Abstract

In many applications, multiple outcomes are measured repeatedly within a sample of subjects, and the research questions of interest cannot be answered without jointly modeling all outcomes. A flexible model that can easily handle unbalanced data, is a mixed model which assumes a random-effects model for each outcome separately and a joint distribution for all random effects in the multivariate mixed model. However, in cases where many outcomes are to be modeled simultaneously, the high dimension of the random-effects distribution poses specific numerical problems. We propose a pairwise model fitting approach in which all possible bivariate models are fitted, and where inference follows from pseudo-likelihood arguments. The approach is applicable for linear, generalized linear, and nonlinear mixed models, or for combinations of those. The methodology will be extensively illustrated in the analysis of several real data sets.