Person explanatory multidimensional item response theory with the instrument package in R.

Abstract

We present the new R package instrument to perform Bayesian estimation of person explanatory multidimensional item response theory. The package implements an exploratory multidimensional item response theory model and a higher-order multidimensional item response theory model, a type of confirmatory multidimensional item response theory. Explanation of person parameters is accomplished by fixed and random effect linear regression models. Estimation is carried out using Hamiltonian Monte Carlo in Stan. In this article, we provide a detailed description of the models; we use the instrument package to demonstrate fitting explanatory item response models with fixed and random effects (i.e., mixed modeling) of person parameters in R; and, we perform a simulation study to evaluate the performance of our implementation of the models.