Growth Curve Modeling - Theory and Applications

Features recent trends and advances in the theory and techniques used to accurately measure and model growth
 
Growth Curve Modeling: Theory and Applications features an accessible introduction to growth curve modeling and addresses how to monitor the change in variables over time since there is no "one size fits all" approach to growth measurement. A review of the requisite mathematics for growth modeling and the statistical techniques needed for estimating growth models are provided, and an overview of popular growth curves, such as linear, logarithmic, reciprocal, logistic, Gompertz, Weibull, negative exponential, and log-logistic, among others, is included.
 
In addition, the book discusses key application areas including economic, plant, population, forest, and firm growth and is suitable as a resource for assessing recent growth modeling trends in the medical field. SAS(r) is utilized throughout to analyze and model growth curves, aiding readers in estimating specialized growth rates and curves. Including derivations of virtually all of the major growth curves and models, Growth Curve Modeling: Theory and Applications also features:
 
* Statistical distribution analysis as it pertains to growth modeling
* Trend estimations
* Dynamic site equations obtained from growth models
* Nonlinear regression
* Yield-density curves
* Nonlinear mixed effects models for repeated measurements data
 
Growth Curve Modeling: Theory and Applications is an excellent resource for statisticians, public health analysts, biologists, botanists, economists, and demographers who require a modern review of statistical methods for modeling growth curves and analyzing longitudinal data. The book is also useful for upper-undergraduate and graduate courses on growth modeling.

Sommario

Preface xiii
 
1 Mathematical Preliminaries 1
 
1.1 Arithmetic Progression, 1
 
1.2 Geometric Progression, 2
 
1.3 The Binomial Formula, 4
 
1.4 The Calculus of Finite Differences, 5
 
1.5 The Number e, 9
 
1.6 The Natural Logarithm, 10
 
1.7 The Exponential Function, 11
 
1.8 Exponential and Logarithmic Functions: Another Look, 13
 
1.9 Change of Base of a Logarithm, 14
 
1.10 The Arithmetic (Natural) Scale versus the Logarithmic Scale, 15
 
1.11 Compound Interest Arithmetic, 17
 
2 Fundamentals of Growth 21
 
2.1 Time Series Data, 21
 
2.2 Relative and Average Rates of Change, 21
 
2.3 Annual Rates of Change, 25
 
2.4 Discrete versus Continuous Growth, 32
 
2.5 The Growth of a Variable Expressed in Terms of the Growth of its Individual Arguments, 36
 
2.6 Growth Rate Variability, 46
 
2.7 Growth in a Mixture of Variables, 47
 
3 Parametric Growth Curve Modeling 49
 
3.1 Introduction, 49
 
3.2 The Linear Growth Model, 50
 
3.3 The Logarithmic Reciprocal Model, 51
 
3.4 The Logistic Model, 52
 
3.5 The Gompertz Model, 54
 
3.6 The Weibull Model, 55
 
3.7 The Negative Exponential Model, 56
 
3.8 The von Bertalanffy Model, 57
 
3.9 The Log-Logistic Model, 59
 
3.10 The Brody Growth Model, 61
 
3.11 The Janoschek Growth Model, 62
 
3.12 The Lundqvist-Korf Growth Model, 63
 
3.13 The Hossfeld Growth Model, 63
 
3.14 The Stannard Growth Model, 64
 
3.15 The Schnute Growth Model, 64
 
3.16 The Morgan-Mercer-Flodin (M-M-F) Growth Model, 66
 
3.17 The McDill-Amateis Growth Model, 68
 
3.18 An Assortment of Additional Growth Models, 69
 
Appendix 3.A The Logistic Model Derived, 71
 
Appendix 3.B The Gompertz Model Derived, 74
 
Appendix 3.C The Negative Exponential Model Derived, 75
 
Appendix 3.D The von Bertalanffy and Richards Models Derived, 77
 
Appendix 3.E The Schnute Model Derived, 81
 
Appendix 3.F The McDill-Amateis Model Derived, 83
 
Appendix 3.G The Sloboda Model Derived, 85
 
Appendix 3.H A Generalized Michaelis-Menten Growth Equation, 86
 
4 Estimation of Trend 88
 
4.1 Linear Trend Equation, 88
 
4.2 Ordinary Least Squares (OLS) Estimation, 91
 
4.3 Maximum Likelihood (ML) Estimation, 92
 
4.4 The SAS System, 94
 
4.5 Changing the Unit of Time, 109
 
4.6 Autocorrelated Errors, 110
 
4.7 Polynomial Models in t, 126
 
4.8 Issues Involving Trended Data, 136
 
Appendix 4.A OLS Estimated and Related Growth Rates, 158
 
5 Dynamic Site Equations Obtained from Growth Models 164
 
5.1 Introduction, 164
 
5.2 Base-Age-Specific (BAS) Models, 164
 
5.3 Algebraic Difference Approach (ADA) Models, 166
 
5.4 Generalized Algebraic Difference Approach (GADA) Models, 169
 
5.5 A Site Equation Generating Function, 179
 
5.6 The Grounded GADA (g-GADA) Model, 184
 
Appendix 5.A Glossary of Selected Forestry Terms, 186
 
6 Nonlinear Regression 188
 
6.1 Intrinsic Linearity/Nonlinearity, 188
 
6.2 Estimation of Intrinsically Nonlinear Regression Models, 190
 
Appendix 6.A Gauss-Newton Iteration Scheme: The Single Parameter Case, 214
 
Appendix 6.B Gauss-Newton Iteration Scheme: The r Parameter Case, 217
 
Appendix 6.C The Newton-Raphson and Scoring Methods, 220
 
Appendix 6.D The Levenberg-Marquardt Modification/Compromise, 222
 
Appendix 6.E Selection of

Info autore

MICHAEL J. PANIK, PHD, is Professor Emeritus in the Department of Economics at the University of Hartford. He has served as a consultant to the Connecticut Department of Motor Vehicles as well as to a variety of healthcare organizations. In addition, Dr. Panik is the author of numerous books and journal articles in the areas of economics, mathematics, and applied econometrics.

Riassunto

Suitable for upper-undergraduate and graduate courses on growth modeling, this title presents an introduction to growth curve modeling and addresses how to monitor the change in variables over time since there is no "one size fits all" approach to growth measurement.

Dettagli sul prodotto

• Autori: Michael J Panik, Michael J. Panik, Michael J. (University of Hartford) Panik, MJ Panik
• Editore: Wiley, John and Sons Ltd
• Lingue: Inglese
• Formato: Copertina rigida
• Pubblicazione: 21.02.2014
• EAN: 9781118764046
• ISBN: 978-1-118-76404-6
• Pagine: 464
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Teoria delle probabilità, stocastica, statistica matematica; Scienze sociali, diritto, economia > Economia > Economia aziendale; Statistik, Regressionsanalyse, Statistics, Longitudinal Analysis, Regression Analysis, Statistical Software / SAS, Statistiksoftware / SAS, Longitudinalanalyse