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Growth Curve Modeling: Theory and Applications

Name: Growth Curve Modeling: Theory and Applications
Author: Michael J. Panik
ISBN: 9781118764046

by Michael J. Panik

January 2014

Intermediate to advanced

454 pages

11h 8m

English

Wiley

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Cover Page
Title Page
Copyright
Dedication
Contents
PREFACE
1: MATHEMATICAL PRELIMINARIES
1.1 ARITHMETIC PROGRESSION1.2 GEOMETRIC PROGRESSION1.3 THE BINOMIAL FORMULA1.4 THE CALCULUS OF FINITE DIFFERENCES1.5 THE NUMBER e1.6 THE NATURAL LOGARITHM1.7 THE EXPONENTIAL FUNCTION1.8 EXPONENTIAL AND LOGARITHMIC FUNCTIONS: ANOTHER LOOK1.9 CHANGE OF BASE OF A LOGARITHM1.10 THE ARITHMETIC (NATURAL) SCALE VERSUS THE LOGARITHMIC SCALE1.11 COMPOUND INTEREST ARITHMETIC
2: FUNDAMENTALS OF GROWTH
2.1 TIME SERIES DATA2.2 RELATIVE AND AVERAGE RATES OF CHANGE2.3 ANNUAL RATES OF CHANGE2.4 DISCRETE VERSUS CONTINUOUS GROWTH2.5 THE GROWTH OF A VARIABLE EXPRESSED IN TERMS OF THE GROWTH OF ITS INDIVIDUAL ARGUMENTS2.6 GROWTH RATE VARIABILITY2.7 GROWTH IN A MIXTURE OF VARIABLES
3: PARAMETRIC GROWTH CURVE MODELING
3.1 INTRODUCTION3.2 THE LINEAR GROWTH MODEL3.3 THE LOGARITHMIC RECIPROCAL MODEL3.4 THE LOGISTIC MODEL3.5 THE GOMPERTZ MODEL3.6 THE WEIBULL MODEL3.7 THE NEGATIVE EXPONENTIAL MODEL3.8 THE VON BERTALANFFY MODEL3.9 THE LOG-LOGISTIC MODEL3.10 THE BRODY GROWTH MODEL3.11 THE JANOSCHEK GROWTH MODEL3.12 THE LUNDQVIST–KORF GROWTH MODEL3.13 THE HOSSFELD GROWTH MODEL3.14 THE STANNARD GROWTH MODEL3.15 THE SCHNUTE GROWTH MODEL3.16 THE MORGAN–MERCER–FLODIN (M–M–F) GROWTH MODEL3.17 THE MCDILL–AMATEIS GROWTH MODEL3.18 AN ASSORTMENT OF ADDITIONAL GROWTH MODELSAPPENDIX 3.A THE LOGISTIC MODEL DERIVEDAPPENDIX 3.B THE GOMPERTZ MODEL DERIVEDAPPENDIX 3.C THE NEGATIVE EXPONENTIAL MODEL DERIVEDAPPENDIX 3.D THE VON BERTALANFFY AND RICHARDS MODELS DERIVEDAPPENDIX 3.E THE SCHNUTE MODEL DERIVEDAPPENDIX 3.F THE MCDILL–AMATEIS MODEL DERIVEDAPPENDIX 3.G THE SLOBODA MODEL DERIVEDAPPENDIX 3.H A GENERALIZED MICHAELIS–MENTEN GROWTH EQUATION
4: ESTIMATION OF TREND
4.1 LINEAR TREND EQUATION4.2 ORDINARY LEAST SQUARES (OLS) ESTIMATION4.3 MAXIMUM LIKELIHOOD (ML) ESTIMATION4.4 THE SAS SYSTEM4.5 CHANGING THE UNIT OF TIME4.6 AUTOCORRELATED ERRORS4.7 POLYNOMIAL MODELS IN t4.8 ISSUES INVOLVING TRENDED DATAAPPENDIX 4.A OLS ESTIMATED AND RELATED GROWTH RATES

