Multiple imputation of hierarchical nonlinear time series data with an application to school enrollment data

International comparisons of hierarchical time series data sets based on survey data, such as annual country-level estimates of school enrollment rates, can suffer from large amounts of missing data due to differing coverage of surveys across countries and across times. A popular approach to handling missing data in these settings is through multiple imputation, which can be especially effective when there is an auxiliary variable that is strongly predictive of and has a smaller amount of missing data than the variable of interest. However, standard methods for multiple imputation of hierarchical time series data can perform poorly when the auxiliary variable and the variable of interest have a nonlinear relationship. Performance can also suffer if the multiple imputations are used to estimate an analysis model that makes different assumptions about the data compared to the imputation model, leading to uncongeniality between analysis and imputation models. We propose a Bayesian method for multiple imputation of hierarchical nonlinear time series data that uses a sequential decomposition of the joint distribution and incorporates smoothing splines to account for nonlinear relationships between variables. We compare the proposed method with existing multiple imputation methods through a simulation study and an application to secondary school enrollment data. We find that the proposed method can lead to substantial performance increases for estimation of parameters in uncongenial analysis models and for prediction of individual missing values.