Minimum Distance Estimation of Multidimensional Diffusion-Based Item Response Theory Models

Abstract

Diffusion-based item response theory models are models for responses and response times on psychological tests, which can be used as measurement models in the same way as standard item response theory models (Tuerlinckx, Molenaar, & van der Maas, 2016). Their range of application, however, is narrowed by the fact that multidimensional versions of the model are not easy to fit. Marginal maximum likelihood estimation (e.g., Molenaar, Tuerlinckx, & van der Maas, 2015a) is computationally intensive and infeasible for multidimensional versions. The weighted least squares estimator of Ranger, Kuhn, and Szardenings (2016) is inefficient. Here, we propose an alternative estimator that is more efficient than the least squares estimator and less demanding than the maximum likelihood estimator. The estimator is based on minimum distance estimation and consists in modeling the sample quantiles and sample covariances. The performance of the estimator is investigated in a simulation study. The simulation study corroborates that the estimator performs well. The application of the estimator is demonstrated with real data.