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Growth curve modeling : theory and applications / Michael J. Panik
Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Verlag: New York : John Wiley & Sons, Incorporated, 2014Auflage: First edition (Online-Ausg.)Beschreibung: Online-Ressource (1 online resource (xv, 437 pages))ISBN:- 1118764048
- 9781306191487
- 1306191483
- 9781118764046
- 9781118763902
- 519.535
- 519.5
- QA276
- QA276 .P224 2013
Inhalte:
Zusammenfassung: 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, WeibulPPN: PPN: 81147190XPackage identifier: Produktsigel: ZDB-26-MYL | ZDB-30-PAD | ZDB-30-PQE
""CONTENTS""; ""TITLE PAGE""; ""COPYRIGHT""; ""DEDICATION""; ""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""; ""2.4 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""; ""APPENDIX 3.A THE LOGISTIC MODEL DERIVED""; ""APPENDIX 3.B THE GOMPERTZ MODEL DERIVED""; ""APPENDIX 3.C THE NEGATIVE EXPONENTIAL MODEL DERIVED""
""APPENDIX 3.D THE VON BERTALANFFY AND RICHARDS MODELS DERIVED""""APPENDIX 3.E THE SCHNUTE MODEL DERIVED""; ""APPENDIX 3.F THE MCDILL-AMATEIS MODEL DERIVED""; ""APPENDIX 3.G THE SLOBODA MODEL DERIVED""; ""APPENDIX 3.H A GENERALIZED MICHAELIS-MENTEN GROWTH EQUATION""; ""4 ESTIMATION OF TREND""; ""4.1 LINEAR TREND EQUATION""; ""4.2 ORDINARY LEAST SQUARES (OLS) ESTIMATION""; ""4.3 MAXIMUM LIKELIHOOD (ML) ESTIMATION""; ""4.4 THE SAS SYSTEM""; ""4.5 CHANGING THE UNIT OF TIME""; ""4.6 AUTOCORRELATED ERRORS""; ""4.7 POLYNOMIAL MODELS IN T""; ""4.8 ISSUES INVOLVING TRENDED DATA""
""APPENDIX 4.A OLS ESTIMATED AND RELATED GROWTH RATES""""5 DYNAMIC SITE EQUATIONS OBTAINED FROM GROWTH MODELS""; ""5.1 INTRODUCTION""; ""5.2 BASE-AGE-SPECIFIC (BAS) MODELS""; ""5.3 ALGEBRAIC DIFFERENCE APPROACH (ADA) MODELS""; ""5.4 GENERALIZED ALGEBRAIC DIFFERENCE APPROACH (GADA) MODELS""; ""5.5 A SITE EQUATION GENERATING FUNCTION""; ""5.6 THE GROUNDED GADA (G-GADA) MODEL""; ""APPENDIX 5.A GLOSSARY OF SELECTED FORESTRY TERMS""; ""6 NONLINEAR REGRESSION""; ""6.1 INTRINSIC LINEARITY/NONLINEARITY""; ""6.2 ESTIMATION OF INTRINSICALLY NONLINEAR REGRESSION MODELS""
""APPENDIX 6.A GAUSS-NEWTON ITERATION SCHEME: THE SINGLE PARAMETER CASE""
Growth Curve Modeling: Theory and Applications; Copyright; 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 Change2.3.1 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 Model3.9 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; Appendix 3.A The Logistic Model Derived; Appendix 3.B The Gompertz Model Derived; Appendix 3.C The Negative Exponential Model Derived
Appendix 3.D The von Bertalanffy and Richards Models DerivedAppendix 3.E The Schnute Model Derived; Appendix 3.F The McDill-Amateis Model Derived; Appendix 3.G The Sloboda Model Derived; Appendix 3.H A Generalized Michaelis-Menten Growth Equation; 4 Estimation of Trend; 4.1 Linear Trend Equation; 4.2 Ordinary Least Squares (OLS) Estimation; 4.3 Maximum Likelihood (ML) Estimation; 4.4 The SAS System; 4.5 Changing the Unit of Time; 4.5.1 Annual Totals versus Monthly Averages versus Monthly Totals; 4.5.2 Annual Totals versus Quarterly Averages versus Quarterly Totals; 4.6 Autocorrelated Errors
4.6.1 Properties of the OLS Estimators When ε Is AR (1)4.6.2 Testing for the Absence of Autocorrelation: The Durbin-Watson Test; 4.6.3 Detection of and Estimation with Autocorrelated Errors; 4.7 Polynomial Models in t; 4.8 Issues Involving Trended Data; 4.8.1 Stochastic Processes and Time Series; 4.8.2 Autoregressive Process of Order p; 4.8.3 Random Walk Processes; 4.8.4 Integrated Processes; 4.8.5 Testing for Unit Roots; Appendix 4.A OLS Estimated and Related Growth Rates; 4.A.1 The OLS Growth Rate; 4.A.2 The Log-Difference (LD) Growth Rate; 4.A.3 The Average Annual Growth Rate
4.A.4 The Geometric Average Growth Rate
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