The Beta-Binomial Multivariate Model for Correlated Categorical Data - Nusar Hajarisman; Asep Saefuddin (Program Studi Statistika Unisba, 2008)
Over the past year, a significant amount of research has explored the logistic regression models foranalyzing correlated categorical data. In these models, it is assumed that the data occur in clusters,where individuals within each cluster are correlated, but individuals from different clusters areassumed independent. A commonly used in modeling correlated categorical univariate data is toassume that individual counts are generated from a Binomial distribution, with probabilities varybetween individuals according to a Beta distribution. The marginal distribution of the counts is thenBeta-Binomial. In this paper, a generalization of the model is made allowing the number ofrespondent m, to be random. Thus both the number units m, and the underlying probability vectorare allowed to vary. We proposed the model for correlated categorical data, which is generalized toaccount for extra variation by allowing the vectors of proportions to vary according to a Dirichletdistribution. The model is a mixture distribution of multinomial and Dirichlet distribution, and wecall the model as the beta-binomial multivariate model.