Growth curve modeling : theory and applications / Michael J. Panik, Department of Economics, University of Hartford, West Hartford, Connecticut.

Includes bibliographical references and index.

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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 growth2.5 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 model3.14 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 equation4 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) models5.5 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; 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.