Faster Confidence Intervals for Item Response Theory via an Approximate Likelihood Profile

Item response theory models the probability of correct responses based on two interacting kinds of parameters: student ability and item difficulty. Whenever we estimate ability, students have a legitimate interest in knowing how certain the estimate is. Confidence intervals are a natural measure of uncertainty. Unfortunately, exact confidence intervals via a likelihood profile technique are computationally demanding. In this paper, we show that confidence intervals can be expressed as the solution to a feature relevance optimization problem. We use this novel formalization to develop two new solvers for confidence intervals and thus achieve speedups by 4-50x while achieving near-indistinguishable results to the state-of-the-art approach.