### Journals Information

Mathematics and Statistics Vol. 11(3), pp. 579 - 585
DOI: 10.13189/ms.2023.110315
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## 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

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

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[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). APA Format:
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.