IRTBEMM: An R Package for Estimating IRT Models With Guessing or Slipping Parameters

Abstract

A recently released R package IRTBEMM is presented in this article. This package puts together several new estimation algorithms (Bayesian EMM, Bayesian E3M, and their maximum likelihood versions) for the Item Response Theory (IRT) models with guessing and slipping parameters (e.g., 3PL, 4PL, 1PL-G, and 1PL-AG models). IRTBEMM should be of interest to the researchers in IRT estimation and applying IRT models with the guessing and slipping effects to real datasets.

Mixture‐modelling‐based Bayesian MH‐RM algorithm for the multidimensional 4PLM

“…For modelling construction, San Martín et al (2006) proposed a one-parameter ability-based guessing (1PL-AG) model, Culpepper (2015) proposed a four-parameter normal Ogive (4PNO) model, and Zhu et al (2019) proposed a two-parameter logistic extension model (2PLE). For parameter estimation, the mixture-modelling-based EM approach (Guo et al, 2020;Zheng et al, 2018), the mixed stochastic approximation EM algorithm (Meng & Xu, 2022), and the optimized MCMC algorithm (Béguin & Glas, 2001;Fu et al, 2009) were proposed to obtain more accurate and robust estimates. This study can be regarded as a natural extension of previous research in a multidimensional case.…”

“…Another obstacle to using the 4PLM is the estimation issue. In the unidimensional scenario, researchers recently developed several methods to obtain relatively stable estimates of the 4PLM with a moderate sample size (about 5000 examinees), including, for example, the fully Bayesian Markov chain Monte Carlo (MCMC) algorithm (Culpepper, 2015), the mixture‐modelling‐based Bayesian expectation–maximization (EM) (so‐called BE3M) algorithm (Guo et al, 2020; Zheng et al, 2021), and the mixed stochastic approximation EM algorithm (Meng & Xu, 2022). However, fast and stable estimation remains a challenge for the multidimensional 4PLM (M4PLM) due to (1) the exponential growth of numerical integration quadrature (curse of dimensionality), (2) the sparse data and information for guessing and unslipping parameters, and (3) extremely high estimation time.…”

Item response theory.

“…In Figure 37.2 we display the IRCs for Item 4 in the 3PL and Item 25 in the 3PLMu to illustrate the concepts of lower and upper asymptotes, respectively. Moving beyond the 3PLM and 3PLMu, many researchers (Feuerstahler & Waller, 2014;Guo et al, 2020;Meng et al, 2020;Reise & Waller, 2003;Waller & Feuerstahler, 2017;Waller & Reise, 2010) have used a 4PLM that includes an upper asymptote parameter (δ) as well as a lower asymptote (γ) for psychopathology items.…”