Statistics 824: Nonlinear Regression

Overview

We will describe the use of nonlinear statistical models in the analysis of data from areas such as chemical kinetics, pharmacokinetics, and biological growth curves. We also discuss the design of experiments with such models. Emphasis will be on the nonlinear regression model but the analysis of multiresponse data and nonlinear mixed effects models will also be covered. Topics will include:

• Review of linear regression
• nonlinear regression models
• computing techniques and other practical matters
• designs for precise parameter estimation
• designs for model discrimination
• multiresponse estimation
• models defined by systems of differential equations
• nonlinear mixed effects models
• inferences about parameters and predictions

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Other References

• Nonlinear Regression by G.A.F. Seber and C.J. Wild, Wiley, 1989
• Nonlinear Statistical Models by A. Ronald Gallant, Wiley, 1987
• Nonlinear Estimation by Gavin J.S. Ross, Springer, 1990
• Handbook of Nonlinear Regression Models by David A. Ratkowsky, Marcel Dekker, 1990.
• Nonlinear Regression Modelling: A Unified Practical Approach by David A. Ratkowsky, Marcel Dekker, 1983
• Nonlinear Parameter Estimation by Yonathon Bard, Academic Press, 1974
• Nonlinear Parameter Estimation by John C. Nash and Mary Walker-Smith, Marcel Dekker, 1987

Computing facilities

The primary computing package for the course will be R. We will use the nls, nlme, and NISTnls packages within R.

Other systems that can be used for nonlinear regression analysis include S-PLUS, SAS and xlisp-stat