Hierarchical Bayesian pattern mixture models for binary data from small area

Abstract

The Purpose of many surveys is to estimate the probability of a group having certain characteristics. However, if the survey has a lot of missing data, we may get incorrect results. So a lot of research has been done on mission data since the past. There are many methods to handle missing data, so it is better to use various methods than one. We estimate the proportion of finite population using the Bayesian method using the pattern mixture model for binary data. We consider a hierarchical Bayesian model to increase the reliability of small data. We have applied various cases on the hyper-parameter of the prior distribution of proportion for nonresponse to confirm that the proportion estimate is not sensitive. We also confirmed that small area estimation is better than the individual area estimation.