Abstract
There is a rekindled interest in the four-parameter logistic item response model (4PLM) after three decades of neglect among the psychometrics community. Recent breakthroughs in item calibration include the Gibbs sampler specially made for 4PLM and the Bayes modal estimation (BME) method as implemented in the R package mirt. Unfortunately, the MCMC is often time-consuming, while the BME method suffers from instability due to the prior settings. This paper proposes an alternative BME method, the Bayesian Expectation-Maximization-Maximization-Maximization (BE3M) method, which is developed from by combining an augmented variable formulation of the 4PLM and a mixture model conceptualization of the 3PLM. The simulation shows that the BE3M can produce estimates as accurately as the Gibbs sampling method and as fast as the EM algorithm. A real data example is also provided.
Highlights
The four-parameter logistic item response model (4PLM) was first mentioned as far back as McDonald (1967) and formally proposed by Barton and Lord (1981)
We propose an alternative Bayesian modal estimation approach that we term Bayesian Expectationmethod, which is developed by using a latent variable augmentation approach for the 4PLM in conjunction with the mixture modeling approach for the 3PLM (Zheng et al, 2017)
The results of two simulation studies will be respectively reported at two levels: the individual level for each type of parameters and the whole level for the item response function of the 4PLM
Summary
The four-parameter logistic item response model (4PLM) was first mentioned as far back as McDonald (1967) and formally proposed by Barton and Lord (1981). Guo and Zheng (2019) found that the item parameter estimates yielded by BME were unstable for the 3PLM when changing priors of guessing parameters.
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