From expectation-3-maximization to bayesian expectation-3-maximization: A latent mixture modeling-based bayesian algorithm for the 4-parameter logistic model

[摘要] There is renewed interest in the four-parameter logistic model (4PLM), but the lack of a user-friendly calibration method constitutes a major barrier to its widespread application. In the present study, this researcher reformulated the 4PLM from a latent mixture modeling view and developed the Expectation-Maximization-Maximization-Maximization (EMMM) method. Combining the EMMM with the Bayesian approach, allowed the Bayesian Expectation-Maximization-Maximization-Maximization (BEMMM) algorithm to be proposed. First, the author compared the EMMM with BEMMM to confirm that the BEMMM method reduced the number of implausible estimates in EMMM. Next, when comparing the BEMMM with the Markov Chain Monte Carlo method (Culpepper, 2016) and Bayesian Modal Estimation (Waller & Feuerstahler, 2017), the results from a simulation study and a real-world data calibration indicated that the BEMMM and the MCMC are more accurate than the BME, while the BEMMM is much faster than the MCMC.

[关键词] Item response theory (IRT), 4PLM, EMMM, BEMMM