fcirt : An R Package for Forced Choice Models in Item Response Theory

Multidimensional forced choice (MFC) formats have emerged as a promising alternative to traditional single statement Likert-type measures for assessing noncognitive traits while reducing response biases. In MFC measures, respondents are presented with items consisting of two or more statements that measure different constructs and are asked to select the statement that best represents them. The statements within each MFC item are matched on social desirability and extremity. By forcing respondents to choose between similarly appealing statements, MFC measures reduce faking (Cao & Drasgow, 2019), mitigate halo effects, and eliminate midpoint and extreme response styles (Brown et al., 2017). Research has also shown that MFC-based scores improve the prediction of outcomes in organizational contexts (Speer et al., 2023; Stark et al., 2014). These findings, along with the development of item response theory (IRT) models for MFC assessments (Brown & Maydeu-Olivares, 2011; Joo et al., 2023; Stark et al., 2005; Zhang et al., 2024), have spurred interest in psychometric improvements and applications in both educational and organizational settings. As MFC formats become more widely used, there is a growing need for tools to support MFC analysis, which motivated the development of the fcirt package.

The fcirt package estimates forced choice model parameters using Bayesian methods. It currently enables estimation of the Generalized Graded Unfolding Model (GGUM; Roberts et al., 2000)-based Multi-Unidimensional Pairwise Preference (MUPP; Stark et al., 2005) model using rstan (Stan Development Team, 2020), which implements the Hamiltonian Monte Carlo (HMC) sampling algorithm. Specifically, the package supports MUPP model estimation for pairwise comparisons using two approaches: the two-step approach developed by Stark et al. (2005) and the direct approach developed by Lee et al. (2019). In the two-step approach, statement parameters are first estimated from single statement response data using the GGUM, which are then used to construct and score MFC tests. In contrast, the direct approach estimates both statement and person parameters directly from forced choice responses. ¹ The package allows for repeated use of the same statements across different items and accounts for correlations between test dimensions, which are estimated during model estimation. It handles missing data automatically using an approach similar to full information maximum likelihood that allows the number of items to vary across respondents. To help evaluate the quality of MFC assessments, fcirt includes functions for calculating item and test information using either quadrature points ranging from −3 to 3 or empirical trait estimates. ² It also provides functions for Bayesian diagnostics, including density plots, trace plots, and autocorrelation plots, to assist with model evaluation and convergence assessment.

The fcirt package was written in the R language (R Core Team, 2021) and is compatible with Windows, Linux, and macOS systems and platforms. All source code and documentation are freely available at https://cran.r-project.org/package=fcirt. The development version of the package can be tracked at https://github.com/Naidantu/fcirt.