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In the current project, the generalized versions of the latent inter-dependence model (LAIDM) and latent non-independence model(LANIM) are developed to model binary and ordered categorical response data. The LAIDM was designed to formulate a mutual-rating process between dyad members. The LANIM refined the explanatory mechanism by including an interaction term (named as latent non-independence) to capture the interactive influence between dyad members’ latent trait scores. The results from a simulation study indicated that all proposed models could be successfully identified and accurately estimated.