Curve Fitting from Probabilistic Emissions and Applications to Dynamic Item Response Theory

TL;DR

This paper introduces DynAEsti, a novel method for modeling dynamic abilities in item response theory using continuous-time curve fitting, enabling analysis of longitudinal performance data such as golf scores.

Contribution

It develops CurvFiFE, a non-parametric continuous-time curve-fitting technique, and grafting, a new approximation method for probabilistic graphical models, enhancing dynamic IRT modeling.

Findings

DynAEsti performs comparably to static IRT in simulations.

Successfully applied to 80-year golf performance data.

Provides insights into human performance dynamics.

Abstract

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.