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

A joint normal-ordinal (probit) model for ordinal and continuous longitudinal data

In biomedical studies, continuous and ordinal longitudinal variables are frequently encountered. In many of these studies it is of interest to estimate the effect of one of these longitudinal variables on the other. Time-dependent covariates have, however, several limitations; they can, for example, not be included when the data is not collected at fixed intervals. The issues can be circumvented by implementing joint models, where two or more longitudinal variables are treated as a response and modeled with a correlated random effect. Next, by conditioning on these response(s), we can study the effect of one or more longitudinal variables on another. We propose a normal-ordinal(probit) joint model. First, we derive closed-form formulas to estimate the model-based correlations between the responses on their original scale. In addition, we derive the marginal model, where the interpretation is no longer conditional on the random effects. As a consequence, we can make predictions for a subvector of one response conditional on the other response and potentially a subvector of the history of the response. Next, we extend the approach to a high-dimensional case with more than two ordinal and/or continuous longitudinal variables. The methodology is applied to a case study where, among others, a longitudinal ordinal response is predicted with a longitudinal continuous variable.

Quantile regression for longitudinal data via the multivariate generalized hyperbolic distribution

While extensive research has been devoted to univariate quantile regression, this is considerably less the case for the multivariate (longitudinal) version, even though there are many potential applications, such as the joint examination of growth curves for two or more growth characteristics, such as body weight and length in infants. Quantile functions are easier to interpret for a population of curves than mean functions. While the connection between multivariate quantiles and the multivariate asymmetric Laplace distribution is known, it is less well known that its use for maximum likelihood estimation poses mathematical as well as computational challenges. Therefore, we study a broader family of multivariate generalized hyperbolic distributions, of which the multivariate asymmetric Laplace distribution is a limiting case. We offer an asymptotic treatment. Simulations and a data example supplement the modelling and theoretical considerations.