Fit Options

The Fit Options GUI is briefly described below. The available GUI parameters depend on the whether you are fitting your data using a linear equation, a nonlinear equations, or a nonparametric fit type. All the options described below are available for nonlinear models. Method, Robust, and coefficient constraints (Lower and Upper) are available for linear models. Interpolants and smoothing spline fit types include Method, but no configurable options.

• Method -- The fitting method.

• The method is automatically selected based on the library or custom model you use. For linear models, the method is LinearLeastSquares. For nonlinear models, the method is NonlinearLeastSquares.

• Robust -- Specify whether to use the robust least squares fitting method. The values are
• Off -- Do not use robust fitting (default).
• On -- Fit with default robust method (bisquare weights).
• LAR -- Fit by minimizing the least absolute residuals (LAR).
• Bisquare -- Fit by minimizing the summed square of the residuals and downweight outliers using bisquare weights. In most cases, this is the best choice for robust fitting.
• Algorithm -- Algorithm used for the fitting procedure:
• Trust-Region -- This is the default algorithm and must be used if you specify coefficient constraints.
• Levenberg-Marquardt -- If the trust-region algorithm does not produce a reasonable fit, and you do not have coefficient constraints, you should try the Levenberg-Marquardt algorithm.
• Gauss-Newton -- This algorithm is included for pedagogical reasons and should be the last choice for most models and data sets.
• DiffMinChange -- Minimum change in coefficients for finite difference Jacobians. The default value is 10^-8.
• DiffMaxChange -- Maximum change in coefficients for finite difference Jacobians. The default value is 0.1.
• MaxFunEvals -- Maximum number of function (model) evaluations allowed. The default value is 600.
• MaxIter -- Maximum number of fit iterations allowed. The default value is 400.
• TolFun -- Termination tolerance used on stopping conditions involving the function (model) value. The default value is 10^-6.
• TolX -- Termination tolerance used on stopping conditions involving the coefficients. The default value is 10^-6.
• Unknowns -- Symbols for the unknown coefficients to be fitted.
• StartPoint -- The coefficient starting values. The default values depend on the model. For rational, Weibull, and custom models, default values are randomly selected within the range [0,1]. For all other nonlinear library models, the starting values depend on the data set and are calculated heuristically.
• Lower -- Lower bounds on the fitted coefficients. The bounds are used only with the trust region fitting algorithm. The default lower bounds for most library models are -Inf, which indicates that the coefficients are unconstrained. However, a few models have finite default lower bounds. For example, Gaussians have the width parameter constrained so that it cannot be less than 0.
• Upper -- Upper bounds on the fitted coefficients. The bounds are used only with the trust region fitting algorithm. The default upper bounds for all library models are Inf, which indicates that the coefficients are unconstrained.