Mathematics and Statistics 11(3): 579-585, 2023 http://www.hrpub.org DOI: 10.13189/ms.2023.110315 Small Area Estimation of Illiteracy Rates based on Beta-Binomial Model using Hierarchical Likelihood Approach Etis Sunandi 1,2 , Khairil Anwar Notodiputro 1,* , Indahwati 1 , Agus M Soleh 1 1 Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University, Indonesia 2 Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Bengkulu, Indonesia Received December 31, 2022; Revised April 20, 2023; Accepted May 9, 2023 Cite This Paper in the Following Citation Styles (a): [1] Etis Sunandi, Khairil Anwar Notodiputro, Indahwati, Agus M Soleh , "Small Area Estimation of Illiteracy Rates based on Beta-Binomial Model using Hierarchical Likelihood Approach," Mathematics and Statistics, Vol. 11, No. 3, pp. 579 - 585, 2023. DOI: 10.13189/ms.2023.110315. (b): Etis Sunandi, Khairil Anwar Notodiputro, Indahwati, Agus M Soleh (2023). Small Area Estimation of Illiteracy Rates based on Beta-Binomial Model using Hierarchical Likelihood Approach. Mathematics and Statistics, 11(3), 579 - 585. DOI: 10.13189/ms.2023.110315. Copyright©2023 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract Small Area Estimation (SAE) is a statistical method used to estimate parameters in sub-populations with small samples. This study aims to develop a Beta- Binomial model on SAE with a Hierarchical Likelihood (HL) approach. The model built is called the SAE-BB-HL model. This research begins by deriving a formula for estimating model parameters analytically. A good fit is calculated with the Mean Square Error of Prediction (MSEP) and bias. This study used simulation data and data from the National Socio-Economic Survey (SUSENAS) and Village Potential (PODES) of Bengkulu Province for 2021 collected by Statistics Indonesia (BPS). The simulation study aims to evaluate the SAE-BB-HL model. Simultaneously, the application study aims to predict the illiteracy rate per sub-district in Bengkulu Province. The simulation study results show that the parameter estimates of random area distribution are very close to the actual parameters. It also reveals that the bias and MSEP estimates of the proportion of HL are lower than the direct estimates. In addition, the results of this study show that the SAE-BB-HL model can improve the accuracy and precision of proportion estimation. Applying the SAE- BB_HL model to real data shows that the predictive value of the illiteracy rate tends to be higher when compared to the direct estimator. Keywords Binary Response, Mean Square Error, Overdispersion, Small Sample 1. Introduction Small Area Estimation (SAE) is a statistical method for estimating parameters in a subpopulation based on a small number of samples to provide estimates with adequate precision [1]. Small area models are classified into two types based on the type of data available. The first is the area-level model. This model connects the direct estimator and the auxiliary area variable. The second model is a unit- level model that connects the unit values of the estimator directly to the unit level of auxiliary variables with known area mean values and certain area auxiliary variables. The SAE model can be applied to both continuous and discrete response variables such as binary. Research using binary data is prone to overdispersion. The Beta-Binomial distribution can be used to overcome the problem of overdispersion in binary data [2]. Beta-Binomial model development on small area estimation has been carried out. The model parameters are estimated through the Bayesian approach. According to [3], parameter estimation in a mixed model with a Beta-Binomial hierarchy can be done through Hierarchical Likelihood (HL). This method is claimed to be better than the Bayes approach analytically. The HL method can reduce the bias of estimating binary data