Considerations on the Impact of Ill-Conditioned Configurations in the CML Approach

Considering complete designs, the configurations of non-existence of the Maximum Likelihood (ML) estimates for the Partial Credit Model are known in the Joint (JML) approach: null categories and ill-conditioned patterns are the only two sources of trouble. In the Conditional (CML) approach, apart from datasets with null categories, the other "anomalous" configurations are not known. In this paper, the impact of ill-conditioned patterns in the conditional approach, as well as the incidence of CML-anomalous configurations, are both studied by a systematic analysis on small-dimensional data matrices. Obtained results emphasize the presence of a large number of additional CML configurations of non-existence, compared to those valid in the JML case.