Title: A new regression model for discrete data allowing for overdispersion
Authors: Roberto Ascari - University of Milano-Bicocca (Italy) [presenting]
Sonia Migliorati - University of Milano Bicocca (Italy)
Eduardo Buono - University of Milano-Bicocca (Italy)
Abstract: Binomial regression is commonly used for modeling discrete data which represent the number of successes in a fixed number of independent trials. This approach is very popular, but is inadequate in case of overdispersion, i.e. when real data show a larger variance than the one assumed by the binomial distribution. This excess of variability is typically due to violation of the i.i.d. assumption of the binary variates forming the binomial outcome. A possible way of dealing with overdispersion is to compound the binomial with a distribution defined on the unit-interval. If the beta distribution is chosen, the beta-binomial is attained. We define a new distribution, the flexible beta-binomial (FBB), obtained compounding the binomial with the flexible beta. The FBB can be expressed as a finite mixture of beta-binomial distributions. Further, we define a GLM-type regression model based on the FBB distribution and show that thanks to its parametrization, it allows for a form of the variance and the intraclass correlation coefficient easily interpretable in terms of overdispersion. Inferential issues are dealt with a Bayesian approach through a Hamiltonian Monte Carlo algorithm.