Modelling The Socio-Demographic and Spatial Determinants of Undernutrition in Zambia: A Comparison of Full Bayesian with Penalised Structured Additive Regression

Abstract

Full Bayes Markov Chain Multi Carlo (MCMC) and Penalised Structured Additive Regression (STAR) models were compared for an underenutrition (measured as stunting) study in Zambia. Spatial correlated effects were specified as a Markov random field prior, continuous covariates were modelled using Bayesian penalised splines and diffused priors were assigned to fixed effects.

A Bayesian Structured Additive Regression Model was developed for the Zambia data. Model estimation and inference was based on both fully Bayesian MCMC and Empirical Bayes (based on mixed method methodology). In a frequentist setting, EB inference is closely related to penalized likelihood estimation. (Approximate) restricted maximum likelihood are used to estimate Variance components which correspond to inverse smoothing parameters. Both inference procedures were then compared based on the results from the Zambia study and were found to be very similar.

The results indicate spatial variations in stunting among the districts of Zambia. Continuous covariates Age and BMI have a significant effect on stunting. There is also significant difference among the factors of all categorical variables except for mother's employment status where no difference was found in stunting between children of employed and unemployed mothers.

Keywords: MCMC, STAR, Full Bayes, Empirical Bayes, spatial, continuous, categorical, model estimation, inference.