http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
PC program for the parameter estimation of nonlinear growth models with unequally spaced correlated observations
xiv, 178 leaves : illustrations ; 28 cm.
This dissertation describes a personal computer (PC) program, PCGrowth, which estimates parameters of nonlinear growth models using data that are unequally spaced and correlated. We discuss other software packages capable of fitting nonlinear growth models. Limitations of these software packages prompted development of PCGrowth. PCGrowth is a Windows-based application that incorporates common nonlinear growth models and the Omstein-Uhlenbeck stochastic process. PCGrowth can fit and/or simulate growth data from a single animal or from multiple independent animals. This dissertation describes the growth models incorporated in PCGrowth: generalized logistic, von Bertalanffy, Gompertz, and Roy-Potthoff polynomial. We present historical and mathematical backgrounds of these growth models. PCGrowth employs a derivative-free algorithm for maximum likelihood estimation of growth model parameters. This dissertation describes both PCGrowth's algorithm and algorithms used in other software. We use quadratic approximation to estimate standard errors and correlations of parameter estimates in PCGrowth. Examples of growth curve estimation using real and simulated data illustrate the utility of PCGrowth. Lastly, we investigate the asymptotic properties of parameter estimators analytically and via simulation.
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Includes bibliographical references: pages 168-177.