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.

Bayesian Multilevel Latent Class Models for the Multiple Imputation of Nested Categorical Data.

With this article, we propose using a Bayesian multilevel latent class (BMLC; or mixture) model for the multiple imputation of nested categorical data. Unlike recently developed methods that can only pick up associations between pairs of variables, the multilevel mixture model we propose is flexible enough to automatically deal with complex interactions in the joint distribution of the variables to be estimated. After formally introducing the model and showing how it can be implemented, we carry out a simulation study and a real-data study in order to assess its performance and compare it with the commonly used listwise deletion and an available R-routine. Results indicate that the BMLC model is able to recover unbiased parameter estimates of the analysis models considered in our studies, as well as to correctly reflect the uncertainty due to missing data, outperforming the competing methods.