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Propensity score analysis has been adopted by researchers of observational studies to replicate the distributional balance achieved in pre-treatment variables of treatment and control groups (in the case of a binary treatment assignment) in randomized control trials. Several studies of Programme for International Student Assessment (PISA) data, a nested structure that utilizes complex sampling, have used propensity score methods, though many studies suffer from methodological shortcomings. This study will compare alternate, flexible approaches such as Bayesian Additive Regression Trees and a Bayesian stick breaking nonparametric causal model to other propensity score methods. A simulation will test whether the more flexible approaches compared to the standard propensity score methods yield better estimates of the true effect on PISA data.