Page 201 - Contributed Paper Session (CPS) - Volume 2

CPS1823 Ishapathik D. et al.
regression models, (i) Model 0, (ii) Model 1, and (iii) Model 2 to fit the data
and then compare them using AIC as a criteria. The descriptions of these three
regression models are given below. Note that since we have only two response
variables, the Gaussian copula parameter is of dimension 2, and it is
determined by a single correlation parameter in all of the three models.
• Model 0: This model is the multivariate Poisson model using Gaussian
copula ignoring the information regarding the inflation in two cells. It
serves as a baseline to see whether the doubly inflated multivariate
Poisson model provides significantly better fit than this model which does
not consider the cell inflations. We assume the linear predictor () is
given by
1()=10 +111 +122 +133
2()=20 +211 +222 +233,
where 1, 2 and 3 represent the covariates sex, age, and income
respectively.

• Model 1: Here we consider the doubly inflated multivariate Poisson
model that is given in Section 4. However, we assume the mixture
probabilities 1() and 2() given in (4.5) do not depend on the covariates.
Thus in this model we have

1()=10
2()=20,
and

1()=10 +111 +122 +133
2()=20 +211 +222 +233.

• Model 2: In this model, we assume the doubly inflated multivariate
Poisson model with the first order polynomial functions for the linear
predictors given by

1()=10+111+122+133
2()=20+211+222+233,
and
1()=10 +111 +122 +133
2()=20 +211 +222 +233.

From the results of the regression models we observed that the AIC for
Model 2 is lowest among the three models described above. Hence, according
to the minimum values of the AIC as a criteria the Model 2 is best among the
three models. Also, the difference between the deviances of Model 0 and
Model 2 is 863.66 with 8 degrees of freedom (-value<0.001) which shows that

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