Zero-inflated negative binomial models in small area estimation.

Abstract

The problem of over-dispersion in Poisson data is usually solved by introducing prior distributions which lead to negative binomial models. Poisson data sometime is also suffered by excess zero problems, a condition when data contains too many zero or exceeds the distribution's expectation. Zero Inflated Negative Binomial (ZINB) method can be utilized to solve such problems. This paper demonstrates the adaption of ZINB methods in Small Area Estimation with excess zero data. It is shown that the excess zero problem has substantially influenced the Empirical Bayes (EB) estimates, and the adaption of ZINB methods has improved the precision and reliability of the estimates. Key Words: Small Area Estimation, Zero-Inflation, Poisson-Gamma, Negative Binomial Regression, Empirical Bayes