  This paper presents a machine learning approach to multidimensional item
response theory (MIRT), a class of latent factor models that can be used to
model and predict student performance from observed assessment data. Inspired
by collaborative filtering, we define a general class of models that includes
many MIRT models. We discuss the use of penalized joint maximum likelihood
(JML) to estimate individual models and cross-validation to select the best
performing model. This model evaluation process can be optimized using batching
techniques, such that even sparse large-scale data can be analyzed efficiently.
We illustrate our approach with simulated and real data, including an example
from a massive open online course (MOOC). The high-dimensional model fit to
this large and sparse dataset does not lend itself well to traditional methods
of factor interpretation. By analogy to recommender-system applications, we
propose an alternative "validation" of the factor model, using auxiliary
information about the popularity of items consulted during an open-book exam in
the course.
