Maximization of Some Types of Information for Unidentified Item Response Models with Guessing Parameters

It is known that a family of fixed-effects item response models with equal discrimination and different guessing parameters has no model identifiability. For this family, some types of information including the Fisher information and a new one are maximized to have model identification. The conditions of monotonicity of these types of information with respect to a tuning parameter are given. In the case of the logistic model with guessing parameters, it is shown that maxima do not exist under some parametrization, where negative lower asymptote can be employed without changing the probabilities of correct responses by examinees.