A Bayesian approach to estimate transition models forzero-inflated count data

Abstract

Zero-inflated count data are commonly modelled by mixing a degenerate distribution at zero with a Poisson or negative binomial component, thereby imposing a parametric form on the counts. The transition model of Berger and Tutz instead specifies the conditional probability of moving from one count to the next and treats excess zeros within a sequence of transition probabilities. We develop a Bayesian formulation of this model, derive its full conditional distributions, and address the treatment of probability above the largest represented category under finite parameterisation. The support is closed using a terminal category, and sensitivity checks show that two natural closure conventions give similar results for the data considered. We compare the Bayesian transition model with Bayesian zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression across three simulated mechanisms and one real dataset. Because the models' coefficients represent different functionals, comparison is restricted to prediction on the expected-count scale. In all simulated scenarios, the transition model performs at least as well as the alternatives, with pairwise differences smaller than replication variability. In the real-data application, it gives lower prediction errors on all reported criteria, including median absolute error, with the largest advantage for observations beyond the training covariate range. The results indicate that the transition model can provide competitive prediction without specifying a fixed count distribution, while its bounded support remains a limitation for counts above the largest represented category.