Open AccessSmall Area Estimation with Bivariate Hierarchical Bayes (HB) Approach to Estimate Monthly Average per Capita Expenditure of Food and Non-Food Commodities in Province of Bali
Author(s) -
Taly Purwa,
Agnes Tuti Rumiati,
Ismaini Zain
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/546/5/052054
Subject(s) - bivariate analysis , univariate , statistics , mean squared error , mathematics , estimation , econometrics , bayes' theorem , per capita , small area estimation , multivariate statistics , bayesian probability , economics , demography , estimator , population , management , sociology
Small Area Estimation (SAE) is an indirect method that has been widely used for estimating parameters in a small area or small domain by borrowing strength of predictor variables from census or registration. This study uses Hierarchical Bayes (HB) method under the univariate and bivariate Fay-Herriot (FH) model to estimate monthly average per capita expenditure of food and non-food commodities for each district level in Province of Bali in 2014. Then estimation results from both models will be compared. The bivariate FH model is expected to increase the accuracy of the results of estimation by taking into account correlation between two types of expenditure rather than perform univariate estimation separately. Thirteen predictor variables from the administrative record of village data (PODES 2014) are included in each model as factors that affect these two types of expenditure. From the result, there are three variables that have significant effect on food expenditure, both in univariate and bivariate FH model. While, for non-food expenditure both model show different result on significant variables. Based on the results of the performance comparison, the best model is bivariate FH model since it has smaller Mean Square Prediction Error (MSPE), Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) value than univariate FH models. In addition, the bivariate FH model produces shorter 95% credible interval of estimated values. These conditions indicate that jointly modeling can improve the accuracy of estimation. Bivariate FH also produces significant improvement in adjusted R 2 value. Finally, the mapping result shows the same pattern for two types of expenditure. The highest monthly average per capita expenditure is more localized in the southern districts of Bali. While the lowest expenditure is more localized in the eastern and western districts of Bali.