IDENTIFIABILITY AND GOODNESS OF RECOVERY IN THE CONSTRAINED GAIN-LOSS MODEL

  • Pasquale Anselmi
  • Luca Stefanutti
  • Egidio Robusto

Abstract

The Gain-Loss Model (GaLoM) is a probabilistic skill multimap model for assessing learning processes proposed within the framework of knowledge space theory. Model parameters are initial probabilities of the skills, effects of learning object on gaining and losing the skills, careless error and lucky guess probabilities of problems. When the skills are assessed through a small number of problems or the data are noisy, model identifiability and goodness of recovery are a concern. An extension of the GaLoM is proposed in which the parameter space of careless error and lucky guess probabilities is constrained. Different ratios between number of problems and skills, and levels of noise in the data are considered in a simulation study. Advantages of the constrained GaLoM with respect to identifiability and goodness of recovery are presented and discussed.

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