The characteristics of unidimensional ability estimates
obtained from data generated using multidimensional
compensatory models were compared with estimates
from noncompensatory IRT models. Reckase,
Carlson, Ackerman, and Spray (1986) reported that
when a compensatory model is used and item difficulty
is confounded with dimensionality, the composition
of the unidimensional ability estimates differs for
different points along the unidimensional ability (θ)
scale. Eight datasets (four compensatory, four noncompensatory)
were generated for four different levels
of correlated two-dimensional θs. In each dataset, difficulty
was confounded with dimensionality and then
calibrated using LOGIST and BILOG. The confounding
of difficulty and dimensionality affected the BILOG calibration
of response vectors using matched multidimensional
item parameters more than it affected the
LOGIST calibration. As the correlation between the
generated two-dimensional θs increased, the response
data became more unidimensional as shown in bivariate
plots of the mean θ̂₁ as opposed to the mean of θ̂₂
for specified unidimensional quantiles. Index terms:
BILOG, compensatory IRT models, IRT ability estimation,
LOGIST, multidimensional item response theory,
noncompensatory IRT models.
Ackerman, Terry A..
Unidimensional IRT calibration of compensatory and noncompensatory multidimensional items.
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