Growth Curve Modeling: Theory and Applications

CONTENTS

Preface

1 Mathematical Preliminaries

1.1 Arithmetic Progression

1.2 Geometric Progression

1.3 The Binomial Formula

1.4 The Calculus of Finite Differences

1.5 The Number e

1.6 The Natural Logarithm

1.7 The Exponential Function

1.8 Exponential and Logarithmic Functions: Another Look

1.9 Change of Base of a Logarithm

1.10 The Arithmetic (Natural) Scale versus the Logarithmic Scale

1.11 Compound Interest Arithmetic

2 Fundamentals of Growth

2.1 Time Series Data

2.2 Relative and Average Rates of Change

2.3 Annual Rates of Change

2.3.1 Simple Rates of Change

2.3.2 Compounded Rates of Change

2.3.3 Comparing Two Time Series: Indexing Data to a Common Starting Point

2.4 Discrete versus Continuous Growth

2.5 The Growth of a Variable Expressed in Terms of the Growth of its Individual Arguments

2.6 Growth Rate Variability

2.7 Growth in a Mixture of Variables

3 Parametric Growth Curve Modeling

3.1 Introduction

3.2 The Linear Growth Model

3.3 The Logarithmic Reciprocal Model

3.4 The Logistic Model

3.5 The Gompertz Model

3.6 The Weibull Model

3.7 The Negative Exponential Model

3.8 The von Bertalanffy Model

3.9 The Log-Logistic Model

3.10 The Brody Growth Model

3.11 The Janoschek Growth Model

3.12 The Lundqvist–Korf Growth Model

3.13 The Hossfeld Growth Model

3.14 The Stannard Growth Model

3.15 The Schnute Growth Model

3.16 The Morgan–Mercer–Flodin (M–M–F) Growth Model

3.17 The McDill–Amateis Growth Model

3.18 An Assortment of Additional Growth Models

3.18.1 The Sloboda Growth Model