Last modified: 2018-06-25

#### Abstract

The three-parameter logistic model is an item response theory model

used with dichotomous items. It is well known that the parameters of

the model are weekly identifiable and that the maximization of the

likelihood, which is performed using numerical algorithms, is prone to

convergence issues. In this paper, we propose the use of a penalized likelihood

for the estimation of the item parameters. In particular, the penalty term

shrinks the guessing parameter toward a known constant.

Cross-validation is used to select such constant and the amount of shrinkage.

The method is both simple and effective, and it is illustrated by means of

a real data example.

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