A New Approach for Dispersion Parameters

This paper presents a new approach to identify and estimate the dispersion parameters for bivariate, trivariate and multivariate correlated binary data, not only with scalar value but also with matrix values. For this direction, we present some recent studies indicating the impact of overdispersion on the univariate data analysis and comparing a new approach with these studies. Following the property of McCullagh and Nelder [1] for identifying dispersion parameter in univariate case, we extended this property to analyze the correlated binary data in higher cases. Finally, we used these estimates to modify the correlated binary data, to decrease its over-dispersion, using the Hunua Ranges data as an ecology problem.