Family of Bayesian EMM Algorithm for Item Response Models R package IRTBEMM version 1.0.8 Applying the family of the Bayesian Expectation-Maximization-Maximization (BEMM) algorithm to estimate: (1) Three parameter logistic (3PL) model proposed by Birnbaum (1968, ISBN:9780201043105); (2) four parameter logistic (4PL) model proposed by Barton & Lord (1981) <doi:10.1002/j.2333-8504.1981.tb01255.x>; (3) one parameter logistic guessing (1PLG) and (4) one parameter logistic ability-based guessing (1PLAG) models proposed by San Martín et al (2006) <doi:10.1177/0146621605282773>. The BEMM family includes (1) the BEMM algorithm for 3PL model proposed by Guo & Zheng (2019) <doi:10.3389/fpsyg.2019.01175>; (2) the BEMM algorithm for 1PLG model and (3) the BEMM algorithm for 1PLAG model proposed by Guo, Wu, Zheng, & Chen (2021) <doi:10.1177/0146621621990761>; (4) the BEMM algorithm for 4PL model proposed by Zheng, Guo, & Kern (2021) <doi:10.1177/21582440211052556>; and (5) their maximum likelihood estimation versions proposed by Zheng, Meng, Guo, & Liu (2018) <doi:10.3389/fpsyg.2017.02302>. Thus, both Bayesian modal estimates and maximum likelihood estimates are available. Software Depends: R (>= 3.5.0) Shaoyang Guo <syguo1992@outlook.com> Comprehensive R Archive Network (CRAN) Shaoyang Guo [aut, cre, cph], Chanjin Zheng [aut], Justin L Kern [aut] GPL (>= 2) 2023-06-06 application/tgz https://CRAN.R-project.org/package=IRTBEMM doi:10.32614/CRAN.package.IRTBEMM