On the modeling of the average value of high school national examination in West Java using Bayesian hierarchical mixture normal approach

National Examination (UN) is one of the standard evaluation systems of education in Indonesia. The results of the UN can be used as a consideration for the development and provision of assistance to educational units in an effort to improve the quality of education. This research is done to get the best model of the average of UN value which is hierarchically structured. This paper would employ a two-level hierarchical linear model with nine characteristics of the school in the first level and four characteristics of the district/city in the second level. The complexity of the model is increasing due to the pattern of average UN value follows a normal mixture distribution pattern. A Bayesian hierarchical mixture normal approach coupled with Markov Chain Monte Carlo (MCMC), therefore, would be employed to estimate the model numerically. The results show that based on DIC value, the hierarchical normal mixture model with four components on the UN value has a better performance than the only one level mixture regression model in explaining the variability of the average value of UN.