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 ...

Get Foundations of Linear and Generalized Linear Models now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.