Implicit Multifunctional Nonlinear Regression Analysis

Abstract

The least squares estimation of parameters in algebraically implicit, nonlinear, multiple response models having only one ezperimentally accessible response variable is treated within the context of a Gauss–Newton—Newton iteration. The algorithm, derived through application of the implicit function theorem to the model, is sufficiently general to cover Bayesian estimation of parameters for multiresponse data.

KEY WORDS:

• Curve fitting
• Least squares estimation
• Gauss–Newton—Newton iteration
• Implicit function theorem
• Bayesian estimation
• Equilibrium data
• Potentiometric titration