Mathematical Optimization Models for Nonparametric Item Response Theory
Yuichi Takano, Shintaro Tsunoda, Masaaki Muraki · Institutional Repositories DataBase (IRDB) · 2015
This paper explores a mathematical optimization approach to nonparametric item response theory (NIRT). Specifically, we develop mathematical optimization models for estimating nonparametric item characteristic curves and latent abilities of examinees simultaneously. These models maximize the log likelihood function under the monotone homogeneity and double monotonicity constraints and are formulated as mixed integer nonlinear programming problems. Since these problems are very hard to solve exactly, we devise heuristic optimization algorithms to efficiently find a good-quality solution. Through the computational experiments, the effectiveness of our mathematical optimization models and heuristic optimization algorithms are demonstrated by comparison to the common two-parameter logistic IRT model.