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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. 

In this article, a testlet hierarchical diagnostic classification model (TH-DCM) was introduced to take both attribute hierarchies and item bundles into account. The expectation-maximization algorithm with an analytic dimension reduction technique was used for parameter estimation. A simulation study was conducted to assess the parameter recovery of the proposed model under varied conditions, and to compare TH-DCM with testlet higher-order CDM (THO-DCM; Hansen, M. (2013). Hierarchical item response models for cognitive diagnosis (Unpublished doctoral dissertation). UCLA; Zhan, P., Li, X., Wang, W.-C., Bian, Y., & Wang, L. (2015). The multidimensional testlet-effect cognitive diagnostic models. Acta Psychologica Sinica, 47(5), 689. https://doi.org/10.3724/SP.J.1041.2015.00689 ). Results showed that (1) ignoring large testlet effects worsened parameter recovery, (2) DCMs assuming equal testlet effects within each testlet performed as well as the testlet model assuming unequal testlet effects under most conditions, (3) misspecifications in joint attribute distribution had an differential impact on parameter recovery, and (4) THO-DCM seems to be a robust alternative to TH-DCM under some hierarchical structures. A set of real data was also analyzed for illustration.