IRTBEMM R package

Applying the family of the Bayesian Expectation-Maximization-Maximization (BEMM) algorithm to estimate: (1) Three parameter logistic (3PL) model proposed by Birnbaum (1968); (2) four parameter logistic (4PL) model proposed by Barton & Lord (1981); (3) one parameter logistic guessing (1PLG) and (4) one parameter logistic ability-based guessing (1PLAG) model proposed by San Martín et al (2006).

The BEMM family includes (1) The BEMM algorithm for 3PL model (Guo & Zheng, 2019); (2) The BEMM algorithm for 4PL model (Zhang, Guo, & Zheng, 2018, April); (3) The BEMM algorithm for 1PL-AG and 1PL-G model (Guo, Wu, Zheng, & Wang, 2018); (4) Their maximum likelihood estimation versions (Zheng, Meng, Guo, & Liu, 2018).

Thus, both Bayesian modal estimates and maximum likelihood estimates are available.

Reference: Barton, M. A., & Lord, F. M. (1981). An upper asymptote for the three-parameter logistic item response model. ETS Research Report Series}, 1981(1), 1-8. doi:10.1002/j.2333-8504.1981.tb01255.x Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 395-479). MA: Adison-Wesley. Guo, S., Wu, T., Zheng, C., & Wang, W.-C. (2018, April). Bayesian Expectation -Maximization-Maximization for 1PL-AG Model}. Paper presented at the 80th NCME Annual Meeting, New York, NY. Guo, S., & Zheng, C. (2019). The Bayesian Expectation-Maximization-Maximization for the 3PLM. Frontiers in Psychology}, 10}(1175), 1-11. doi:10.3389/fpsyg.2019.01175 San Martín, E., Del Pino, G., & De Boeck, P. (2006). IRT models for ability-based guessing. Applied Psychological Measurement}, 30}(3), 183-203. doi:10.1177/0146621605282773 Zhang, C., Guo, S., & Zheng, C. (2018, April). Bayesian Expectation-Maximization- Maximization Algorithm for the 4PLM}. Paper presented at the 80th NCME Annual Meeting, New York, NY. Zheng, C., Meng, X., Guo, S., & Liu, Z. (2018). Expectation-Maximization-Maximization: A feasible MLE algorithm for the three-parameter logistic model based on a mixture modeling reformulation. Frontiers in Psychology}, 8}(2302), 1-10. doi:10.3389/fpsyg.2017.02302


You can install IRTBEMM from CRAN using:



To use the IRTBEMM package, load it into R using:


Inside the package, the estimation routines can be viewed as:

Shaoyang Guo, Chanjin Zheng, Justin L Kern

Citing the IRTBEMM package

To ensure future development of the package, please cite IRTBEMM package if used during an analysis or simulation study. Citation information for the package may be acquired by using in R:



GPL (>= 2)