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The current high‐dimensional linear factor models fail to account for the different types of variables, while high‐dimensional nonlinear factor models often overlook the overdispersion present in mixed‐type data. However, overdispersion is prevalent in practical applications, particularly in fields like biomedical and genomics studies. To address this practical demand, we propose an overdispersed generalized factor model (OverGFM) for performing high‐dimensional nonlinear factor analysis on overdispersed mixed‐type data. Our approach incorporates an additional error term to capture the overdispersion that cannot be accounted for by factors alone. However, this introduces significant computational challenges due to the involvement of two high‐dimensional latent random matrices in the nonlinear model. To overcome these challenges, we propose a novel variational EM algorithm that integrates Laplace and Taylor approximations. This algorithm provides iterative explicit solutions for the complex variational parameters and is proven to possess excellent convergence properties. We also develop a criterion based on the singular value ratio to determine the optimal number of factors. Numerical results demonstrate the effectiveness of this criterion. Through comprehensive simulation studies, we show that OverGFM outperforms state‐of‐the‐art methods in terms of estimation accuracy and computational efficiency. Furthermore, we demonstrate the practical merit of our method through its application to two datasets from genomics. To facilitate its usage, we have integrated the implementation of OverGFM into the R package GFM. [ABSTRACT FROM AUTHOR]

Herein, the osteogenic properties of bone repair scaffolds are improved by combining mechanical and biochemical stimulations. In the bone microenvironment, fluid shear stress (FSS) is the primary mechanical stimulation. The FSS of the cells is closely related to the scaffold structure. Scaffolds with the same wall thickness (400 μm) and different pore sizes (700, 800, and 900 μm) are established. The FSS of the cells on the scaffold surface is analyzed using the two‐way fluid–structure interaction (FSI) method to obtain the ideal structure. The 400–900 polylactic acid (PLA) scaffold with optimal mechanical stimulation is fabricated using selective laser sintering (SLS). BMP‐2/PLGA microspheres are loaded onto the 400–900 scaffold to further enhance the osteogenic properties through the synergistic effect of biochemical stimulations. The results indicate that the FSS of cells decreases with an increase in the pore size, and the pore size of 900 μm yields the best osteogenic differentiation. At 8 weeks after implantation, the 400–900 microspheres scaffold have the highest ratio of bone volume to total volume (BV/TV) and a uniform distribution of new bone. The results show that BMP‐2/PLGA microspheres can accelerate the formation of new bone. [ABSTRACT FROM AUTHOR]