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International comparisons of hierarchical time series data sets based onsurvey data, such as annual country-level estimates of school enrollment rates,can suffer from large amounts of missing data due to differing coverage ofsurveys across countries and across times. A popular approach to handlingmissing data in these settings is through multiple imputation, which can beespecially effective when there is an auxiliary variable that is stronglypredictive of and has a smaller amount of missing data than the variable ofinterest. However, standard methods for multiple imputation of hierarchicaltime series data can perform poorly when the auxiliary variable and thevariable of interest are have a nonlinear relationship. Performance of standardmultiple imputation methods can also suffer if the substantive analysis modelof interest is uncongenial to the imputation model, which can be a commonoccurrence for social science data if the imputation phase is conductedindependently of the analysis phase. We propose a Bayesian method for multipleimputation of hierarchical nonlinear time series data that uses a sequentialdecomposition of the joint distribution and incorporates smoothing splines toaccount for nonlinear relationships between variables. We compare the proposedmethod with existing multiple imputation methods through a simulation study andan application to secondary school enrollment data. We find that the proposedmethod can lead to substantial performance increases for estimation ofparameters in uncongenial analysis models and for prediction of individualmissing values.

Multiple Imputation of Hierarchical Nonlinear Time Series Data with an Application to School Enrollment Data