Estimation of Daily Smoking Prevalence for Disaggregated Statistical Areas in Australia

Motivated by the need to estimate prevalence at multiple disaggregated level hierarchies, rather than only one, this study extends widely used area-level models in Bayesian and frequentist framework. We propose adding additional unstructured random effects at higher level disaggregated domains to the traditional models. Using our extension, we find major benefits for unbiasedness and coverage. The penalty in using additional random effects can be slightly higher standard errors (SEs), but if small, this increase is warranted because it can improve coverage of the model-based estimator. The proposed model is robust in the sense that it can better account for unexplained variation at the higher aggregation levels compared to traditional spatial and non-spatial area-level models. When applied to Australian smoking data, the extended model shows the benefit of including both unstructured random effects at the detailed target levels, that is, statistical areas level 3 and 4 (SA3 and SA4), and structured random effects at the more detailed (SA3) level. Using the extended model that has very strong fixed-effect components confirms unbiasedness for the targeted domains at both SA3 and SA4 levels.