It is shown in this paper that the unconditional or
simultaneous maximum likelihood estimation procedure
for the one-parameter logistic model gives rise to
biased estimators. This bias cannot be removed by a
correction factor (K - 1)/K (where K is the number of
items), contrary to the contention of several authors.
The bias is dependent not only on the number of
items, but also on the distribution of the item parameters,
which makes correcting for bias practically impossible.
Furthermore, it is shown that the minimum
chi-square estimation procedure, as introduced by
Fischer, results in unbiased estimates. In addition, this
method is computationally fast, so that it seems to be
a good alternative for CML estimation when the latter
method meets practical impediments. Index terms:
Maximum likelihood estimation, conditional; Maximum
likelihood estimation, unconditional; Minimum
chi-square estimation; One-parameter logistic model;
Van den Wollenberg, Arnold L, Wierda, Folkert W & Jansen, Paul G. (1988). Consistency of Rasch model parameter estimation: A simulation study. Applied Psychological Measurement, 12, 307-313. doi:10.1177/014662168801200308
Van den Wollenberg, Arnold L.; Wierda, Folkert W.; Jansen, Paul G. W..
Consistency of Rasch model parameter estimation: A simulation study.
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