Identifying Risk Factors for Severe Childhood Malnutrition by Boosting Additive Quantile Regression

We investigated the risk factors for childhood malnutrition in India based on the 2005/2006 Demographic and Health Survey by applying a novel estimation technique for additive quantile regression. Ordinary linear and generalized linear regression models relate the mean of a response variable to a linear combination of covariate effects, and, as a consequence, focus on average properties of the response. The use of such a regression model for analyzing childhood malnutrition in developing or transition countries implies that the estimated effects describe the average nutritional status. However, it is of even greater interest to analyze quantiles of the response distribution, such as the 5% or 10% quantile, which relate to the risk of extreme malnutrition. Our investigation is based on a semiparametric extension of quantile regression models where different types of nonlinear effects are included in the model equation, leading to additive quantile regression. We addressed the variable selection and model choice problems associated with estimating such an additive quantile regression model using a novel boosting approach. Our proposal allows for data-driven determination of the amount of smoothness required for the nonlinear effects and combines model choice with an automatic variable selection property. In an empirical evaluation, we compared our boosting approach with state-of-the-art methods for additive quantile regression. The results suggest that boosting is an appropriate tool for estimation and variable selection in additive quantile regression models and helps to identify yet unknown risk factors for childhood malnutrition. This article has supplementary material online.