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Growth Curve Modeling: Theory and Applications by Michael J. Panik

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3

PARAMETRIC GROWTH CURVE MODELING

3.1 INTRODUCTION

The preceding chapter considered the computation of a variety of growth rates for a generic variable measured over time, with time either expressed in terms of discrete units or treated as a continuous variable. Also included was a very special type of parametric growth model that exhibited a constant relative rate of growth, namely, the exponential growth model. In this chapter we shall explore a whole host of alternative growth models that have been employed to study growth behavior in diverse fields such as forestry, agriculture, biology, engineering, and economics, to name but a few.

While linear or exponential growth may at times be appropriate, we shall, for the most part, concentrate on sigmoidal (S-shaped) growth curves. In this regard, some of the more common parametric growth models covered herein are:

Linear Janoschek
Logarithmic reciprocal Lundqvist–Korf
Logistic Hossfeld
Gompertz Stannard
Weibull Schnute
Negative exponential Morgan–Mercer–Flodin (M–M–F)
von Bertalanffy McDill–Amateis
Chapman–Richards (C–R) Levakovic (I, III)
Log logistic Yoshida (I)
Brody Sloboda

Although this list is by no means exhaustive, it gives a very good account of the mainstream types of growth models, which have become popular over the recent past.

We have referred to the aforementioned growth models as being “parametric” in nature. This is because these functions (and their properties) have been defined in terms ...

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