5: DYNAMIC SITE EQUATIONS OBTAINED FROM GROWTH MODELS
5.1 INTRODUCTION5.2 BASE-AGE-SPECIFIC (BAS) MODELS5.3 ALGEBRAIC DIFFERENCE APPROACH (ADA) MODELS5.4 GENERALIZED ALGEBRAIC DIFFERENCE APPROACH (GADA) MODELS5.5 A SITE EQUATION GENERATING FUNCTION5.6 THE GROUNDED GADA (g-GADA) MODELAPPENDIX 5.A GLOSSARY OF SELECTED FORESTRY TERMS
6: NONLINEAR REGRESSION
6.1 INTRINSIC LINEARITY/NONLINEARITY6.2 ESTIMATION OF INTRINSICALLY NONLINEAR REGRESSION MODELSAPPENDIX 6.A GAUSS–NEWTON ITERATION SCHEME: THE SINGLE PARAMETER CASEAPPENDIX 6.B GAUSS–NEWTON ITERATION SCHEME: THE r PARAMETER CASEAPPENDIX 6.C THE NEWTON–RAPHSON AND SCORING METHODSAPPENDIX 6.D THE LEVENBERG–MARQUARDT MODIFICATION/COMPROMISEAPPENDIX 6.E SELECTION OF INITIAL VALUES
7: YIELD–DENSITY CURVES
7.1 INTRODUCTION7.2 STRUCTURING YIELD–DENSITY EQUATIONS7.3 RECIPROCAL YIELD–DENSITY EQUATIONS7.4 WEIGHT OF A PLANT PART AND PLANT DENSITY7.5 THE EXPOLINEAR GROWTH EQUATION7.6 THE BETA GROWTH FUNCTION7.7 ASYMMETRIC GROWTH EQUATIONS (FOR PLANT PARTS)APPENDIX 7.A DERIVATION OF THE SHINOZAKI AND KIRA YIELD–DENSITY CURVEAPPENDIX 7.B DERIVATION OF THE FARAZDAGHI AND HARRIS YIELD–DENSITY CURVEAPPENDIX 7.C DERIVATION OF THE BLEASDALE AND NELDER YIELD–DENSITY CURVEAPPENDIX 7.D DERIVATION OF THE EXPOLINEAR GROWTH CURVEAPPENDIX 7.E DERIVATION OF THE BETA GROWTH FUNCTIONAPPENDIX 7.F DERIVATION OF ASYMMETRIC GROWTH EQUATIONSAPPENDIX 7.G CHANTER GROWTH FUNCTION
8: NONLINEAR MIXED-EFFECTS MODELS FOR REPEATED MEASUREMENTS DATA
8.1 SOME BASIC TERMINOLOGY CONCERNING EXPERIMENTAL DESIGN8.2 MODEL SPECIFICATION8.3 SOME SPECIAL CASES OF THE HIERARCHICAL GLOBAL MODEL8.4 THE SAS/STAT NLMIXED PROCEDURE FOR FITTING NONLINEAR MIXED-EFFECTS MODEL
9: MODELING THE SIZE AND GROWTH RATE DISTRIBUTIONS OF FIRMS
9.1 INTRODUCTION9.2 MEASURING FIRM SIZE AND GROWTH9.3 MODELING THE SIZE DISTRIBUTION OF FIRMS9.4 GIBRAT'S LAW (GL)9.5 RATIONALIZING THE PARETO FIRM SIZE DISTRIBUTION9.6 MODELING THE GROWTH RATE DISTRIBUTION OF FIRMS9.7 BASIC EMPIRICS OF GIBRAT'S LAW (GL)9.8 CONCLUSIONAPPENDIX 9.A KERNEL DENSITY ESTIMATIONAPPENDIX 9.B THE LOG-NORMAL AND GIBRAT DISTRIBUTIONS (AITCHISON AND BROWN, 1957; KALECKI, 1945)APPENDIX 9.C THE THEORY OF PROPORTIONATE EFFECTAPPENDIX 9.D CLASSICAL LAPLACE DISTRIBUTIONAPPENDIX 9.E POWER-LAW BEHAVIORAPPENDIX 9.F THE YULE DISTRIBUTIONAPPENDIX 9.G OVERCOMING SAMPLE SELECTION BIAS
10: FUNDAMENTALS OF POPULATION DYNAMICS
10.1 THE CONCEPT OF A POPULATION10.2 THE CONCEPT OF POPULATION GROWTH10.3 MODELING POPULATION GROWTH10.4 EXPONENTIAL (DENSITY-INDEPENDENT) POPULATION GROWTH10.5 DENSITY-DEPENDENT POPULATION GROWTH10.6 BEVERTON–HOLT MODEL10.7 RICKER MODEL10.8 HASSELL MODEL10.9 GENERALIZED BEVERTON–HOLT (B–H) MODEL10.10 GENERALIZED RICKER MODELAPPENDIX 10.A A GLOSSARY OF SELECTED POPULATION DEMOGRAPHY/ECOLOGY TERMSAPPENDIX 10.B EQUILIBRIUM AND STABILITY ANALYSISAPPENDIX 10.C DISCRETIZATION OF THE CONTINUOUS-TIME LOGISTIC GROWTH EQUATIONAPPENDIX 10.D DERIVATION OF THE B–H S–R RELATIONSHIPAPPENDIX 10.E DERIVATION OF THE RICKER S–R RELATIONSHIP
APPENDIX A
REFERENCES
INDEX

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Growth Curve Modeling: Theory and Applications

by Michael J. Panik

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