This study conducted a comprehensive comparison of Item Response Theory (IRT) linking methods applied to a bifactor model, examining their performance on both multiple choice (MC) and mixed format tests within the common item nonequivalent group design framework. Four distinct multidimensional IRT linking approaches were explored, consisting of two methods that incorporated linking coefficients, namely extensions of Haebara and Stocking-Lord, and two methods that did not involve linking coefficients, specifically concurrent calibration and fixed item parameter calibration (FIPC). The study involved an evaluation of the linked item parameters, with a focus on their bias, standard error of estimate (SEE), and root mean squared error (RMSE). The findings revealed that both linking methods, those with and without linking coefficients, demonstrated proficient recovery of item parameters. Notably, the methods lacking linking coefficients exhibited superior performance compared to their counterparts with coefficients. Remarkably, the FIPC linking method emerged as particularly adept at recovering item parameters, especially with regard to difficulty parameters, within the context of the bifactor model.