Stratum-specific health outcome estimation in Pakistan using double goal CART

Post-stratification is applied when the subpopulation membership is observed only for sampled values and the goal is to estimate stratum-specific parameters which leads the survey statisticians towards primary goals i.e., classification of non-sampled units into different strata and prediction of the values of the study variables. Regression models, on one side, optimize the prediction of the study variable's non-sampled values while the classification algorithms, on the other side, look for the classification of non-sampled cases into different strata. Hence, it is crucial to deal with these two goals simultaneously for the estimation of stratum-specific parameters. This study introduces the idea of a double-objective classification and regression trees (CARTs) approach for estimating stratum-specific parameters. Theoretical properties of the total estimator are derived. An application on the estimation of health outcomes in different domains is given to delineate the practical significance as well as the efficiency of the proposed CART-based method. The proposed estimator of population total performs better than the existing stratum-specific estimator in terms of relative efficiency for all choices of parameters. As an ensemble model, the random forest CART outperforms the other competing tree-based models and homogenous population model without using any auxiliary variable.