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The recent surge in computerized testing brings challenges in the analysis of testing data with classic item response theory (IRT) models. To handle individually varying and irregularly spaced longitudinal dichotomous responses, we adopt a dynamic IRT model framework and then extend the model to link with individual characteristics at a hierarchical level. Further, we have developed an algorithm to select important characteristics of individuals that can capture the growth changes of one’s ability under this multi-level dynamic IRT model, where we can compute the Bayes factor of the proposed model including different covariates using a single Markov chain Monte Carlo output from the full model. In addition, we have shown the model selection consistency under the modified Zellner–Siow prior, and we have conducted simulations to illustrate the properties of the model selection consistency in finite samples. Finally, we have applied our proposed model and computational algorithms to a real data application, called EdSphere dataset, in educational testing. 

Abstract Porous noble metal nanoparticles have received particular attention recently for their unique optical, thermal, and catalytic functions in biomedicine. However, limited progress has been made to synthesize such porous metallic nanostructures with large mesopores (≥25 nm). Here, a green yet facile synthesis strategy using biocompatible liposomes as templates to mediate the formation of mesoporous metallic nanostructures in a controllable fashion is reported. Various monodispersed nanostructures with well‐defined mesoporous shape and large mesopores (≈ 40 nm) are successfully synthesized from mono‐ (Au, Pd, and Pt), bi‐ (AuPd, AuPt, AuRh, PtRh, and PdPt), and tri‐noble metals (AuPdRh, AuPtRh, and AuPdPt). Along with a successful demonstration of its effectiveness in synthesis of various mesoporous nanostructures, the possible mechanism of liposome‐guided formation of such nanostructures via time sectioning of the synthesis process (monitoring time‐resolved growth of mesoporous structures) and computational quantum molecular modeling (analyzing chemical interaction energy between metallic cations and liposomes at the enthalpy level) is also revealed. These mesoporous metallic nanostructures exhibit a strong photothermal effect in the near‐infrared region, effective catalytic activities in hydrogen peroxide decomposition reaction, and high drug loading capacity. Thus, the liposome‐templated method provides an inspiring and robust avenue to synthesize mesoporous noble metal‐based nanostructures for versatile biomedical applications.