Multiple imputation of longitudinal categorical data through bayesian mixture latent Markov models

Standard latent class modeling has recently been shown to provide a flexible tool for the multiple imputation (MI) of missing categorical covariates in cross-sectional studies. This article introduces an analogous tool for longitudinal studies: MI using Bayesian mixture Latent Markov (BMLM) models. Besides retaining the benefits of latent class models, i.e. respecting the (categorical) measurement scale of the variables and preserving possibly complex relationships between variables within a measurement occasion, the Markov dependence structure of the proposed BMLM model allows capturing lagged dependencies between adjacent time points, while the time-constant mixture structure allows capturing dependencies across all time points, as well as retrieving associations between time-varying and time-constant variables. The performance of the BMLM model for MI is evaluated by means of a simulation study and an empirical experiment, in which it is compared with complete case analysis and MICE. Results show good performance of the proposed method in retrieving the parameters of the analysis model. In contrast, competing methods could provide correct estimates only for some aspects of the data.