Identifying the best network structure from a myriad of candidates is not an easy task, and we propose a supervised learning method for this task. We test the idea with an instance of learning student models from students' responses to test items, because student models are very important for intelligent tutoring systems. The training data for the classifiers were simulated based on the expectation about students' item responses when students learn in different ways, and the trained classifier was used to select the model from the list of candidate models based on the observed item responses. Experimental results indicate that, even when item responses do not faithfully reflect students' competence in the concepts, our classifiers still help us differentiate very similar models with indirect observations.
IRT-based models with a general ability and several specific ability dimensions are useful. Studies have looked at item response models where the general and specific ability dimensions form a hierarchical structure. It is also possible that the general and specific abilities directly underlie all test items. A multidimensional IRT model with such an additive structure is proposed under the Bayesian framework. Simulation studies were conducted to evaluate parameter recovery as well as model comparisons. A real data example is also provided. The results suggest that the proposed additive model offers a better way to represent the test situations not realized in existing models.
Stratified versions of coefficients for reliability are defined as extensions of the unstratified coefficients given by Guttman and Cronbach: Lambda 3 (Alpha), Lambda 2 and Lambda 6. One of the stratified coefficients is already available as stratified alpha. Among the four stratified coefficients dealt with in this article, two coefficients are for a stratified test with set (stratum)-specific true scores while the other two are for a stratified test with errors correlated within each set. Conditions of some coefficients being equal to population reliability are shown. For the sampling behavior, asymptotic distributions of the sample coefficients with and without stratification are derived using the asymptotic expansions under nonnormality with simulations for confirmation.
For square contingency tables, Tomizawa (1994), Tomizawa, Seo and Yamamoto (1998) and Tomizawa, Miyamoto and Hatanaka (2001) considered the power-divergence-type measures to represent the degree of departure from symmetry. These measures lie between 0 and 1, and have a characteristic that the degree of departure from symmetry is the minimum when the symmetry holds and the maximum when one of the probabilities in any two symmetric cells is zero. This paper proposes the generalization of these measures so that the degree of departure from symmetry can attain the maximum value 1 even when each of cell probabilities is not zero. Two kinds of measures are proposed. One is applied to the nominal data and the other is applied to the ordinal data. These measures would be useful for representing the degree of departure from symmetry when each of cell probabilities is not zero.