Parameter Estimates from Nonlinear Models

This chapter focuses on parameter estimates from nonlinear models. The methods require some extra computing after the model has been fitted to a data set but the computing is efficient and easily accomplished. Fitting nonlinear models to data relies heavily on procedures used to fit linear models. The chapter presents a review of fitting linear models, including how to assess the quality of parameter estimates for such fits and discusses fitting nonlinear models and application of linear model methods for assessing the quality of parameter estimates for nonlinear models. The chapter also discusses a more accurate and valid procedure for characterizing the behavior of estimates of parameters in nonlinear models, illustrating the approach and the insights it gives using a model for frontal elution affinity chromatography and a compartment model. Profile plots can be extremely useful in nonlinear model building because they remove the gross dangers involved when using linear approximation standard errors and confidence regions.