Fast and highly efficient pseudo-likelihood methodology for large and complex ordinal data

In longitudinal studies, continuous, binary, categorical, and survival outcomes are often jointly collected, possibly with some observations missing. However, when it comes to modeling responses, the ordinal ones have received less attention in the literature. In a longitudinal or hierarchical context, the univariate proportional odds mixed model (POMM) can be regarded as an instance of the generalized linear mixed model (GLMM). When the response of the joint multivariate model encompass ordinal responses, the complexity further increases. An additional problem of model fitting is the size of the collected data. Pseudo-likelihood based methods for pairwise fitting, for partitioned samples and, as introduced in this paper, pairwise fitting within partitioned samples allow joint modeling of even larger numbers of responses. We show that that pseudo-likelihood methodology allows for highly efficient and fast inferences in high-dimensional large datasets.