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The standard generalized linear mixed effects model may result in severe underestimation of standard errors of estimated regression parameters in such cases and hence potentially bias the statistical inference. In this paper, we propose a longitudinal beta\u2010binomial model for overdispersed binomial data and estimate the regression parameters under a probit model using the generalized estimating equation method. A hybrid algorithm of the Fisher scoring and the method of moments is implemented for computing the method. Extensive simulation studies are conducted to justify the validity of the proposed method. Finally, the proposed method is applied to analyze functional impairment in subjects who are at risk of Huntington disease from a multisite observational study of prodromal Huntington disease. 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