Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.

The normal and Poisson distribution assumptions in the normal-Poisson mixed effects regression model are often too restrictive for many real count data. Several works have independently relaxed the Poisson conditional distribution assumption for counts or the normal distribution assumption for random effects. This work couples some recent advances in these two regards to develop a skew t–discrete gamma regression model in which the count outcomes have full dispersion flexibility and random effets can be skewed and heavy tailed. Inference in the model is achieved by maximum likelihood using pseudo-adaptive Gaussian quadature. The use of the proposal is demonstrated on a popular owl sibling negotiation data. It appears that, for this example, the proposed approach outperforms models based on normal random effects and the Poisson or negative binomial count distribution.

In this age of mass media and, in particular, social media-driven perception of reality, coupling disease and prophylactic opinion dynamics models can provide better insights into disease evolution than using a disease model alone. We develop in this work two disease-opinion dynamics models based on the epidemiology of the new coronavirus disease (COVID-19) and the availability or not of imperfect vaccines. We assume that susceptibility to infection decreases with the level of prophylactic attitude (personal hygiene, social distancing), and changes in prophylactic attitudes of susceptible individuals occur in response to perceived disease prevalence and vaccination coverage and efficacy in the population. We derive and discuss the disease-free equilibriums and reproduction numbers in the introduced models. We further assess the impacts of the distribution of opinions at disease introduction, the ability to detect presymptomatic, asymptomatic and symptomatic positive COVID-19 cases, the behavioural responses to the outbreak and the introduction of vaccination, and the effects of distortions of disease prevalence by public policy and mass media on disease dynamics. The insights highlighted from the proposed models are expected to make informative contributions to public policy in a context of opinion fluxes in response to perceived disease prevalence.