated.
Each item was defined in terms of its combination
of facet elements, and the ith item on each form
represented the same selection of facets. The dichotomously
scored responses to the two forms were analyzed
using the computer programs NOHARM and
BICAL. Misfitting items were identified by use of the
residual covariances in the case of NOHARM and Total-t and Between-t in the case of BICAL. The consistency
of misfit was measured by the extent of
agreement in selection of misfitting items across the
parallel forms. It was found that the analysis of residual
covariances provided a more consistent means of
determining item misfit. It was concluded that the use
of the Between-t and Total-t indices as a basis for editing
items should be viewed cautiously. In addition,
misfitting items were grouped according to common
facet elements and reasons for misfit were postulated.
Thus, the analysis of residual covariances of items defined
in terms of their combination of facet elements
seems to provide a very satisfactory method of item
Balla, John R.; McDonald, Roderick P..
Latent trait item analysis and facet theory--a useful combination..
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