nonlinear regression analysis


  • For example, the Michaelis–Menten model for enzyme kinetics has two parameters and one independent variable, related by by:[a] This function is nonlinear because it cannot
    be expressed as a linear combination of the two s. Systematic error may be present in the independent variables but its treatment is outside the scope of regression analysis.

  • Regression statistics The assumption underlying this procedure is that the model can be approximated by a linear function, namely a first-order Taylor series: where .

  • For error distributions that belong to the exponential family, a link function may be used to transform the parameters under the Generalized linear model framework.

  • In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters
    and depends on one or more independent variables.

  • On the other hand, depending on what the largest source of error is, a nonlinear transformation may distribute the errors in a Gaussian fashion, so the choice to perform a
    nonlinear transformation must be informed by modeling considerations.

  • In general, there is no closed-form expression for the best-fitting parameters, as there is in linear regression.

  • Again in contrast to linear regression, there may be many local minima of the function to be optimized and even the global minimum may produce a biased estimate.

  • In practice, estimated values of the parameters are used, in conjunction with the optimization algorithm, to attempt to find the global minimum of a sum of squares.

  • For details concerning nonlinear data modeling see least squares and non-linear least squares.

  • Segmented regression with confidence analysis may yield the result that the dependent or response variable (say Y) behaves differently in the various segments.

  • Linearization Transformation[edit] Further information: Data transformation (statistics) Some nonlinear regression problems can be moved to a linear domain by a suitable transformation
    of the model formulation.


Works Cited

[“1. R.J.Oosterbaan, 1994, Frequency and Regression Analysis. In: H.P.Ritzema (ed.), Drainage Principles and Applications, Publ. 16, pp. 175-224, International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. ISBN
90-70754-33-9 . Download as PDF : [1]
2. ^ R.J.Oosterbaan, 2002. Drainage research in farmers’ fields: analysis of data. Part of project “Liquid Gold” of the International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands.
Download as PDF : [2]. The figure was made with the SegReg program, which can be downloaded freely from [3]
3. This model can also be expressed in the conventional biological notation:

Photo credit:”]