Scaling Outcome Correlated Binary Big Data Using Estimates of Bivariate Dispersion Parameters

Abstract— Dispersion parameter should be the unity in the case of the univariate Bernoulli data. But there may be some deviations if there is a sequence of the Bernoulli outcomes, that may lead to Binomial case. Over (lower) dispersion criterion is happened if the variance of actual response, var(y), is more (less) than the nominal variance as a function of the mean, var(μ). This paper presents the mathematical form for estimating and modifying the dispersion parameters for the outcome correlated binary (0,1) Big data, with scalar and matrix values, in Bivariate case. The impact of the estimates of dispersion parameter on the outcome correlated binary Big data is indicated. In general, the aim is making the dispersion parameters are close or equal to the unity. The purpose is controlling of marginal probabilities of the correlated binary outcomes. Since the increasing of marginals, increases the values of dispersion estimates. We can use these property to decrease the over-dispersion to close to the unity. The R program and its packages, is used to generate and fit the binary correlated Big data. Scaling and Roots techniques that depend on the estimates of dispersion parameters are used to modify the outcome correlated binary data. We have found that Scaling and Roots processes have similar results and good effects, only for binary Big data. Since the manner is different when deal with Small observations. Keywords— VGAM, VGLM, Binary outcomes, Dispersion parameters, Big data, Scaling data, Correlated data.