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

Abstract 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.

[1]  R. Chao,et al.  DSM‐IV‐TR: Diagnostic and Statistical Manual of Mental Disorders , 2013 .

[2]  Jean-Paul Doignon.  Knowledge Spaces and Skill Assignments , 1994 .

[3]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[4]  Dc Washington.  Diagnostic and Statistical Manual of Mental Disorders, 4th Ed. , 1994 .

[5]  R. Hodgson,et al.  Obsessional-compulsive complaints. , 1977, Behaviour research and therapy.

[6]  L. Stefanutti.  A logistic approach to knowledge structures , 2006 .

[7]  Dietrich Albert,et al.  Construction of Knowledge Spaces for Problem Solving in Chess , 1994 .

[8]  Dietrich Albert,et al.  Applying Competence Prerequisite Structures for eLearning and Skill Management , 2003, J. Univers. Comput. Sci..

[9]  Jean-Paul Doignon,et al.  A Markovian procedure for assessing the state of a system , 1988 .

[10]  Jean-Claude Falmagne,et al.  Knowledge spaces , 1998 .

[11]  Ivo Düntsch,et al.  Skills and knowledge structures , 1995 .

[12]  Andrea Spoto,et al.  Knowledge space theory, formal concept analysis, and computerized psychological assessment , 2010, Behavior research methods.

[13]  E. Sanavio,et al.  The components of the Maudsley Obsessional-Compulsive Questionnaire. , 1985, Behaviour research and therapy.

[14]  Mathieu Koppen,et al.  Introduction to knowledge spaces: How to build, test, and search them , 1990 .

[15]  E. Sanavio,et al.  A computerized approach to cognitive behavioural assessment: an introduction to CBA-2.0 primary scales. , 1990, Journal of behavior therapy and experimental psychiatry.

[16]  Sandra P. Marshall.  Sequential item selection: Optimal and heuristic policies , 1981 .

[17]  Luca Stefanutti,et al.  Recovering a Probabilistic Knowledge Structure by Constraining its Parameter Space , 2009 .

[18]  Jean-Claude Falmagne,et al.  Spaces for the Assessment of Knowledge , 1985, Int. J. Man Mach. Stud..