Zero Inflated Binomial Models in Small Area Estimation with Application to Unemployment Data in Indonesia

Abstract

Binary response variables are commonly modeled by binomial models. The binomial overdispersion occurs if the variability is greater than the variance of assumed model. The overdispersion can be caused by excess zeros. The overdispersion may produce underestimated standard error which in turn will produce underestimated p-value. Therefore, Zero Inflated Binomial (ZIB) models are considered to overcome the excess zeros in binomial data. A simulation study is employed to evaluate the performance of models by using RRMSE and relative bias. The simulation showed that the proposed method SAE ZIB has better fit than SAE ZIB Synthetic in terms of the smaller RRMSE. The proposed SAE ZIB method applies to unemployment data to estimate proportion of unemployment in each district/regency during period of August 2016 In Jambi Province, Indonesia. The real data application showed that SAE ZIB method is better than the direct estimates method in terms of the smaller standard error.