  Analyzing ordinal data becomes increasingly important in psychology,
especially in the context of item response theory. The generalized partial
credit model (GPCM) is probably the most widely used ordinal model and finds
application in many large scale educational assessment studies such as PISA. In
the present paper, optimal test designs are investigated for estimating
persons' abilities with the GPCM for calibrated tests when item parameters are
known from previous studies. We will derive that local optimality may be
achieved by assigning non-zero probability only to the first and last category
independently of a person's ability. That is, when using such a design, the
GPCM reduces to the dichotomous 2PL model. Since locally optimal designs
require the true ability to be known, we consider alternative Bayesian design
criteria using weight distributions over the ability parameter space. For
symmetric weight distributions, we derive necessary conditions for the optimal
one-point design of two response categories to be Bayes optimal. Furthermore,
we discuss examples of common symmetric weight distributions and investigate,
in which cases the necessary conditions are also sufficient. Since the 2PL
model is a special case of the GPCM, all of these results hold for the 2PL
model as well.
