The problem of obtaining designs that result in
the greatest precision of the parameter estimates is
encountered in at least two situations in which
item response theory (IRT) models are used. In so-called
two-stage testing procedures, certain designs
may be specified that match difficulty levels of test
items with abilities of examinees. The advantage of
such designs is that the variance of the estimated
parameters can be controlled. In situations in
which IRT models are applied to different groups,
efficient multiple-matrix sampling designs are
applicable. The choice of matrix sampling designs
will also influence the variance of the estimated
parameters. Heuristic arguments are given here to
formulate the efficiency of a design in terms of an
asymptotic generalized variance criterion, and a
comparison is made of the efficiencies of several
designs. It is shown that some designs may be
found to be most efficient for the one- and two- parameter
model, but not necessarily for the three-parameter
model. Index terms: efficiency, generalized
variance, item response theory, optimal design.
Berger, Martijn P. (1991). On the efficiency of IRT models when applied to different sampling designs. Applied Psychological Measurement, 15, 293-306. doi:10.1177/014662169101500310
Berger, Martijn P. F..
On the efficiency of IRT models when applied to different sampling designs.
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