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Computer-based tests provide researchers with abundant detailed information, such as response times (RTs). A full cross-loadings hierarchical model (FCHM) was proposed to concurrently model RTs and response accuracy (RA), by adding cross-loadings to the hierarchical framework (HM, van der Linden, 2007; CHM, Bolsinova & Tijmstra, 2017). A real data study showed the conditional independence between RA and speed (a key assumption of HM and CHM) was violated, so relaxing this assumption is relevant and necessary. In addition, FCHM fit better with the real data. A simulation study was conducted to investigate the recovery of FCHM. The results indicated FCHM recovered some item and person parameters better than other models and showed the best goodness-of-fit.