ABSTRACT
In many health surveys, a large collection of measurements are recorded, often containing measurements of different types. Perhaps the most common non-commensurate situation is that of a continuous, often assumed normally distributed, outcome, and a binary or ordinal outcome. For example, in dose-toxicology experiments, both the body temperature (typically recorded on a continuous scale) and specific reflexes (recorded on a binary or ordinal scale) are measured as indicators for toxicity (Faes et al., 2008). In addition, it is not uncommon that these measurements are recorded repeatedly in time, for example, in a repeated-dose toxicity experiment; or that sampling units are clustered, for example, in surveys where individuals within the same households are interviewed. In this chapter, our general interest is in the analysis of multivariate hierarchical, also called multivariate multi-level, data. The strength of association between the different endpoints as well as the association of measurements within the same sampling unit might be important questions of interest in this case.
