| This study focuses on the comparison of Vomlel's (2004) Bayesian Network model of basic arithmetic skills, to a simple Bayes posterior probability update approach under strong independence assumptions, named POKS (Desmarais, Maluf, and Liu 1995). The models are compared on the ground of their predictive accuracy.; The results show that both approaches can classify examinees as master or non-master effectively and efficiently. The simulation results shows that item-to-item structures provide higher predictive power at the item level than the Bayesian network approach, but lower predictive accuracy for concepts. Another experiment combining the two approaches provides further insights. In this experiment the observed items are first processed by POKS. The initial set of observed items is thereby augmented by POKS inferences before it is fed to the BN.; Both simulations provide evidence that POKS does add information to a BN organized in a hierarchy of concepts with items as leaf nodes. Item to item knowledge structures do seem to provide information that is not modeled by such BN. On the other hand, the BN in this experiment does provide better concept assessment. That confirms the ability of a BN to model complex, non-linear relationships among concepts and items. (Abstract shortened by UMI.)... |
