Item Response Theory for Peer Assessment

As an assessment method based on a constructivist approach, peer assessment has become popular in recent years. However, in peer assessment, a problem remains that reliability depends on the rater characteristics. For this reason, some item response models that incorporate rater parameters have been proposed. Those models are expected to improve the reliability if the model parameters can be estimated accurately. However, when applying them to actual peer assessment, the parameter estimation accuracy would be reduced for the following reasons. 1) The number of rater parameters increases with two or more times the number of raters because the models include higher-dimensional rater parameters. 2) The accuracy of parameter estimation from sparse peer assessment data depends strongly on hand-tuning parameters, called hyperparameters. To solve these problems, this article presents a proposal of a new item response model for peer assessment that incorporates rater parameters to maintain as few rater parameters as possible. Furthermore, this article presents a proposal of a parameter estimation method using a hierarchical Bayes model for the proposed model that can learn the hyperparameters from data. Finally, this article describes the effectiveness of the proposed method using results obtained from a simulation and actual data experiments

An Item Response Theory for Peer Assessment

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Bayesian Agent in E-learning

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IRT-Based Adaptive Hints to Scaffold Learning in Programming

Over the past few decades, many studies conducted in the field of learning science have described that scaffolding plays an important role in human learning. To scaffold a learner efficiently, a teacher should predict how much support a learner must have to complete tasks and then decide the optimal degree of assistance to support the learner\u27s development. Nevertheless, it is difficult to ascertain the optimal degree of assistance for learner development. For this study, it is assumed that optimal scaffolding is based on a probabilistic decision rule: Given a teacher\u27s assistance to facilitate the learner development, an optimal probability exists for a learner to solve a task. To ascertain that optimal probability, we developed a scaffolding system that provides adaptive hints to adjust the predictive probability of the learner\u27s successful performance to the previously determined certain value, using a probabilistic model, i.e., item response theory (IRT). Furthermore, using the scaffolding system, we compared learning performances by changing the predictive probability. Results show that scaffolding to achieve 0.5 learner success probability provides the best performance. Additionally, results demonstrate that a scaffolding system providing 0.5 probability decreases the number of hints (amount of support) automatically as a fading function according to the learner\u27s growth capability

Exact Learning Augmented Naive Bayes Classifier

Earlier studies have shown that classification accuracies of Bayesian networks (BNs) obtained by maximizing the conditional log likelihood (CLL) of a class variable, given the feature variables, were higher than those obtained by maximizing the marginal likelihood (ML). However, differences between the performances of the two scores in the earlier studies may be attributed to the fact that they used approximate learning algorithms, not exact ones. This paper compares the classification accuracies of BNs with approximate learning using CLL to those with exact learning using ML. The results demonstrate that the classification accuracies of BNs obtained by maximizing the ML are higher than those obtained by maximizing the CLL for large data. However, the results also demonstrate that the classification accuracies of exact learning BNs using the ML are much worse than those of other methods when the sample size is small and the class variable has numerous parents. To resolve the problem, we propose an exact learning augmented naive Bayes classifier (ANB), which ensures a class variable with no parents. The proposed method is guaranteed to asymptotically estimate the identical class posterior to that of the exactly learned BN. Comparison experiments demonstrated the superior performance of the proposed method.Comment: 29 page

An extended depth-first search algorithm for optimal triangulation of Bayesian networks

The junction tree algorithm is currently the most popular algorithm for exact inference on Bayesian networks. To improve the time complexity of the junction tree algorithm, we need to find a triangulation with the optimal total table size. For this purpose, Ottosen and Vomlel have proposed a depth-first search (DFS) algorithm. They also introduced several techniques to improve the DFS algorithm, including dynamic clique maintenance and coalescing map pruning. Nevertheless, the efficiency and scalability of that algorithm leave much room for improvement. First, the dynamic clique maintenance allows to recompute some cliques. Second, in the worst case, the DFS algorithm explores the search space of all elimination orders, which has size n!, where n is the number of variables in the Bayesian network. To mitigate these problems, we propose an extended depth-first search (EDFS) algorithm. The new EDFS algorithm introduces the following two techniques as improvements to the DFS algorithm: (1) a new dynamic clique maintenance algorithm that computes only those cliques that contain a new edge, and (2) a new pruning rule, called pivot clique pruning. The new dynamic clique maintenance algorithm explores a smaller search space and runs faster than the Ottosen and Vomlel approach. This improvement can decrease the overhead cost of the DFS algorithm, and the pivot clique pruning reduces the size of the search space by a factor of O(n2). Our empirical results show that our proposed algorithm finds an optimal triangulation markedly faster than the state-of-the-art algorithm does

An Analysis Using Eye-Mark Recorder of the Effectiveness of Presentation Methods for E-learning

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Empirical comparison of item response theory models with rater\u27s parameters

In various assessment contexts including entrance examinations, educational assessments, and personnel appraisal, performance assessment by raters has attracted much attention to measure higher order abilities of examinees. However, a persistent difficulty is that the ability measurement accuracy depends strongly on rater and task characteristics. To resolve this shortcoming, various item response theory (IRT) models that incorporate rater and task characteristic parameters have been proposed. However, because various models with different rater and task parameters exist, it is difficult to understand each model\u27s features. Therefore, this study presents empirical comparisons of IRT models. Specifically, after reviewing and summarizing features of existing models, we compare their performance through simulation and actual data experiments