Detecting latent components in ordinal data with overdispersion by means of a mixture distribution

The paper describes a mixture distribution generated by Beta Binomial and Uniform random variables to allow for a possible overdispersion in surveys when the response of interest is an ordinal variable. This approach considers the joint presence of feeling, uncertainty and a possible dispersion sometimes present in the evaluation contexts. After a discussion of the main properties of this class of models, asymptotic likelihood methods have been applied for efficient statistical inference. The implementation on the survey on household income and wealth (SHIW) will confirm the versatility of this distribution and the usefulness to distinguish the determinants of uncertainty and overdispersion in real data.