Multiple imputation for discrete data: Evaluation of the joint latent normal model

Missing data are ubiquitous in clinical and social research, and multiple imputation (MI) is increasingly the methodology of choice for practitioners. Two principal strategies for imputation have been proposed in the literature: joint modelling multiple imputation (JM-MI) and full conditional specification multiple imputation (FCS-MI). While JM-MI is arguably a preferable approach, because it involves specification of an explicit imputation model, FCS-MI is pragmatically appealing, because of its flexibility in handling different types of variables. JM-MI has developed from the multivariate normal model, and latent normal variables have been proposed as a natural way to extend this model to handle categorical variables. In this article, we evaluate the latent normal model through an extensive simulation study and an application on data from the German Breast Cancer Study Group, comparing the results with FCS-MI. We divide our investigation in four sections, focusing on (i) binary, (ii) categorical, (iii) ordinal, and (iv) count data. Using data simulated from both the latent normal model and the general location model, we find that in all but one extreme general location model setting JM-MI works very well, and sometimes outperforms FCS-MI. We conclude the latent normal model, implemented in the R package jomo, can be used with confidence by researchers, both for single and multilevel multiple imputation.