The random-threshold generalized unfolding model (RTGUM) was developed by treating the thresholds in the generalized unfolding model as random effects rather than fixed effects to account for the subjective nature of the selection of categories in Likert items. The parameters of the new model can be estimated with the JAGS (Just Another Gibbs Sampler) freeware, which adopts a Bayesian approach for estimation. A series of simulations was conducted to evaluate the parameter recovery of the new model and the consequences of ignoring the randomness in thresholds. The results showed that the parameters of RTGUM were recovered fairly well and that ignoring the randomness in thresholds led to biased estimates. Computerized adaptive testing was also implemented on RTGUM, where the Fisher information criterion was used for item selection and the maximum a posteriori method was used for ability estimation. The simulation study showed that the longer the test length, the smaller the randomness in thresholds, and the more categories in an item, the more precise the ability estimates would be. (Contains 2 tables and 8 figures.)