Bayesian regularized tobit quantile to construct stunting rate model

Abstract

This study aims to identify the best model for the stunting rate by applying and comparing several methods based on the Tobit quantile regression method's modification. The stunting rate dataset is left censored and violated with linear model assumptions; thus, Tobit quantile approaches are used. The Tobit quantile regression is adjusted by combining it with the Bayesian approach since the Bayesian method can produce the best model in small-size samples. Three kinds of modified Tobit quantile regression methods considered here are the Bayesian Tobit quantile regression, the Bayesian Adaptive Lasso Tobit quantile regression, and the Bayesian Lasso Tobit quantile regression. This article implements the skewed Laplace distribution as the likelihood function in Bayesian analysis. This study used the data of 3534 stunting children obtained from the Health Departments of several districts and municipals in West Sumatra, Indonesia. The result of this study indicated that Bayesian Lasso quantile regression performed well compared to the other two methods. Criteria of better method are based on a smaller absolute bias and a shorter Bayesian credible interval which are obtained from the simulation study and empirical study. This study also found that exclusive breastfeeding give impact to stunting rate only at middle quantiles, while comorbidity tend to affect all distribution of stunting rate.