Abstract Reducing neonatal and child mortality is a global priority. In countries without comprehensive vital registration data to inform policy and planning, statistical modelling is used to estimate the distribution of key causes of death. This modelling presents challenges given that the input data are few, noisy, often not nationally representative of the country from which they are derived, and often do not report separately on all of the key causes. As more nationally representative data come to be available, it becomes possible to produce country estimates that go beyond fixed-effects models with national-level covariates by incorporating country-specific random effects. However, the existing frequentist multinomial model is limited by convergence problems when adding random effects, and had not incorporated a covariate selection procedure simultaneously over all causes. We report here on the translation of a fixed effects, frequentist model into a Bayesian framework to address these problems, incorporating a misclassification matrix with the potential to correct for mis-reported as well as unreported causes. We apply the new method and compare the model parameters and predicted distributions of eight key causes of death with those based on the previous, frequentist model.