Model criticism for log-normal hierarchical Bayesian models on household expenditure in Indonesia

Hierarchical models are formulated for analyzing data with complex sources of variation. In many cases, those complex sources of variation refer to hierarchical structure of data. Since, the hierarchical modeling process takes into account the characteristics of each data level, it leads to a complex model. Commonly, the issues of interest are how well the model fit the data and how well the random effects fit their assumed distribution. In that case, the problem is often viewed on hierarchical Bayesian modeling is confounding across level which means whether the problem comes due to mis-specification of likelihood on the lowest level of mis-specification prior on higher level. In general, there are two different proposed methods for Bayesian model criticism, i.e. Bayes factors and Deviance Information Criterion (DIC). However, there is practical and theoretical limitation of Bayes factors due to complexity of model. This paper proposes to discuss and generate a Bayesian predictive model criticism based on trade off between model fit and complexity through DIC and graphs for two alternative Lognormal hierarchical Bayesian models on household expenditure data. Result shows that there is a slightly different result between the two-parameter log-normal hierarchical model and the three-parameter log-normal hierarchical model. However, the three-parameter log-normal hierarchical model yields a better fit and a bit lower complexity compare to the two-parameter Log-Normal hierarchical model.