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Abstract:
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We compare students' scores between public and private schools in Ireland, using data collected for PISA. This survey employs a two stage sampling design of schools and pupils, but the choice of school by pupils is not under control. Hence, pupils of the two types of school can differ in unknown characteristics, and direct comparison of the sample scores may lead to erroneous conclusions. We compare the performance of commonly used approaches to deal with this problem, such as Hajek and Greg type estimators with weights equal the inverse propensity scores, instrumental and latent variables models and an alternative approach that we developed. This approach fits a model to the data by modeling the outcome distribution under ignorable assignment and the school selection probabilities, which are modeled as functions of the outcome and covariates, thus accounting for informative selection.
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