Foundations of Linear and Generalized Linear Models

CHAPTER 9 Modeling Correlated Responses

Many studies have multivariate response variables. For example, a social survey might ask a subject's opinion about whether government spending should decrease, stay the same, or increase in each of several areas (defense, health, education, environment, ...). A clinical trial studying patients taking a new drug might measure whether each of several side effects (e.g., headaches, nausea) occurs, and its severity. Longitudinal¹ studies observe a response variable repeatedly for each subject, at several times. A clinical trial comparing treatments for some malady, for example, might randomize patients to take either a new drug or a placebo and then observe them after 1 month, 3 months, and 6 months to evaluate whether the treatment response is positive.

In this chapter, we present models for a d-dimensional response variable . Each subject has a cluster of d observations. In a longitudinal study, for example, a cluster consists of the observations over time for a particular subject. Often d varies by cluster, such as when some subjects drop out of the study and are missing some observations. For multivariate data, observations within a cluster are typically correlated, and models need to account for that correlation. Section 9.1 presents two primary types of models for multivariate responses. One type, a marginal model, simultaneously models ...