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CPS1823 Ishapathik D. et al.
the doubly inflated multivariate Poisson model provides significantly better fit
over multivariate Poisson model. So, we get a significantly better fit using the
doubly inflated multivariate Poisson models instead of using the multivariate
Poisson model which ignores the information of the inflation in the respective
cells for this data.

5. Summary
In this paper, we studied regression method for multivariate count data
having inflations in two cells. The responses are assumed to follow a doubly
inflated multivariate Poisson distribution. A method to find a probability mass
function for a doubly inflated multivariate Poisson random variate using a
Gaussian copula is described and an algorithm to estimate the unknown
parameters of the model using the MLE is also provided. The proposed
method is illustrated using a real data containing multivariate count data
having inflation in two cells. We observe that the regression using the doubly
inflated multivariate Poisson model provides significantly better fit over the
multivariate Poisson model ignoring the cells inflation in the data with respect
to the AIC criteria.

References
1. N. R. Chaganty. An alternative approach to the analysis of longitudinal
data via generalized estimating equations. Journal of Statistical Planning
and Inference, 63:39–54, 1997.
2. Yves Croissant. Ecdat: Data Sets for Econometrics, 2016. R package
version 0.3-1.
3. Harry Joe. Dependence Modeling with Copulas. Chapman & Hall. CRC
Press, 2014.
4. Norman Lloyd Johnson and Samuel Kotz. Distribution in statistics:
discrete distribution. Wiley, 1969.
5. Dimitris Karlis and Loukia Meligkotsidou. Multivariate poisson regression
with covariance structure. Statistics and Computing, 15(4):255–265, 2005.
6. Dimitris Karlis and Ioannis Ntzoufras. Analysis of sports data by using
bivariate poisson models. Journal of the Royal Statistical Society: Series
D (The Statistician), 52(3):381–393, 2003.
7. Subrahmaniam Kocherlakota and Kathleen Kocherlakota. Regression in
the bivariate poisson distribution. 2001.
8. Alan J Lee. Modeling scores in the premier league: is manchester united
really the best? Chance, 10(1):15–19, 1997.
9. JungBok Lee, Byoung Cheol Jung, and Seo Hoon Jin. Tests for zero
inflation in a bivariate zero-inflated poisson model. Statistica
Neerlandica, 63(4):400–417, 2009.

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