Multistage tests are a generalization of computerized adaptive tests (CATs), that allow to ask batches of questions before starting to adapt the process, instead of asking questions one by one. In order to be provided in real-world scenarios, they should be assembled on the fly, and recent models have been designed accordingly (Zheng & Chang, 2015). We will present a new algorithm for assembling multistage tests, based on a recent technique in machine learning called determinantal point processes. We will illustrate this technique on various student data that come from fraction subtraction items, or massive online open courses.

In multidimensional CATs, feature vectors are estimated for students and questions, and the probability that a student gets a question correct depends on how much their feature vector is correlated with the question feature vector. In other words, questions that are close in space lead to similar response patterns from the students. Therefore, in order to maximize the information of a batch of questions, the volume spanned by their feature vectors should be as large as possible. Determinantal point processes allow to sample efficiently batches of items from a bank that are diverse, i.e., that span a large volume: it is actually possible to draw k items among n with a O(nk3 ) complexity, which is convenient for large databases of 10,000s of items.

References

Zheng, Y., & Chang, H. H. (2015). On-the-fly assembled multistage adaptive testing. Applied Psychological Measurement, 39(2), 104-118.

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