Estimating Abilities With an Elo-Informed Growth Model

Two common methods for modeling abilities that change over time are generalized linear mixed models (GLMMs) and the Elo algorithm. GLMM specifications that avoid assumptions about the shape of the growth curve tend to be computationally heavy. The Elo algorithm is both flexible and computationally inexpensive but produces estimates that tend to lag when the true latent state changes rapidly from one response to the next, as can occur when the responses are sparse over time. We propose the Elo-informed growth model, a hybrid method that uses the Elo algorithm to rank respondents and combines this with the assumption that the abilities at each iteration in a sequence of responses follow a distribution that can be estimated. Using both simulated data and real learning data, we show that the proposed method performs better than the standard Elo algorithm under rapid ability growth. It achieves accuracy similar to a flexible GLMM while requiring less training data and a fraction of the fitting time. This combination lowers the threshold for implementing robust ability tracking.