On selection of a robust multilevel model for child nutrition measure in Bangladesh

The multilevel modeling has been utilizing in the prediction of child anthropometric nutrition measure due to children are nested within households (HHs) and households are nested to other hierarchies of the population including community (cluster) and sub-district. However, it is challenging to construct an efficient multilevel model by eliminating higher level variation because of complexity in survey design and unavailability of contextual variables (such as sub-district and district level information) in the survey data. The main aim of this study is to determine a robust multilevel model with minimal variation at higher-level administrative units utilizing contextual variables collected from census data.
Children anthropometric data are extracted from the 2011 Bangladesh Demographic and Health Survey (BDHS) and sub-district specific contextual variables are extracted from the published report of the 2011 Bangladesh population and Housing Census. Height-for-age Z-score (HAZ) calculated based on WHO 2006 child growth chart is considered as the child nutrition measure. The explanatory variables at different hierarchies are chosen in such a way that the prediction can be made using the developed multilevel model under a small area estimation (SAE) method (such as World Bank method) if unit-level auxiliary variables are available from a census data.
Methodology: Several multilevel models are developed considering child, HH, cluster, sub-district, and district as the consecutive hierarchies of the population based on the data structure. Models are developed with and without considering contextual variables for examining their impact to capture the higher-level variations. As model diagnostics tools, conditional Akaike Information Criteria (cAIC), likelihood ratio tests (LRT), and conditional r-squared values are calculated. The fitted models are used for estimating mean HAZ score and the share of stunted children at the division level.
Results: The inclusion of contextual variables helped to capture both sub-district and district level variations that aid to select a three-level model as the best model. The estimated mean HAZ score and proportion of stunted children at division level are comparable with the unbiased direct estimates.
Conclusion: Findings of the study support the application of the census information at higher-level administrative units as contextual variables for minimizing the higher-level variation and selecting a simpler three-level model rather than a complex multilevel model.