  Poisson random effect models with a shared random effect have been widely
used in actuarial science for analyzing the number of claims. In particular,
the random effect is a key factor in a posteriori risk classification. However,
the necessity of the random effect may not be properly assessed due to the dual
role of the random effect; it affects both the marginal distribution of the
number of claims and the dependence among the numbers of claims obtained from
an individual over time. In line with such observations, we explain that one
should be careful in using the score test for the nullity of the variance of
the shared random effect, as a sufficient condition for the existence of the
posteriori risk classification. To safely perform the a posteriori risk
classification, we propose considering an alternative random effect model based
on the negative binomial distribution, and show that safer conclusions about
the a posteriori risk classification can be made based on it. We also derive
the score test as a sufficient condition for the existence of the a posteriori
risk classification based on the proposed model.
