Monotonicity in practice of adaptive testing
  In our previous work we have shown how Bayesian networks can be used for
adaptive testing of student skills. Later, we have taken the advantage of
monotonicity restrictions in order to learn models fitting data better. This
article provides a synergy between these two phases as it evaluates Bayesian
network models used for computerized adaptive testing and learned with a
recently proposed monotonicity gradient algorithm. This learning method is
compared with another monotone method, the isotonic regression EM algorithm.
The quality of methods is empirically evaluated on a large data set of the
Czech National Mathematics Exam. Besides advantages of adaptive testing
approach we observed also advantageous behavior of monotonic methods,
especially for small learning data set sizes. Another novelty of this work is
the use of the reliability interval of the score distribution, which is used to
predict student's final score and grade. In the experiments we have clearly
shown we can shorten the test while keeping its reliability. We have also shown
that the monotonicity increases the prediction quality with limited training
data sets. The monotone model learned by the gradient method has a lower
question prediction quality than unrestricted models but it is better in the
main target of this application, which is the student score prediction. It is
an important observation that a mere optimization of the model likelihood or
the prediction accuracy do not necessarily lead to a model that describes best
the student.
