Growth curve modeling : theory and applications

Growth curve modeling theory and applications

Features recent trends and advances in the theory and techniques used to accurately measure and model growthGrowth 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 &qu...

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Bibliographic Details
Main Author: Panik, Michael J. (-)
Format: eBook
Language:Inglés
Published: Hoboken, New Jersey : John Wiley & Sons, Inc 2014.
Edition:1st ed
Subjects:
Mathematical statistics.
Time-series analysis.
Regression analysis.
Multivariate analysis.
See on Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009849091306719
Table of Contents:
  • Intro
  • 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 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
  • 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
  • 4.5.1 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
  • 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
  • 5.5.1 ADA Derivations
  • 5.5.2 GADA Derivations
  • 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
  • 6.2.1 Nonlinear Least Squares (NLS).
  • 6.2.2 Maximum Likelihood (ML)
  • Appendix 6.A Gauss-Newton Iteration Scheme: The Single Parameter Case
  • Appendix 6.B Gauss-Newton Iteration Scheme: The r Parameter Case
  • Appendix 6.C The Newton-Raphson and Scoring Methods
  • Appendix 6.D The Levenberg-Marquardt Modification/Compromise
  • Appendix 6.E Selection of Initial Values
  • 6.E.1 Initial Values for the Logistic Curve
  • 6.E.2 Initial Values for the Gompertz Curve
  • 6.E.3 Initial Values for the Weibull Curve
  • 6.E.4 Initial Values for the Chapman-Richards Curve
  • 7 Yield-Density Curves
  • 7.1 Introduction
  • 7.2 Structuring Yield-Density Equations
  • 7.3 Reciprocal Yield-Density Equations
  • 7.3.1 The Shinozaki and Kira Yield-Density Curve
  • 7.3.2 The Holliday Yield-Density Curves
  • 7.3.3 The Farazdaghi and Harris Yield-Density Curve
  • 7.3.4 The Bleasdale and Nelder Yield-Density Curve
  • 7.4 Weight of a Plant Part and Plant Density
  • 7.5 The Expolinear Growth Equation
  • 7.6 The Beta Growth Function
  • 7.7 Asymmetric Growth Equations (for Plant Parts)
  • 7.7.1 Model I
  • 7.7.2 Model II
  • 7.7.3 Model III
  • Appendix 7.A Derivation of the Shinozaki and Kira Yield-Density Curve
  • Appendix 7.B Derivation of the Farazdaghi and Harris Yield-Density Curve
  • Appendix 7.C Derivation of the Bleasdale and Nelder Yield-Density Curve
  • Appendix 7.D Derivation of the Expolinear Growth Curve
  • Appendix 7.E Derivation of the Beta Growth Function
  • Appendix 7.F Derivation of Asymetric Growth Equations
  • Appendix 7.G Chanter Growth Function
  • 8 Nonlinear Mixed-Effects Models for Repeated Measurements Data
  • 8.1 Some Basic Terminology Concerning Experimental Design
  • 8.2 Model Specification
  • 8.2.1 Model and Data Elements
  • 8.2.2 A Hierarchical (Staged) Model
  • 8.3 Some Special Cases of the Hierarchical Global Model.
  • 8.4 The SAS/STAT NLMIXED Procedure for Fitting Nonlinear Mixed-Effects Model
  • 9 Modeling the Size and Growth Rate Distributions of Firms
  • 9.1 Introduction
  • 9.2 Measuring Firm Size and Growth
  • 9.3 Modeling the Size Distribution of Firms
  • 9.4 Gibrat's Law (GL)
  • 9.5 Rationalizing the Pareto Firm Size Distribution
  • 9.6 Modeling the Growth Rate Distribution of Firms
  • 9.7 Basic Empirics of Gibrat's Law (GL)
  • 9.7.1 Firm Size and Expected Growth Rates
  • 9.7.2 Firm Size and Growth Rate Variability
  • 9.7.3 Econometric Issues
  • 9.7.4 Persistence of Growth Rates
  • 9.8 Conclusion
  • Appendix 9.A Kernel Density Estimation
  • 9.A.1 Motivation
  • 9.A.2 Weighting Functions
  • 9.A.3 Smooth Weighting Functions: Kernel Estimators
  • Appendix 9.B The Log-Normal and Gibrat Distributions (Aitchison and Brown, 1957
  • Kalecki, 1945)
  • 9.B.1 Derivation of Log-Normal Forms
  • 9.B.2 Generalized Log-Normal Distribution
  • Appendix 9.C The Theory of Proportionate Effect
  • Appendix 9.D Classical Laplace Distribution
  • 9.D.1 The Symmetric Case
  • 9.D.2 The Asymmetric Case
  • 9.D.3 The Generalized Laplace Distribution
  • 9.D.4 The Log-Laplace Distribution
  • Appendix 9.E Power-Law Behavior
  • 9.E.1 Pareto's Power Law
  • 9.E.2 Generalized Pareto Distributions
  • 9.E.3 Zipf's Power Law
  • Appendix 9.F The Yule Distribution
  • Appendix 9.G Overcoming Sample Selection Bias
  • 9.G.1 Selection and Gibrat's Law (GL)
  • 9.G.2 Characterizing Selection Bias
  • 9.G.3 Correcting for Selection Bias: The Heckman (1976, 1979) Two-Step Procedure
  • 9.G.4 The Heckman Two-Step Procedure Under Modified Selection
  • 10 Fundamentals of Population Dynamics
  • 10.1 The Concept of a Population
  • 10.2 The Concept of Population Growth
  • 10.3 Modeling Population Growth
  • 10.4 Exponential (Density-Independent) Population Growth
  • 10.4.1 The Continuous Case.
  • 10.4.2 The Discrete Case
  • 10.4.3 Malthusian Population Growth Dynamics
  • 10.5 Density-Dependent Population Growth
  • 10.5.1 Logistic Growth Model
  • 10.6 Beverton-Holt Model
  • 10.7 Ricker Model
  • 10.8 Hassell Model
  • 10.9 Generalized Beverton-Holt (B-H) Model
  • 10.10 Generalized Ricker Model
  • Appendix 10.A A Glossary of Selected Population Demography/Ecology Terms
  • Appendix 10.B Equilibrium and Stability Analysis
  • 10.B.1 Stable and Unstable Equilibria
  • 10.B.2 The Need for a Qualitative Analysis of Equilibria
  • 10.B.3 Equilibria and Stability for Continuous-Time Models
  • 10.B.4 Equilibria and Stability for Discrete-Time Models
  • Appendix 10.C Discretization of the Continuous-Time Logistic Growth Equation
  • Appendix 10.D Derivation of the B-H S-R Relationship
  • Appendix 10.E Derivation of the Ricker S-R Relationship
  • Appendix A
  • Table A.1 Standard Normal Areas (Z Is N(0, 1))
  • Table A.2 Quantiles of Student's t Distribution (T Is tv)
  • Table A.3 Quantiles of the Chi-Square Distribution (X Is χv2)
  • Table A.4 Quantiles of Snedecor's F Distribution (F Is Fv1,v2)
  • Table A.5 Durbin-Watson DW Statistic-5% Significance Points dL and dU (n is the sample size and k′ is the number of regressors excluding the intercept)
  • Table A.6 Empirical Cumulative Distribution of τ for ρ = 1
  • References
  • Index.

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