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Random responding is a complex source of measurement bias and threatens the reliability of forced-choice assessments, which are essential in high-stakes organizational testing scenarios, such as hiring decisions. The traditional measurement models rely heavily on non-random, construct-relevant responding to yield accurate parameter estimates. When survey data contain many random responses, fitting traditional models may yield biased results, which could attenuate the reliability of measurement and invalidate factor analyses. This study presents a new forced‐choice measure-based mixture item response theory model (called M-TCIR) for simultaneously modeling normal and random responses (distinguishing completely and incompletely random). The feasibility of the M-TCIR was investigated via a Monte Carlo simulation study.