Ch. 28. Growth and wear curves

Abstract

Publisher Summary A growth curve is generally a polynomial in time fitted to the values of a growth or decay variable, measured at different times on a number of subjects or specimens. The pattern of growth for a subject may be referred to as its profile. Comparing the profiles of different groups of subjects is an important objective in the statistical analysis of growth curves. Also, utilizing the estimated growth curve to forecast future observations is another objective. Models other than polynomial models also sometimes can be more meaningful. Potthoff and Roy originally suggested a polynomial type growth model for a single growth variable, when measurements are taken at the same set of time points for specimens coming from different groups. These groups may be different treatments or different methods or procedures. The chapter provides a detailed statistical account of this model because it plays an important role in many applications. A growth curve model combines in it all important features of regression analysis, analysis of variance, analysis of covariance, experimental design model, response surface methodology, random variance components, and multivariate analysis of variance. It has, therefore, a lot of flexibility and is useful in a wide variety of applications.