On the unidentifiability of a certain class of skill multi map based probabilistic knowledge structures

In the process of fitting a probabilistic knowledge structure to data, standard goodness-of-fit statistics only partially describe the correctness of the fitted model. Irrespectively of how good the fit is, a too-high value of the error rates (careless error and lucky guess probabilities) might be a symptom of a misspecification of the model. In this situation, it could be critical to interpret those values as error rates. A more reasonable solution would be to hypothesize that some modifications have to be introduced in the model. In this paper, we show that in specific cases, these modifications yield basic local independence model parameterizations that are not identifiable. The applicative consequences of the theoretical results are displayed by means of an example carried out on a set of clinical data collected through the Maudsley Obsessional-Compulsive Questionnaire.