This paper introduces a new technique for estimating the parameters of models with continuous latent data. Using the Rasch model as an example, it is shown that existing Bayesian techniques for parameter estimation, such as the Gibbs sampler, are not always easy to implement. Then, a new sampling-based Bayesian technique, called the DA-T-Gibbs sampler, is introduced. The DA-T-Gibbs sampler relies on the particular latent data structure of latent response models to simplify the computations involved in parameter estimation.