Multivariate Time Series Analysis and Applications

7Repeated measurements

Repeated measurements occur in many areas of study. The measurements repeat in time, space, or both. However, they are normally relatively short, and therefore the standard time series methods cannot be used. In this chapter, we will introduce some methods and various models that are useful for analyzing repeated measures data. Empirical examples will be used for illustration.

7.1 Introduction

Many fields of study, such as medical and biological science, social science, and education, involve sets of relatively short time series where the application of standard time series methods introduced earlier is difficult, if not impossible. For instance, an experiment may involve measurements taken at some selected times (or locations) from subjects associated with several treatments. The term “subject” is often used because the phenomenon of repeated measurements commonly occurs in the areas of medical, social, and educational studies, where human subjects are involved. However, the term may refer to an animal, a company, or even a tool. For example, the following is a study involving the growth curve data on the body weights of 27 rats from Box (1950) given in Table 7.1. The subject is a rat that is assigned to one of three treatment groups (Control, Thiouracil, Thyroxin) and its weight is measured weekly for 5 weeks. The objective of the study is to test whether there are differences in growth rates between groups.

Table 7.1 Body weight of rats under three ...