Skip to main content
NCBI home page
Applied Psychological Measurement logoLink to Applied Psychological Measurement
. 2021 Sep 15;45(7-8):553–555. doi: 10.1177/01466216211040488

bmggum: An R Package for Bayesian Estimation of the Multidimensional Generalized Graded Unfolding Model With Covariates

Naidan Tu 1,✉, Bo Zhang 2, Lawrence Angrave 3, Tianjun Sun 3,4
PMCID: PMC8640348  PMID: 34866713

Abstract

Over the past couple of decades, there has been an increasing interest in adopting ideal point models to represent noncognitive constructs, as they have been demonstrated to better measure typical behaviors than traditional dominance models do. The generalized graded unfolding model (GGUM) has consistently been the most popular ideal point model among researchers and practitioners. However, the GGUM2004 software and the later developed GGUM package in R can only handle unidimensional models despite the fact that many noncognitive constructs are multidimensional in nature. In addition, GGUM2004 and the GGUM package often yield unreasonable estimates of item parameters and standard errors. To address these issues, we developed the new open-source bmggum R package that is capable of estimating both unidimensional and multidimensional GGUM using a fully Bayesian approach, with supporting capabilities of stabilizing parameterization, incorporating person covariates, estimating constrained models, providing fit diagnostics, producing convergence metrics, and effectively handling missing data.

Keywords: multidimensional generalized graded unfolding model, ideal point model, Bayesian estimation, item response theory, Hamiltonian Monte Carlo

An increasing number of studies have shown that ideal point models better describe how people respond to items measuring noncognitive constructs than dominance models (Drasgow et al., 2010). The generalized graded unfolding model (GGUM; Roberts et al., 2000) -- the most popular ideal point model -- has been widely adopted for noncognitive constructs, largely because of the availability of the GGUM2004 software (Roberts et al., 2006). However, GGUM2004 and its R package counterpart GGUM (Tendeiro & Castro-Alvarez, 2019) can only handle unidimensional GGUM despite that many noncognitive constructs are multidimensional in nature. In addition, GGUM2004 and the GGUM package often yield unreasonable estimates of item parameters and standard errors. To address these issues, we developed the new bmggum R package that is capable of estimating both unidimensional and multidimensional GGUM using a fully Bayesian approach.

The purpose of the bmggum R package is to estimate the multidimensional GGUM and its variants using rstan that implements the state-of-the-art Hamiltonian Monte Carlo (HMC) sampling algorithm as the backend estimation engine. Some important features of the bmggum package include: (1) allowing the estimation of both unidimensional and multidimensional GGUM, (2) allowing user-specified priors to stabilize parameter estimates and eliminate extreme estimates often seen in other packages, (3) allowing the incorporation of person covariates into the estimation process to improve efficiency, (4) allowing the estimation for two additional constrained versions of GGUM, (5) providing multiple model fit diagnostics, (6) producing multiple graphic and numeric metrics to evaluate the degree of model convergence, and (7) handling missing data effectively. User-friendly functions for model fitting, result extraction, and plotting are also available.

Specifically, in addition to the base GGUM, bmggum can also estimate two constrained variants of GGUM: (1) the partial credit unfolding model, where all alphas are fixed to one, and (2) the generalized rating scale unfolding model, where the threshold parameters are constrained to be equal across items. With regard to estimation, Bayesian estimation allows users to specify reasonable priors for parameters to stabilize estimation so that users can obtain more reliable estimates. Furthermore, bmggum also allows users to incorporate both continuous and categorical person covariates into the estimation process in hopes of further boosting estimation efficiency, especially for person parameters. The bmggum package uses the R package rstan (Stan Development Team, 2020) as the backend estimation engine which implements the more efficient HMC sampling algorithm. Moreover, the bmggum package deals with missing data in a way similar to the full information maximum likelihood approach. Aside from estimating parameters and scoring respondents, wrapper functions are provided to check model fit using three indices: (1) the widely applicable information criterion, (2) the leave-one-out cross-validation (LOO), as implemented in the R package loo (Vehtari et al., 2020), and (3) the adjusted χ2/df (Drasgow et al., 1995), as implemented in GGUM (Tendeiro & Castro-Alvarez, 2019). Functions are also available for plotting model convergence diagnostics and item characteristics curves.

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

Footnotes

Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding: The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Naidan Tu https://orcid.org/0000-0002-5179-4133

Bo Zhang https://orcid.org/0000-0002-6730-7336

Tianjun Sun https://orcid.org/0000-0002-3655-0042

References

  1. Drasgow F., Chernyshenko O. S., Stark S. (2010). 75 years after Likert: Thurstone was right! Industrial and Organizational Psychology, 3(4), 465-476. [Google Scholar]
  2. Drasgow F., Levine M. V., Tsien S., Williams B., Mead A. D. (1995). Fitting polytomous item response theory models to multiple-choice tests. Applied Psychological Measurement, 19(2), 143-166. [Google Scholar]
  3. R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org [Google Scholar]
  4. Roberts J. S., Donoghue J. R., Laughlin J. E. (2000). A general item response theory model for unfolding unidimensional polytomous responses. Applied Psychological Measurement, 24(1), 3-32. [Google Scholar]
  5. Roberts J. S., Fang H.-R., Cui W., Wang Y. (2006). GGUM2004: A windows-based program to estimate parameters in the generalized graded unfolding model. Applied Psychological Measurement, 30(1), 64-65. [Google Scholar]
  6. Stan Development Team (2020). RStan: The R interface to Stan. R package version 2.21.2. http://mc-stan.org
  7. Tendeiro J. N., Castro-Alvarez S. (2019). GGUM: An R package for fitting the generalized graded unfolding model. Applied Psychological Measurement, 43(2), 172-173. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Vehtari A., Gabry J., Magnusson M., Yao Y., Bürkner P., Paananen T., Gelman A. (2020). “loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models.”. R package version 2.4.1. https://mc-stan.org/loo/ [Google Scholar]

Articles from Applied Psychological Measurement are provided here courtesy of SAGE Publications

RESOURCES