Nonlinear Least Squares Model Estimation - Advanced Tab

Select the Advanced tab of the Nonlinear Least Squares Model Estimation dialog box to access the options described here.

Estimation method. The Estimation method box contains two options: Levenberg-Marquardt and Gauss-Newton.

Levenberg-Marquardt. For most applications, the default Levenberg-Marquardt (nonlinear least squares) method will yield the best performance, that is, it is the method that is most efficient and fastest to converge. The algorithm is described in detail in Moré (1977). In summary, this method is a modification (improvement) of the Gauss-Newton algorithm. Like the Gauss-Newton algorithm, when using the least-squares loss function, the second-order partial derivatives do not have to be computed (or approximated) in order to find the least-squares parameter estimates; instead, the algorithm will in each iteration solve a set of linear equations to compute the gradient.

Gauss-Newton. This method is an implementation of the classic Gauss-Newton algorithm for solving nonlinear least squares regression problems; e.g., see Dennis and Schnabel (1983).

Maximum number of iterations. Use the Maximum number of iterations box to specify the maximum number of iterations to be performed. The estimation of parameters in nonlinear regression is an iterative procedure (see Nonlinear Estimation Procedures). At each iteration, STATISTICA evaluates whether the fit of the model (to the data) has improved from the previous iteration.

Convergence criterion. Use the Convergence criterion box to change the convergence criterion value. The Levenberg-Marquardt (nonlinear least squares) algorithm checks for convergence at various stages during the parameter estimation; for details refer to the description of the algorithm in Moré (1977).

Start values. Click the Start values button to display the Specify start values dialog box, in which you enter the individual start values for each parameter or one common value for all parameters. The start values are used in the first iteration of each estimation method (see also, Nonlinear Estimation Procedures).