  Item response theory (IRT) models are widely used in psychometrics and
educational measurement, being deployed in many high stakes tests such as the
GRE aptitude test. IRT has largely focused on estimation of a single latent
trait (e.g. ability) that remains static through the collection of item
responses. However, in contemporary settings where item responses are being
continuously collected, such as Massive Open Online Courses (MOOCs), interest
will naturally be on the dynamics of ability, thus complicating usage of
traditional IRT models. We propose DynAEsti, an augmentation of the traditional
IRT Expectation Maximization algorithm that allows ability to be a continuously
varying curve over time. In the process, we develop CurvFiFE, a novel
non-parametric continuous-time technique that handles the
curve-fitting/regression problem extended to address more general probabilistic
emissions (as opposed to simply noisy data points). Furthermore, to accomplish
this, we develop a novel technique called grafting, which can successfully
approximate distributions represented by graphical models when other popular
techniques like Loopy Belief Propogation (LBP) and Variational Inference (VI)
fail. The performance of DynAEsti is evaluated through simulation, where we
achieve results comparable to the optimal of what is observed in the static
ability scenario. Finally, DynAEsti is applied to a longitudinal performance
dataset (80-years of competitive golf at the 18-hole Masters Tournament) to
demonstrate its ability to recover key properties of human performance and the
heterogeneous characteristics of the different holes. Python code for CurvFiFE
and DynAEsti is publicly available at github.com/chausies/DynAEstiAndCurvFiFE.
This is the full version of our ICDM 2019 paper.
