The influence of economic conditions on the movement of a variable between states (for example a change in credit rating from A to B) can be modelled using a multi-state latent factor intensity framework. Estimation of this type of model is, however, not straightforward, as transition probabilities are involved and the model contains a few highly analytically intractable distributions. In this paper, a Bayesian approach is adopted to manage the distributions. The innovation in the sampling algorithm used to obtain the posterior distributions of the model parameters includes a particle filter step and a Metropolis–Hastings step within a Gibbs sampler. The feasibility and accuracy of the proposed sampling algorithm is supported with a few simulated examples. The paper contains an application concerning what caused 1049 firms to change their credit ratings over a span of ten years.