Regression trees for poverty mapping

Poverty mapping is used to facilitate efficient allocation of aid resources, with the objective of ending poverty, the first of the United Nations Sustainable Development Goals. Levels of poverty across small geographic domains within a country are estimated using a statistical model, and the resulting estimates displayed on a poverty map. Current methodology for small area estimation of poverty utilises various forms of regression modelling of household income or expenditure. Fitting sound models requires skill and time, especially where there are many candidate regressors and even more possible interactions. Tree‐based methods have the potential to screen more quickly for interactions and also to provide reliable small area estimates in their own right. A classification tree technique has been presented by Bilton et al. (Comput Stat Data Anal115: 53–66, 2017) for estimating poverty incidence, but although adjustments were made to incorporate complex survey designs and estimate mean square error, classification trees are unable to estimate the associated non‐categorical deprivation measures of poverty gap and poverty severity. The focus of this paper is regression trees, because they enable all three core poverty measures of incidence, gap and severity to be estimated. Using regression trees, two alternative methodologies, parametric and non‐parametric, are explored for producing household level predictions that are then amalgamated up to small‐area level. New methods are developed for mean square error estimation. The properties of the small area estimates based on these regression tree techniques are then evaluated and compared with linear mixed models both by simulation and by using real poverty data from Nepal.