In modelling the succession of states occupied by individuals over time, it is important to include state dependence, duration-of-stay effects, and variation between individuals over and above that explained by covariates. It has been long recognized that omission of any one of these characteristics can result in seriously misleading inference about the other two and the effects of covariates. Mixed Markov renewal models are the most parsimonious general class of model which incorporate all three characteristics. However, problems over the detailed specification and the complex computational requirements of such models have inhibited their use in social science research. This paper is concerned with one specific problem: ensuring sufficient flexibility for the multivariate mixing distribution by correcting the tendency to under predict the number who remain in the same state throughout. It is shown how an efficient EM-type algorithm based on weighted GLMs is readily extended to include stayers within a mixed Markov renewal formulation. In contrast to the direct maximization of the log-likelihood using a Newton-Raphson (or similar) algorithm, stayers may improve significantly the convergence performance of the EM-GLM approach.