Graduate Thesis Or Dissertation

Inference about missing mechanisms in longitudinal studies with a refreshment sample

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  • Missing data is one of the major methodological problems in longitudinal studies. It not only reduces the sample size, but also can result in biased estimation and inference. It is crucial to correctly understand the missing mechanism and appropriately incorporate it into the estimation and inference procedures. Traditional methods, such as the complete case analysis and imputation methods, are designed to deal with missing data under unverifiable assumptions of MCAR and MAR. The purpose of this dissertation is to provide an overview of procedures dealing with missing data. We especially focus on identifying and estimating attrition (missing) parameters under the non-ignorable missingness assumption using the refreshment sample in two-wave panel data. We propose a full-likelihood parametric approach which sets benchmarks for the performance of estimators in this setting. We also propose a semi-parametric method to estimate the attrition parameters by marginal density estimates with the help of two constraints from Hirano et al. (2001) and the additional information provided by the refreshment sample. We derive asymptotic properties of the semi-parametric estimators and illustrate their performance with simulations. Inference based on bootstrapping is proposed and verified through simulations. A real data application is attempted in the Netherlands Mobility Panel. Finally, we extend the semi-parametric method to incorporate a time-invariant binary covariate and evaluate its large-sample performance with simulations.
  • Keywords: Refreshment sample, Longitudinal study, Missing mechanism
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