Abstract:

Count data from surveys, such as the American Community Survey (ACS), often exhibits more variability than the standard Poisson distribution and as an alternative they can be modeled as a generalized Poisson distribution (Consul and Jain, 1973). If the total is constrained between two categories then the binomial distribution is a natural choice as it is the conditional distribution on the sum of two Poisson random variables. The analog for the generalized Poisson distribution is the quasibinomial distribution of type II (QBDII) (Consul, 1975). QBDII has an additional parameter which serves as a control for overdispersion. A small area model using QBDII is applied to estimating poverty rates for the Small Area Poverty and Income Estimates (SAPIE) program. A beta distribution regression forms a linking model with the small areas. Small area predictions and formulations are formulated through Bayesian procedures.
