Study on the Effects of Cluster Information in Prediction of Non-sampled Area (A Case Study of per Capita Expenditures at Subdistrict Level in Regency and Municipality of Bogor).

Abstract

Empirical Best Linear Unbiased Predictor (EBLUP) has been widely used to predict parameters in area with small or even zero sample size, known as non-sampled area. It has been noted that there is a problem when this model will be used to predict the parameters of non-sampled area. Usually EBLUP is used to predict the parameters using a synthetic model ignoring the area random effects due to lack of non-sampled area information. Hence, this prediction will be distorted based on a single line of the synthetic model. The idea developed in this thesis is to modify the prediction model by adding cluster information assuming that there are similiarities among particular areas. These information have been incorporated into the model to modify the intercept of prediction models as well as both intercept and slope of the prediction model. In this paper, a simulation is carried out to study the performance of the proposed models compared with ordinary EBLUP. All models were evaluated based on the value of Relative Bias (RB) and Relative Root Mean Squares Error (RRMSE). It was shown, by mean of simulation, that the addition of cluster information has improved the ability of the model to predict non-sampled areas. Restricted Maximum Likelihood (REML), a common method for estimating variance component in EBLUP models, requires normality assumption. But the conditions in which the area random effects or sampling error are not normally distributed may encountered in many applications. Therefore we also used different scenarios, such as either one of random component was not normally distributed or both of area random effects and sampling error area were not normally distributed, to study the performance of the proposed models when the area random effects or auxiliary variables are not normally distributed. The result showed that under these conditions, the proposed models has been able to estimate the parameter with smaller Relative Bias (RB) and Relative Root Mean Squares Error (RRMSE) than ordinary EBLUP, especially in non-sampled areas. It was shown that all models could be used to predict average per capita expenditures per month at subdistrict level in regency and municipality in Bogor. The analysis was based on SUSENAS 2010 and PODES 2011 data sets. Even though the resulting predictions of the models were different, similar pattern among them has been observed. Clustering technique played an important role in implementing the proposed model in the case study. Clustering pattern which tend not to be linearly correlated with response variable can lead to the result that proposed model was not better than standard EBLUP model. However, there were some proposed models that showed a better accuracy than the standard EBLUP prediction of non-sampled subdistrict parameter.