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In this paper, we compare the performances of several models for tting over-dispersed binarydata. The distribution models considered in this study include the binomial (BN), the beta-binomial (BB), the multiplicative binomial (MBM), the Com-Poisson binomial (CPB) and thedouble binomial (DBM) models. Applications of these models to several well known data setsexhibiting under-dispersion and over-dispersion were considered in this paper. We applied thesemodels to two frequency data sets and two data sets with covariates that have been variouslyanalysed in the literature. The rst relates to the Portuguese version of Duke Religiosity Indexin a sample of 273 (202 women, 71 Male) postgraduate students of the faculty of Medicine ofUniversity of Sao Paulo. The second set that employs the Generalize Linear Model (GLM) is thecorrelated binary data which studies the cardiotoxic e ects of doxorubicin chemoteraphy on thetreatment of acute lymphoblastic leukemia in childhood. In the rst data set, we have a singlecovariate, Sex (0,1) and two covariates in the second data set (dose and time).Our results indicate that all the models considered here (excluding the binomial) behavereasonably well in modeling over-dispersed binary data with or without covariates, although boththe multiplicative binomial and the double binomial models slightly behave better for thes

Employing the Double, Multiplicative and The Com-Poisson Binomial Distributions for modeling Over and Under-dispersed Binary Data