Abstract
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 over-dispersion 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.
Highlights
The dispersion parameter should be the unity in case of the univariate Bernoulli data, but there may be deviation if there is a sequence of the Bernoulli outcomes included in a study that may lead to a binomial variable
The second one when we have a matrix values of dispersion parameters. These estimates can be extended to the trivariate and multivariate correlated binary data
We present a new approach to identify and estimate the dispersion parameters, in scalar and matrix values, for the bivariate, trivariate and multivariate correlated binary data
Summary
The dispersion parameter should be the unity in case of the univariate Bernoulli data, but there may be deviation if there is a sequence of the Bernoulli outcomes included in a study that may lead to a binomial variable. The second one when we have a matrix values of dispersion parameters These estimates can be extended to the trivariate and multivariate correlated binary data. We present a new approach to identify and estimate the dispersion parameters, in scalar and matrix values, for the bivariate, trivariate and multivariate correlated binary data. After obtaining these estimates we can modify the correlated binary data, this happens to obtain a dispersion parameter equal or near to the unity. A proposed approach for identifying and estimating the dispersion parameters in a scalar and matrix values, and the impact of over-dispersion in the case of bivariate, trivariate and multivariate binary outcomes associated with covariates, are demonstrated in the Sections 3, 4 and 5, respectively.
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