C(Alpha) Tests for Testing Homogeneity of Proportions in Presence of McDONALD Generalized Beta-Binomial Over-Dispersion

An important problem in toxicology, teratology, consumers purchasing behavior, drinking behavior of alcohol, in studies of dental caries in children and other similar fields is to compare proportions of certain characteristic in several groups. A special case is to compare the proportions in a control group with that in a treatment group. However, these proportions often exhibit variation greater than predicted by a simple binomial model. Continuous distribution defined on the standard unit interval is used to test homogeneity of proportion as one way of handling over-dispersion of the binomial distribution. The Kumaraswamy-Binomial (KB) distribution, Beta-Binomial (BB) distribution and the new McDonald Generalized Beta-Binomial (McGBB) distributions are prominent members of Binomial mixture distribution. The new McDonald Generalized Beta-Binomial distribution model has shown to give better fit than the Kumaraswamy-Binomial distribution and Beta-Binomial distribution on both the simulation study and the real data set in handling binomial outcome data. In this paper we focus on testing homogeneity of proportions in presence the new McGBB distribution over-dispersion by deriving the C (alpha) tests using the Quasi-likelihood and the Extended Quasi-likelihood estimating functions. The performance of the derived C (alpha) tests are better when compared, through simulations, with the Likelihood ratio test.