Beta-Binomial model in small area estimation using adjusted profile Hierarchical Likelihood approach

Small Area Estimation (SAE) is a statistical technique for estimating parameters in subpopulations with small sample sizes. Generally, the Bayes approach is used to estimate binary model parameters in SAE. Researchers have developed a Beta-Binomial model in SAE using a Hierarchical Likelihood approach called SAE-BB-HL. However, the results of the fixed effect estimators are biased. According to previous research, this problem can be solved using the Adjusted Profile Hierarchical Likelihood (APHL) approach. This study proposes a Beta-Binomial model in SAE using the APHL approach, namely SAE-BB-APHL. The model’s performance is investigated through simulation data with eight scenarios considering five factors. The analysis of combination factors uses an ANOVA test with the Mean Squared Error of Prediction (MSEP) as the response. The SAE-BB-APHL is also applied to illiteracy rate data at the sub-district level in Bengkulu Province. The results show that the SAE-BB-APHL had a much smaller bias than the SAE-BB-HL. There is significant interaction among the five factors. SAE-BB-APHL has the smallest MSEP in the first population, sample size, sample percentage, and random effect area variance of 15, 2%, and 2, respectively. From the empirical data results, the SAE-BB-APHL illiteracy rate estimator has the same tendency as the SAE-BB-HL estimator.