Combining Multiple Imputation and Hidden Markov Modeling to Obtain Consistent Estimates of Employment Status

Recently, a method was proposed that combines multiple imputation and latent class analysis (MILC) to correct for misclassification in combined data sets. A multiply imputed data set is generated which can be used to estimate different statistics of interest in a straightforward manner and can ensure that uncertainty due to misclassification is incorporated in the estimate of the total variance. In this article, MILC is extended by using hidden Markov modeling so that it can handle longitudinal data and correspondingly create multiple imputations for multiple time points. Recently, many researchers have investigated the use of hidden Markov modeling to estimate employment status rates using a combined data set consisting of data originating from the Labor Force Survey (LFS) and register data; this combined data set is used for the setup of the simulation study performed in this article. Furthermore, the proposed method is applied to an Italian combined LFS-register data set. We demonstrate how the MILC method can be extended to create imputations of scores for multiple time points and thereby show how the method can be adapted to practical situations.