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Abstract In this paper, we develop a mixed stochastic approximation expectation‐maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four‐parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of the stochastic approximation expectation‐maximization (SAEM) algorithm for multidimensional data, but it also alleviates the potential instability caused by label‐switching, and then improved the estimation accuracy. Simulation studies are conducted to illustrate the good performance of the proposed MSAEM method, where MSAEM consistently performs better than SAEM and some other existing methods in multidimensional item response theory. Moreover, the proposed method is applied to a real data set from the 2018 Programme for International Student Assessment (PISA) to demonstrate the usefulness of the 4PNO model as well as MSAEM in practice.
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A Note on Standard Errors for Multidimensional Two-Parameter Logistic Models Using Gaussian Variational Estimation
Accurate item parameters and standard errors (SEs) are crucial for many multidimensional item response theory (MIRT) applications. A recent study proposed the Gaussian Variational Expectation Maximization (GVEM) algorithm to improve computational efficiency and estimation accuracy ( Cho et al., 2021 ). However, the SE estimation procedure has yet to be fully addressed. To tackle this issue, the present study proposed an updated supplemented expectation maximization (USEM) method and a bootstrap method for SE estimation. These two methods were compared in terms of SE recovery accuracy. The simulation results demonstrated that the GVEM algorithm with bootstrap and item priors (GVEM-BSP) outperformed the other methods, exhibiting less bias and relative bias for SE estimates under most conditions. Although the GVEM with USEM (GVEM-USEM) was the most computationally efficient method, it yielded an upward bias for SE estimates.
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- PAR ID:
- 10526327
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Applied Psychological Measurement
- Volume:
- 48
- Issue:
- 6
- ISSN:
- 0146-6216
- Format(s):
- Medium: X Size: p. 276-294
- Size(s):
- p. 276-294
- Sponsoring Org:
- National Science Foundation
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