13 - Multivariate Response Models

Summary

In many studies the objective is to model more than one response variable. For each unit in the sample a vector of correlated response variables, together with explanatory variables, is observed. Two cases are most important:

• repeated measurements, when the same variable is measured repeatedly at different times or/and under different conditions;

• different response variables, observed on one subject or unit in the sample.

Repeated measurements occur in most longitudinal studies. For example, in a longitudinal study measurements on an individual may be observed at several times under possibly varying conditions. In Example 1.4 (Chapter 1) an active ingredient is compared to a placebo by observing the healing after 3, 7, and 10 days of treatment. In Example 13.1, the number of epileptic seizures is considered at each of four two-week periods. Although they often do, repeated responses need not refer to different times. Response variables may also refer to different questions in an interview or to the presence of different commodities in a household. In Example 13.2 the two, possibly correlated responses are the type of birth (Ceaserian or not) and the stay of the child in intensive care (yes or no). Responses may also refer to a cluster of subjects; for example, when the health status of the members of a family is investigated, the observed responses form a cluster linked to one family. In Example 10.8, where the health status of trees is investigated, clusters are formed by the trees measured at the same spot.